| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1+2+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=2 |
| Comment: | the preface of the reprinted QQTS by Zhang Pengfen (publisher) in 1829. |
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| Translation: | *Preface for Reprinting QQTS of the revered Mr. Wang Zhongjie*
QQTS was compiled by the revered Wang Zhongjie (Wang Zheng) from Jinyang county of Shan’xi Province. He was born in the late Ming Dynasty. After becoming a jinshi (the title of people who passed the highest imperial examination, similar to ‘Doctor’), he successively administered Guangping and Yangzhou, where his good fame spread and all the people of high rank and low rank associated with him and trusted him. When he was deposed and returned home, roving bandits happened to be rampant and all the counties robbed by the bandits were not intact. Only in one county, Jingyang, bandits were defeated repeatedly by surprise actions so that they did not dare further invasion into the western land. This was really the achievement of his defence. It’s a pity that, thwarted by crafty and fawning officials, he was not used (by the court) at last, (although) at that time, the two prime ministers Ye Taishan and Xu Yuanhu, as well as such men of honour as Li Songyu and Yang Zhonglie, recommended him (to the court) in accordance with his ability for assisting the monarch. While (the Ming) Dynasty was changed, he became well-known for his dying from a fast. Until Gaozong (the emperor Qianlong) in our Qing Dynasty, he was entitled zhong jie (loyalty) to comfort the spirit of this martyr. It means that his political integrity such as loyalty and kindness had been splendid like the sun, the moon, large rivers and high mountains. How can (his loyalty) be seen in the remaining memorial (to an emperor)? Even if refering to the ingenuity of diagrams and explanations according to the remaining (works), they were all about the national economy and the people's livelihood, and were far from the one-thousand-dan jiu zhong (cup) made by Fu Chai, the King of Wu State, and the eight-chi yin ping (silver vase) made by Qi Yingzhi in the Tang Dynasty, which were not comparable (to Wang Zheng's works). Moreover, I heard from elders that before Wang Zheng became an official, he usually made wooden puppets for use every spring and summer, the cultivating season. Some pounded grain, another winnowed grain, another lifted water, another made a fire, another used a rolling pole, and another operated bellows. The mechanisms were turning as if they were real persons. When the harvesting season was coming, (Wang Zheng) always made the self-moving quadricycle to help with binding and transporting the bundles of stalk, which brought twice the result with half the effort. Countrymen admired him and followed him. And the revered Mr. (Wang) once made a hole in the wall of his house to speak to other people through it. Whenever there were such ceremonies as marking a man's coming of age at 20, weddings, funerals and offering sacrifices to gods or ancestors, the words could be heard in several dozens of linked rooms when one person was asked to speak to the hole. This is called transmitting sound in an empty house, namely an approach to solve complicated problems in a simple way. And when the revered Mr. Wang lived in privacy in 1644, he heard Li Zicheng (the revolt leader at that time) had attacked Beijing. He piled up rubble into an interior city and an exterior city as a miniature of Beijing. He walked around the 'city' and silently prayed for seven days and nights. Suddenly a dog came from the southeast to drag one corner of the city and (the city) collapsed so revered Mr. Wang knew that the situation couldn’t be changed so he looked into the sky and yowled and died from a seven-day fast for the national calamity. Could anybody who did not understand Heaven’s will and occurrences in human life act like this? I don't know what the motive of giving him life and making him die is if Heaven gave birth to this talent and did not consider using him? Or could the leisure time let him do his best to make various implements in order to reveal the profound knowledge unrevealed by former worthies? But people talked much about this book and said that Heaven has its universal laws, sages have their own instructions and the common people have their implements, and that was there any need to pursue secrets and behave strangely to surprise other people? I should say that's not right. The people who were taught to bind up their hair and to put on hats to cover their heads cut wood as weapons to fight (but they) did not know how to plough. They held a block of wood to swim, (but they) did not understand how to cross a river. Since the era of Shengnong (legendary god of farming) and Huangdi (Yellow Emperor), (they) cut wood into a spade-like plough，and bent wood sticks by toasting close to a fire into a fork-like farm tool and hollowed out wood to build boats, and scraped wood into oars. Their function was already supernatural and their efficacy was great. Try to recall the people who lived by begging for food and had no shelter. Was there any one who felt calm without being astonished when they saw (the implements) for the first time? Until the people used them one by one for a long time, they didn’t feel surprised, as if they (the implements) were clothing and grain. Moreover, there were not only these (implements). Zhuge, Wuhou (prime minister) of Kingdom of Shu, constructed the Wooden Ox and Gliding Horse to transport army provisions, which saved material resources, namely, to store up people’s wealth. This is the best action in military affairs. However, there were some people in following generations who still criticized his accomplishment as not following the Doctrine of the Mean. How were other ones criticized? Now the revered Mr. Wang, depending on his aptitude given by Heaven, accepted the benefit from the far western teachers and accomplished the book on preparing things for use. (I) certainly dare not compare him to the ancient gods presumptuously. Was he still inferior to such people as Wuhou? It is better urgently to spread (this book) widely. And let common people use it in their daily life without noticing it. (The people of) all ages will follow it owing to not being abandoned. Then how come man does the thing that he is surprised at a camel being a back-swelled horse? When I lived at home, I heard that the printing-block of this book had already been illegible and the reliable text was difficult to obtain. (Therefore) I didn’t hesitate spending a large sum of money buying one and wished to spread the revered Mr. Wang's goodwill to pass it on endlessly. Suffering from lack of time and energy, I tried many times, and then stopped (doing) it repeatedly. Nowadays, a backup officer of Jinguan took out this book in an accidental situation and showed it to those with same interest. All lookers said that, as for officials, it was good for official affairs; as for the common people, it was beneficial for themselves and their families. Why not reprint and publish it nationally? Since all had the same idea, I called in a sculptor to discuss it, and wrote down a few anecdotes I had heard to supplement what the history books didn’t have. Date:
In the first part of the 8th month, namely, Autumn of the 9th year of the Daoguang emperor-reign (in 1829). Written at Shuangxi Jingshe in Jinguan by Zhang Pengfen (Bushan) from Ankang, upon whom (the following titles) were according to the regulation: Cheng de lang, Fang zheng recommended in the Zhike imperial examination, Ju ren who passed the Enke imperial examination at the provincial level in 1821, Ba gong who passed the Guiyouke imperial examination in 1813, Zhou pan who was in Sichuan (province) but substituted for Zhili (province). |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=8 |
| Comment: | The preface of the book entitled "The General Records of Shanxi" between 1644 and 1829. |
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| Translation: | *The General Records of Shanxi*
Wang Zheng, styled himself as Liangpu, and with his alias as Kuixin, was from Jingyang County. He got his title as Jinshi (similar to doctorate degree) in the second year of Tianqi (1622). At the beginning, he was appointed Tuiguan, an administrator, in Guangping County. He protected the good and punished the evil. Being sage and fair, he got praise. He suppressed the rebellion of the White Lotus Society and preserved myriad people. He constructed the Qinghe floodgate, whose benefit would assist many following generations. When he reassumed Tuiguan, an administrator at Yangzhou, he accompanied the three princes, during which he was not perplexed by many nuisances. He cut off the salt tax, which brought him false accusation. He refused to worship the temple of Wei-faction eunuchs , which showed his stern moral integrity. According to his talent in administering border area, he was specially recommended to be the jianjun qianshi (an official to supervise military affairs) in Penglai, Dengzhou (now Yantai city in Shangdong Province). Less than one month (later), he was sent back to his hometown because of the mutiny of rebel military officers. When the roving bandits rose in rebellion, (Wang Zheng) called for loyalty (to the emperor), he blocked off the bandits and protected the people. Jingyang County got security again. When hierarchs respectively recommended him (to the emperor) according to his talent to assist the monarch, his capability was not put to good use. When the rebel, Chuang, took control of Shanxi, Wang Zheng hid in the countryside. The rebels intimidated him repeatedly, (but Wang Zheng) carried his sword and kept integrity by himself. He didn’t go to the provincial capital in the end. When he heard that Beijing had fallen, he set up a seat of memorial tablet for the emperor and wept (for the emperor) at home. He died from fasting for seven days. What he wrote and was spread in society includes Liang Li Lue (The Outline of the Two Theories), Qiqi Tu (Diagrams of Wonderful Machines), Liaoxindan，Bai Zi Jie (Explanations of Baizi), Xue Yong Jie (Explanation of Xueyong), Tian Wen Ci (Words of Heaven-Inquiring), Shi Yue，Bing Yue，Yuan Zhen Ren Zhuan (Biography of Yuanzhengren), Lidai Fa Meng，Bian Dao Shuo (Explanations of Biandao)，and Shan Ju Yong (Praising of the Life in the Mountain). Scholars honored him as Mr. Right and Moral Integrity in private.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1+10+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=10 |
| Comment: | *The preface of the reprinted QQTS by Wu Weizhong in 1628.* The day of the Mid-Autumn Festival of the first year (Gaiyuan) of Chongzhen emperor-reign means one day of Autuum of 1628. |
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| Translation: | *Postscript for Qi Qi Tu*
In this world, the extraordinary things should be done by extraordinary persons. Extraordinary means wonderful. Those cowardly and narrow-minded scholars plead obedience to the Doctrine of the Mean to cover their ill-informed situation and ignorance. Sometimes, the Doctrine of the Mean does not work, is it not strange? There are wonderful articles in the center of art and literature; there are ingenious military moves in the battle array; there is the magic skill of being invisible in divination; there are wonderful talents concerning human relations; there are rare things in mountains and oceans, and there are strange states among ghosts and gods. Does it mean there won’t be anything wonderful among machines? The key point is that extraordinary persons with obvious ingenuity just place hope on machines. Mr. Wang (Zheng) from Shanxi Province administered Yangzhou. He was lenient, brilliant, kind and tolerant; he acted solemnly, respectfully, properly and peacefully; he made administrative proceedings simplified and punishment clear and bright; and the noble and the humble all were changed. As to the job of rectifying music, what he explicitly explained for me and let me study and practice was also quite elegant, which could be compared with the custom handed down from the Six Dynasties. Since he thought that I was worthy of education, he showed me his book, Qi Qi Tu Shuo, in which what he compiled were three chapters and what he wrote was one chapter. (He) gave me (them) to learn. The revered gentleman (Wang Zheng) was a great talent with courage and intelligence. He could unveil the natural disposition of Heaven and wash the axis of the earth. (His study) was in interdisciplinary fields, and he was capable of lots of things. These were just his after hours achievements. I have tried to study people who were good at wonderful things in ancient times. (Gong)shu Ban and Mo Di (invented) were known to be used at their time and were beneficial to society. They are the most famous. After them, the ones such as Zu Chongzi, Zhang Pingzi, Majun and Yiyuan were all known as ingenious persons in their time. However, their achievements were not practical and their benefit couldn’t reach people. (Hence), they had no redeeming feature finally. Only the Muniu Liuma (wooden ox and gliding horse) was praised till today. Except it, most (of the other machines and inventions) belonged to the false, and was not the truth. Therefore, the self-moving quadricycle and the weight-driven geared mill made by the revered Mr. (Wang Zheng) can be as good as or better than Wuhou’s (wooden ox and gliding horse). However, the single-cylinder force-pump and flume-beamed swape are prepared for drought and flood; the combined clock inherits the clepsydra; the water cannon (is used to) put out fire; the multiple crossbow (is used to) resist formidable enemies; and the winch-driven cable plough saved (the power of) the oxen and horses. (They) rely on wind and water, and do not bother manpower. All of them were beneficial in quick traction, transport, army, agriculture and commerce, and affairs as trivial as a grain of rice and salt. Everything，big or small, was completely equipped (with machines). (They) free labor remarkably. In the past, people said that consummate articles were written by Han Yu, that most wonderful poems were written by Du Fu, that most beautiful calligraphy was Yan Zhenqing’s, and that perfect paintings were drawn by Wu Daoyuan. If so, all valuable things in the world were completely finished. However, as to the emergencies of a country and the need of people’s daily life, what has a little benefit? It is this book (QQTS). If this book is made known widely, it surely will be what benefits mankind and help matters, like a big ship. How can it only benefit Yangzhou? Yinfu read: "Then there were wonderful implements and these produced every phenomenon." However, I would like to say: "The revered Mr. (Wang Zheng) has wonderful machines which are really beneficial to everybody; according to his quality, he was surely a useful scholar; and his book is surely a great exploit. How can it not be spread?" (therefore,) I respectfully draw it down and congratulate it on its being printed.
The date:
the day of the Mid-Autumn Festival of the first year of Chongzhen emperor-reign. A Confucian teacher of Yangzhou prefecture, Wu Weizhong, composes it and handwrites with obeisance.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1+22+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=22 |
| Comment: | The preface by Wang Zheng, one of the authors of QQTS, in 1627.K |
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| Translation: | *The Selected and the Best of QQTS* QQTS is a western book brought to China by several scholars from the far West. This is one category of more than 7,000 books. Just in this category, this one is only a tenth part of the thousands or hundreds of books. I am not smart enough. (But) I have ever admired and pried about machine-making and image-showing principles in private, and I have made a deep study of the xuanji（an instrument concerning the first four stars in the bowl of the Big Dipper）and the yuheng (an instrument which simulates the running of the Little Bear), and then constructed an instrument that followed the law of the Heaven and the order of the earth. All the sun, the moon and five planets were there, and are perpetuated after tens of thousands of generations. How astonishing! Kao Gong Ji and the south-pointing implement were completed extremely long before. There wasn’t a lack of great masters and skilful craftsmen in the following generations. However, except for the born marvelous hands, no consummate techniques were handed down. And then, the Muniu Liuma (wooden ox and gliding horse) became the only excellent one through the ages. I admired and loved it very much. Occasionally, I tried not to estimate my superficiality and at random made such machines as a hongxi (single-cylinder force-pump), heyin (the flume-beamed swape), lunhu (combined clock), daigeng (winch-driven cable plough), zizhuanmo (weight-driven geared mill) as well as a zixingche (self-moving quadricycle). The people who saw these said (they were) quite wonderful, too. But in my mind, I was especially not very happy. I had read about those strange persons and things recorded in Zhi Fang Wai Ji (Record of the Places Outside the Jurisdiction of the Office of Geography) by chance. Having not read many pages, I counted one or two wonderful machines among them, with which what we saw and heard here were absolutely not comparable. For example, it is said that in Duoleduo city, people at the top of a mountain carried water from the foot of the mountain to supply (the people) up (it). The transporting was very difficult. Within a hundred years, there was an ingenious person who made a water-lifting device. It could make water spiral up to the city on the mountain without relying on manpower, and this machine could run day and night by itself. Another example (in this book) said that Yaerjimode (Archimedes), who was an astronomer, took the king’s order to build a huge seagoing ship. After being built, the ship would be transported into the sea. Calculating, it was impossible to transport, though with all the country’ capability, tens of thousands of oxen, horses and camels would be used, Jimode (Archimedes) invented an ingenious method. This ensured that the ship like a mountain would run and go down into the sea instantly as soon as the kind raised his hand to draw it. Then (he) made an automatic armillary sphere, on which the sun, the moon and five planets moved independently by themselves; the running speed of each constellation was not different from (their speed in) Heaven. This instrument was made of glass and could be looked through completely, which was a rare treasure in the world. Zhi Fang Wai Ji was written by a western scholar, Mr. Ai (Aleni). His words in it should not be false. I was almost at a loose end and yearned (for it) in private. I sighed: "Wow! What fortune can I have to have a look at those wonderful machines in my life?" In the winter of the sixth year of Tianqi emperor-reign (1626), I went to the capital waiting for my appointment, and met Long Jinghua (N. Longobardi), Deng Hanpu (Johann Schreck Terrenz) and Tang Daowei (Adam Schall von Bell), the three gentlemen，who were living in their old residence to wait for the imperial decree to compile the calendar. (Therefore), I could meet them everyday and could consult them. I felt all the more joyous. One day when we were free, because of talking what Wai Ji had recorded, I asked them. The three gentlemen politely smiled and said: “There were quite many machines and they all had diagrams with explanations. You can read now. How dare we talk about them at random?” I immediately borrowed and read. (They are) different in thickness, the only ones that belonged to diagrams and explanations of the wonderful machine were not less than a thousand or more than a hundred kinds. These machines usually used little power to make bigger weights turn, or made them lifted, or made them cover a long distance, or assisted in construction, or transported fodder and food for the army, or were convenient to drain or to pour water, or lifted boats and ships up or put them down, or guarded against catastrophes, or focused on keeping things out of damage, or automatically pounded and sawed, or produced sound and wind. All kinds of wonderful machines were prepared. Some used manpower or other things as power; some were powered by wind and water, others were used wheels, mechanisms, hollowness (vacuum) or even weight as power. All these wonderful usages delighted me and made me think clearly. There are several styles among them which corresponded with what I was thinking. I looked at their diagrams, which were incomparably delicate and skillful. With such things and their diagrams, I could both look at them and imagine them. But their explanations were in Western language. Though, when I was in my hometown, I had ever got the instruction from Mr. Jin Sibiao (Nicola Trigault) on the alphabet with the 25 consonants and vowels of the Western language, and I published a book, Xi Ru Er Mu Zi (An aid to Western scholars in reading and listening), I also knew a little about their pronunciation. But considering the whole meaning of all the text, I was at a loss and didn’t understand the meaning. So I asked to translate (them) into Chinese. However, Mr. Deng (Terrenz) said: “Translating is not difficult, however, although this knowledge belongs to a trivial technique in the art of force, at first surveying and mathematics must be learned, and then (the translation) could be done. The reason is that, (as to) the details of all the devices, there must be dimensions and numbers at first. Because of dimensions, measurement appeared, and because of numbers, calculation grew. Because of measurement and calculation, there was proportion. Because of proportion, thus (one) could know all the reason of things. Having got the reason, one could establish the method. Without knowing measurement and calculation, one certainly couldn’t know proportion; without knowing proportion, one surely couldn’t be acquainted with the diagrams and explanations of these machines. There is another special book on measurement, calculation is completely in Tong Wen (A Guide to Algorithm in Common Language) and proportion is mostly seen in Ji He Yuan Ben (Euclid’s Elements).” Mr. (Terrenz) indicated and explained them to me. I studied them for several days and also quite understood the main idea. Thereupon, (Mr. Terrenz) took out whole books on the diagrams and explanations of various machines, classified (them) and dictated (them to me). Then, I wrote freely and quickly without sequence and decoration. I always wished it would be simple, clear and easy to understand so that every one could read (them). However, among the diagrams and explanations, there were extremely many ingenious machines. But, either (some of them) were not related to people’s lives and daily use, such as flying bird and water-driven organ, or (some of them) were not in urgent need by the nation. Hence, they were not recorded. We just recorded what were urgently needed among them, the really very necessary machines. But if the method to make it is too difficult, such as a machine with too many screws and worm gears, which could not be made by craftsmen according to the pattern, or perhaps the cost of a machine was quite high, thus, (we) didn’t record (them). (We) only recorded the simplest and most convenient ones, the machines which were completely urgently needed and convenient. However, one method had many varieties, and each variety had many machines. For example, the water-lifting machine had over a hundred and ten varieties. Some of them were too heavy, and some were too complicated. Therefore, we didn’t record (these). We only recorded the most ingenious ones. The record had been complied, then, we named it "Yuan Xi Qi Qi Tu Shuo Lu Zui" (The Best Selection of Diagrams and Explanations of the Wonderful Machines of the Far West). A visitor who cared about me read (it) and said: “My gentleman，Xi Ru Er Mu Zi that you published before is still not (considered) useless by literati and scholars. Now what you’ve recorded here is only such class as craftsmen's skills. A man of honour doesn’t think highly of utensils. Why exhaust yourself by doing this? Furthermore, these western scholars live in our country, China, and we have deep friendship. Of course, we really know they are worthy. However, those persons are in a far desolate area ten of thousands of li away, and they are just only scholars in the west remote place. Why are you particularly addicted to them like this?” I replied to it: “As to learning, (I) don’t mind whether it is profound or shallow, but always expect it to benefit society; as for a person, I don’t care whether he is a Chinese or a westerner but always hope that he is not against Heaven. What is recorded here belongs to trivial techniques, but they actually benefit people’s daily use and the urgent need of nation’s prosperity. If we look down on them by holding the excuse of not thinking highly of utensils, then why did Ni Fu (Confucius) always remember Zhou Yi, which said: ‘Prepare things for future use and make utensils to benefit all people.’ Who can be greater than the holy Confucius? Moreover, extraordinary persons are rarely met with; consummate learning is seldom heard; to get along together is the most difficult. The years wait for no person. If I have clearly seen they are wonderful and haven’t recorded to spread them, my desire can’t be stopped. Hence, I sought the things, of which eyes and ears could have the aid in the past. Now, I have further sought the things, of which hands and feet can have the aid. Is it necessary to care for other things? These Western scholars have lived here for many years. There is no scholar official who has associated with them but is not attracted by them. And they are not arrogant and mean. How has our generation seen them but let them go? The ancient people who were eager to learn wrapped food and carried book boxes, and went to the trouble of traveling several thousands of li to visit (learned people). At present, the talented persons crossed the border and brought the books from tens of thousand of li away and imparted them to us. On the contrary, can we have the heart to reject them? They are only a few persons and all of them are learned scholars. (When) vassal states paid tribute to an emperor and princes had audience with an imperial court, the old Yuetang and Sushen were regarded as the states that were farther than the faraway places. (The faraway westerners’ visit) just shows the Holy Morality of our Ming dynasty and incurs the rarely-comparable flourishing through the ages. Recently, a stele was dug out in our province with "In praise of the popularity of Jing Religion (Christianity) in China" written on the top of it, which was carved around the time of Guo Ziyi in the Tang Dynasty. It looks very new although it had lasted for a thousand years. (What was written on it) corresponds with the Catholicism these talented scholars are preaching. It is recorded by a Fu Jie (local officer) that every one of the six emperors after Tang Taizhong (second emperor of the Tang Dynasty) continuously worshipped it very much. It was already liked in the past, why would we dislike and detest it nowadays?" Another visitor smiled and said to me: "It is that. But as far as your words are concerned, eyes and ears need aids, hands and feet need aids, too. Will only mind need no aid? The western scholars’ room is full of books. There must be a lot of books helpful to the mind. You didn't translate these kinds of books, but only translated the book on machines? Why?” I nodded and said: "The apparatuses with shapes can be explained a little，while the shapeless reasons are huge and difficult to find out their outcome immediately. I am not nimble and it is enough for me to do these things merely. As to the Western scholars’ books on reasons, (if they) were not those masters in Mutian (the Imperial Academy) and Shi Qu (the Imperial Library), (they) couldn’t translate them. Of course, this is what I yearn for each morning and night but my ability can’t reach it. It still needs to wait till the future." The visitors then nodded and left. I thereby wrote down what he said here in order to memorize the time. The date:
in Spring of the 7th year of Tianqi time (in 1627). Writtten by Liaoyidaoren, Wang Zheng, from Jingyang County of the central Shanxi plain.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=47 |
| Comment: | Notes on Content and Stylistic Rules and Layout of QQTS-References |
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| Translation: | -References*
References (of QQTS)
*Gou gu fa yi (Gougu Methods)
*Yuan rong jiao yi
*Gai xian tong kao
*Tai xi shui fa (Hydraulic technology of the Far West, 1612)
*Ji he yuan ben (1607, Clavius, Euclidis Elementorum libri XV, Rom)
*Kun yu quan tu (Whole map of the World)
*Jian ping yi (Astrolabe)
*Hun tian yi (Armillary sphere)
*Tian wen lue
*Tong wen suan zhi (1613, A Guide to Algorithm in Common Language, namely, C. Clavius, Epitome Arithmeticae Practicae, Rom, 1583)
*Jing tian shi yi
*Ji ren shi pian’ (Biographies of Ten Special People)
*Qi ke
*Zi ming zhong shuo’ (Explanations of the Automatic Striking Clock)
*Wang yuan jing shuo’ (Explanations of the Telescope, 1629)
*Zhi fang wai ji (Record of the Places outside the Jurisdiction of the Office of Geography, 1623)
*Xi xue huo wen (An Inquiry about Western Learning)
*Xi xue fan (A General Introduction to Western Learning)
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=49 |
| Comment: | Notes on Content and Stylistic Rules and Layout of QQTS-Instruments of machine-building |
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| Translation: | -Instruments of machine-building*
*du shu chi
*yan di ping chi (surveyor’s water level)
*he yong fen fang fen yuan chi (combined ruler to divide square and circle)
*he bi fen fang fen yuan ge you yi fen qi zhi shi fen chi (openable ruler to divide square and circle from one fen to ten fen)
*gui ju (compasses and carpenter’s square)
*liang zu gui ju (two-feet divider or compasses)
*san zu gui ju (three-feet compasses)
*liang luo si zhuan kai bi ding yong gui ju’ (special openable compasses with two screws)
*dan luo si zhuan he bi ren yong gui ju’ (multifunctional openable compasses with one screw)
*hua tong tie gui ju (compasses and square to draw on copper and iron)
*hua zhi gui ju (compasses and square to draw on paper)
*zuo ji dan xing gui ju’(instrument to make ellipses)
*zuo luo si zhuan xing gui ju’ (instrument to make screw-shape)
*yi yuan hua jin gui ju (ruler to zoom out or zoom in)
*xie zi yi da zuo xiao, yi xiao zuo da gui ju’ (instrument to enlarge or shorten characters)
*luo si zhuan mu (outside screw, nut)
*huo ju (movable saw)
*shuang yi zuan (two-wing drill)
*luo si zhuan tie qian (pliers with screw)
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1/+51+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=51 |
| Comment: | Notes on Content and Stylistic Rules and Layout of QQTS-Marks (Latin letters) |
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| Translation: | -Marks (Latin letters)*
Western letters must be used as marks. It seems western letters are difficult to remember. However, because they not easily remembered, the reader wonders at them and searches for them in order that he must master them. Moreover, there are only twenty marks, which have different forms; and they are neither very complicated nor very difficult. Now the western letters are listed as following, and Chinese characters are juxtaposed with them and are used to explain them in order to read them conveniently. And we wish (you) know only twenty western letters for the use of various pronunciations and various words.
THE FOLLOWING TABLE NEEDS CHECKING, MAYBE.
a E i O u c ch K p t
a1 e2 yi1 a1 wu3 ze2 zhe3 ge2 bai3 de2
j V f G l m n S x h
ri4 Wu4 fu2 e2 ??? le1 mai4 nuo4 se4 shi2 hei1
Because there are various machines in diagrams, the above marks must be used to label (them), and then are indicated in explanation one by one. Their endless usages are no longer discussed. They are not used if a diagram is simple and is easily understood.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1/+52+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=52 |
| Comment: | Notes on Content and Stylistic Rules and Layout of QQTS-Names of machines and their parts |
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| Translation: | -Names of machines and their parts*
column
*long column
*short column
*beam
*crossbeam
*side beam
*rack
*high rack
*cubic rack
*short rack
*lever
*shaft
*vertical shaft / upright shaft
*horizontal shaft
*oblique shaft
*angular shaft
*wheel
*vertical wheel
*capstan
*horizontal wheel
*blique wheel
*flywheel
*drum-treadmill
*star-shaped wheel
*drum wheel / lantern-shaped wheel
*gear
*fu lun (wheel with spokes)
*gu lun (arc-wheel)
*lantern-shaped wheel
*water-wheel
*wind-wheel
*vertical cross wheel
*horizontal cross wheel
*obliquely cut semi-conical cam
*vertical wheel made of wood board
*horizontal wheel made of wood board
*ratchet wheel
*semi-ratchet wheel
*shang xia xiang cuo ratchet wheel
*zuo you xiang cuo ratchet wheel
*crank
*zuo you dui zhuan crank
*shang xia li zhuan crank
*single windlass with a crank
*double windlass
*pulley
*handcart
*hauled cart
*jia che
*Ctesibian force-pump
*screw, water-screw, Archimedean screw
*suction lift-pump
*rope
*hauling rope
*beetling rope
*turning rope
*twining rope
*noria
*water-spoon
*noria like chair of pearls
*gemel like crane’s knee
*sail
*fan
*moving wooden roller
*huo di ping
*movable swape
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1/+65+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=65 |
| Comment: | Notes on Content and Stylistic Rules and Layout of QQTS-Diagrams and explanations of whole machines |
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| Translation: | -Diagrams and explanations of whole machines*
Diagrams and explanations of weight-hoisting*
Diagrams and explanations of weight-hauling*
Diagrams and explanations of weight-hoisting by rotating*
Diagrams and explanations of water-lifting*
Diagrams and explanations of grinding-mills*
Diagrams and explanations of wood-sawing*
Diagrams and explanations of stone-sawing*
Diagram and explanation of pestle-driving*
Diagram and explanation of turning a book-wheel*
Diagram and explanation of a sundial (clock) driven by water*
Diagram and explanation of mechanical cable ploughing*
Diagrams and explanations of the water cannon (force pump for firefighting)*
qu li shui tu shuo (Diagrams and explaations of water-lifting)*
Diagram and explanation of a bookcase*
Diagrams and explanations of flying puppets*
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol1/+68+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=68 |
| Comment: | *There two "chaper one". This is the beginning of the first one. * It is actually the general introduction which consists of two main parts, namely "Biao de yan" and "Biao xing yan". |
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| Translation: | *Chapter one of Yuanxi Qiqi Tushuo Luzui*
Interpreted by Johann (Schreck) Terrenz, a Jesuit missionary from the West*
Expressed in Chinese and drawn by Wang Zheng, a catholic scholar from Guangxi*
Checked by Wu Weizhong, a scholar from Jinling*
Printed by Zhang Pengfen from Ankang*
QQTS was written on the basis of translation of western texts. In the west, every kind of learning has its original name. The original name of this learning is li yi (the art of force). (With regard to) the learning of the art of force, in the west there is firstly biao xing yan (introduction to qualities), as well as explanations, which are used to show the inner excellence of this learning. Secondly, there is biao de yan (introduction to virtue), which is used to show the outer excellence of this learning . Now (we) translate all their original text and meanings, and list them as follows.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=69 |
| Comment: | Biao xing yan, the first introduction, the first part of the first "chaper one". |
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| Translation: | *The art of force (the original name)/Biao Xing Yan (introduction to qualities)*
Li yi (the art of force) is zhong xue (the science of weight).
Li (force) means qi li (physical strength) and li liang (power), such as manpower, horsepower, waterpower, wind power. Additionally, man also says yong li (put forth one’s strength or use power), jia li (exert strength). For instance, to use manpower, to use horsepower, to use waterpower and to use wind power. Yi (art) means the ingenious methods and machines to use power (or to exert strength) so that it is the general name of being good at using li (power, strength) and at lightening li (power) and saving li (strength or power). Xue (learning or science) of zhong xue (the science of weight) is a general name, its zhong is an individual name. Wen xue (literature), li xue (Confucian school of idealist philosophy of the Song and Ming dynasties), suan xue (arithmetic) and so on are named by xue (learning), hence (xue) is named as gong (general). This li yi zhi xue (the learning of the art of force) is individually named zhong xue (the science or learning of weight) because its meaning pertains to zhong (weight).
The original explanation of Biao xing yan (introduction to qualities)
The science of weight always takes charge of only one thing, namely, moving weight.
Every (branch of) learning takes charge of something. For instance, what yi xue (medicine) takes charge of is to treat patients; what suan xue (arithmetic) takes charge of is to count amount. But this li yi zhi xue (the learning of the art of force), regardless it is soil, water, wood, stone and so on, always takes charge of moving weight.
Its fen suo (places) include two parts: one is ben suo (the natural place) inwardly, namely, ming wu (understanding, comprehension); another is jie suo (lodging place) outward, namely, diagrams and books.
Human spirit takes charge of three things: the first is to understand; the second is to remember (something); the third is love and greed. Any external thing and external matter that any scholar takes is understood and then is hidden in his memory. It is adequate that man can directly take something from memory when he understands something, loves it, and desires to use it in coming days. This means that ben suo (the natural place) of this learning locates inwardly. The methods by which the ancients had already made implements were recorded in diagrams and in books, which are jie suo (lodging places) of this learning. Therefore they are named exteriority.
Its attainments rest with three approaches: firstly, through the master’s impartation; secondly, through patterns; thirdly, through watching more, thinking more and doing more.
All learning must go through these three approaches before success. The learning of the art of force relies on them even more. Without the master’s impartation, man does not know how to do; without patterns, man cannot do without foundation. However, although man has both of them, he still cannot be accomplished in this learning if his eyes are not careful enough, and his thinking is not detailed enough, his hands are not diligent enough. A great master can offer people rules, but cannot make them skillful, the skillfulness must result from practice and familiarity. So man says that a habit is the same as naturalness. All three approaches are paid equal attention to, but the third is especially close to (skillfulness). Why? It is easily understandable that a master imparts (the learning of the art of force), but (a prentice) will feel difficulty if his master is unable to be at (his) side. The pattern is the most convenient, however, there is a man who still cannot easily understand although he has a pattern. Therefore, the approach, which is especially close to skillfulness, is to observe more, to think more, and to do more.
It has four functions. The first is the reason of things, the second is weighing and measuring, the third is movement, the forth is the mastery of a thing.
Li (reason) is just like the root of a tree. A tree has its root, from which a thousand branches and ten thousand fruits grow. Therefore, when a man has already got to the reason of things, he can naturally understand the qualities of things. When he understands one reason, he can understand other reasons. Getting one method means that he can get thousands of other methods. To get to the reason of things is originally scholars’ urgent affair, and the first of what must be done for the learning of the art of force. While the reason has been understood, man must weigh and measure two reasons if he does not know which of them is heavy or light. Reasons can be compared with each other, and then can be distinguished naturally. Therefore, weighing and measuring take second place. Having got to the reason and having weighed and measured, namely, having already examined, if (man) encounters a heavy thing which cannot be carried or moved by manpower, it is not difficult (for him) to move it when (he) uses the methods and implements of the learning of art of force. So movement holds the third place. What is movement then? It always desires to incur its thing. If man lives, there is hunger, there is cold (he will suffer from hunger and cold, so he will think of eating and drinking, as well as such things as clothing. To avoid wind and rain, he will think of such things as city, palace and room. To prevent disaster, prevent enemy aggression, he will think of weapons of war and firearms and so on. All these things cannot be got to without learning the art of force. Therefore, what ends with something happening (thing-incurring) is just one that ends with understanding the important function of this learning. The four functions seem to follow an order, but in fact they are linked. If man wants to master things, he will not master them without an understanding of the manner of movement; if man wants movement, he will depart from the manner of movement without an understanding of weighing and measuring; what will be weighed and measured if weighing and measuring is not based on getting to the reason? So the four functions need each other, together as a big use of this learning.
It is imparted because of five (factors): firstly, the primogenitor imparted it successively; secondly, discomfort makes man oversensitive; thirdly, touching things stirs up ideas; fourthly, (Something) results from occasional understanding; fifthly, exceeding thought results in thorough understanding.
The impartation started with the fact that the human primogenitor Adam got something from God. After that, it (the learning of the art of force) was successively imparted to descendants. However, cultivating implements were in particular imparted. Nearly four thousand years later, there was a great person, namely, Yaximode (Archimedes), who created such devices as water-screws and small screws, and could record the reason of various devices. Nowadays, there are persons who can best understand the reason of various implements: one names Wei duo, one names Xi men. There are also persons who draw and print the diagrams: one is called Geng tian (ploughing), the other is called La mo li. They are all persons who impart knowledge in the field of the learning of the art of force. The above-mentioned ‘discomfort makes man oversensitive’ is the fact that, constrained by hunger and cold, man thinks of making drink, food and such things as clothing; constrained by wind and rain, he thinks of building such things as cities, palaces and rooms; constrained by disaster and enemy aggression, he thinks of weapons of war and firearms, and so on. ‘Touching things stirs up ideas’ is like the fact that seeing that the fish sways its tail in water, (man) therefore invented the rudder; that seeing that the fish (moves) left or right by its fins, (man) therefore invented a scull; that seeing that the squirrel ferries by bending over a board and erecting its tail, (man) invented the sail. Something resulting from occasional understanding is like such things as the example: A king took pure gold and ordered a craftsman to make a utensil. The craftsman secretly mixed silver in. The king wanted to check this fraud, but he failed. While bathing, Yaximode (Archimedes) realized how: gold and silver are (respectively) divided into two equal (weight) parts, but their volumes are not equal; gold is heavy but small; silver heavy and big. The utensils are put into water to see which of them makes more or less water remain in the container, then gold and silver were distinguished, the fraud was clear in the end, therefore the craftsman pleaded guilty. Exceeding thought resulting in thorough comprehension is that man is able to think and consider frequently, his thinking becomes naturally detailed, his understanding is naturally developed. It is said that if thinking again and again, but the thinking results in nothing, ghosts and gods will (make him) understand thoroughly. These few (things), although they do not come from impartation, but arise from this cause, are listed together as another kind of cause under impartation.
Such a few (factors) result from some reasons, although they do not rely on impartation. Therefore they are listed together as causes under impartation.
Talking about its liao (material), (we) say that reasons and methods, even if (there are) thousands and hundreds, are still endless.
Liao means materials in the learning of the art of force. If it is difficult to lift a heavy object, manpower or horsepower or mechanism or wheels are used. If one method is not enough (to lift it), one hundred methods will assist it. Its mechanisms differ in various ways, (but) its materials do not exceed reason and method, two kinds of things, which are understood by different people, who comparatively consider adopting and using them, ever changing without limit.
Check its mo (pattern), (we know) there is ti (body), there is zhi (system), (which) actually carry on one after another.
Mo (pattern) means ti zhi (system). With only materials, but no system as a pattern, a machine cannot come into being. However, although systems are various, they actually carry on one after another without interrupting each other. For example, the automatic striking clock (has) big wheels and small wheels, in which items are very numerous. (They) must join each other one by one, and then (the clock) may strike automatically. Once they are disordered, it cannot be used.
What is justly relied on and is not often departed from is du shu zhi xue (surveying and mathematics).
The Creator made a thing which has shu (quantity), du (measure) and zhong (weight), all things are like that. Shu means mathematics; du means surveying; and zhong means zhong xue (the science of weight) of the art of force. Weight has its qualities and nature’s laws. Comparison between this weight and that weight relies on mathematics. Then comparison of the shape and size between this weight and that weight relies on surveying. Therefore, mathematics and surveying are just what the science of weight needs. The three kinds of learning are derived from qualities and nature’s laws, like brothers and relatives on their wives’ side who may not be separated from each other.
What are consulted are perspective and lu lu zhi xue (the learning of temperament), which and (the learning of art of force) may complement each other.
The use of the study of weight originally depends on hands and feet; the eye takes charge of perspective; the ear takes charge of the learning of temperament (music and acoustics); it seems they are not deeply concerned. However, without perspective, the square, circle, plane and beeline cannot be made; without the learning of temperament, such rhythms as lightness, heaviness, quickness, slowness, sweetness, bitterness, highness and lowness are difficult to harmonize; moreover, all the devices to cause wind and to be blown and to strike automatically rely on the learning of temperament. Therefore, these two kinds of learning are friends of the science of weight, although they are not close relatives. They may complement each other and are absolutely necessary.
Here it gets much refinement, and then its effect must be great. Therefore its capability is very strong, and it benefits the human world very much, and is called zhong xue (the science of weight). How can scholars neglect it?
The science of weight is derived from such studies as surveying and mathematics, it may be said that its learning is plentiful and succinct. (To learn) is originally accomplished in an action, (and one) may naturally immediately do the deed while learning. Use only the part qi zhong (weight hoisting) to explain it. Provided that here exists a weight, a few hundred people can hoist it, or cannot hoist it. However, only two or three people who are expert at this learning are able to hoist it. How about its capability? (It) not only saves much labour, but also saves heavy expenses. Additionally, (it is) natural and does not result in danger. How about its benefiting the human world? Therefore, it is named the science of weight. Although (it) is specifically named for moving weight, it is found that this learning is related to the important. Who has a will to work at administering affairs should not look down on it.
Or ask: biao xing yan (introduction to qualities) is only one sentence, why are there so many explanations? Say: this learning is most wonderful and most profound. If it is not explained in detail, man is not able to have a quick understanding of the wonderfulness, methods, qualities and natural laws of this study. Therefore, it has been explained in detail. And I annotate it in detail again and always expect every reader will easily have a thorough understanding of it.
Illustration of the inner qualities of the art of force
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| Comment: | Biao de yan, the second introduction, the second part of the first "chapter one" |
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| Translation: | *The Art of Force/Biao De Yan (Introduction to Virtue of the Art of Force)*
Introduction to Virtue
What is shown before is the inner qualities of the science of weight, now, its exterior virtue will be shown.
The science of weight is the most exact and proper (knowledge) without any mistake.
Of all kinds of learning under the sun, some are entirely ideal, and some are half ideal. Many of them are undoubtedly all correct, but those with errors are not few. Only arithmetic and measurement are of free of errors. And this learning of the art of force is based on surveying and mathematics, and is entirely derived from surveying and arithmetic, and there are theories and methods in a variety of (parts). So, only this learning can be regarded as the most exact and proper (knowledge) and without any mistake. It is not like other learning, where it is possible that someone thinks that (this result) is right, while the other thinks that it is wrong; someone regards one thing as true, but the other may refute it. As everyone possesses comprehension and awareness, (if he) knows the reason for things, (he) cannot help but justify it, it is not (reached) by force. (If) there is a mistake sometimes, the mistake is not in the learning, but the quality of the machine is poor; if (the quality is) not poor, it depends on whether the person operates according to the method or not.
It is the simplest and easiest, and practicable.
There is only one common thing for the machine; and there is only one reason for the machine. And (the reason) is extremely clear, it does not rely on lots of objects. Besides, there are not many objects which are connected, if (one) can understand one object, (he) would be able to deduce (the principle of) the other object. So, whenever (one) pays attention (to the learning of the art of force), (one) can become acquainted with it naturally. It is not like other learning, (even if one) exhausts his mental efforts, it is possible that the (the learning) is still not easy to understand. Its principles are easy to understand; its methods, in which there are traces, are easy to find; there are ready-made patterns for its machines, which can be imitated. Therefore, this learning is the easiest and simplest one, and every one can be engaged in it.
However, it is rare and strange, (so) most people seem to be very amazed to hear it
It is strange that lots of people conquer lots of people, or that lots of people conquer few people. That few people conquer lots of people may be wondered at. Why is it worth wondering if man uses powerful force to transport great weight? Now, using a small machine, (one) can immediately lift a great weight, elevate it, and let it travel a long distance. There are few who would not be surprised by its extraordinariness. However, if (one) is accomplished in this learning, and knows the reasons of the machine, then this thing to be wondered at is just normal. Let’s observe a thousand-jun crossbow, it only needs a one-cun trigger. The ten-thousand-hu ship is (controlled) only by a one-xun rudder, is it worth wondering at? But as they are frequently used, they are only regarded as homely articles of everyday use.
It is indescribably fine and ingenious, (persons) who catch sight of it are naturally greatly gratified.
(One) will get food when (one) is hungry, and get drink when thirsty, so one is naturally gratified. These fine and ingenious machines are the delicacies of our comprehension. How could (a person) who possesses both comprehension and awareness not relish it? Furthermore, there is a great weight that can not be lifted by great force or more force, now, by a small force, the great force can be elevated, could anyone not be gratified by seeing this? Therefore, the fineness and the ingeniousness of the machine can not be described by writing and talking. But no one would not be exultant when seeing the excellence of the machines. In the past, Yaximode (Archimedes) wanted to analyze the reason for the intermixing of gold and silver, (he) did not succeed. (He) understood the reason in the bath by chance, and was so joyful that he forgot to put on his clothes, and, naked, reported the (result) to the king, that is one example.
It could serve as the military office of engineering.
There are two grades of craftsman, one is superior, one is inferior. The inferior receives orders from the superior, does all the work personally, like a servant. The superior makes the general plan, but does not use the axe and the chisel personally. After the establishment of this learning, the superior of all handicrafts become also inferior, and only this learning is at the top. Take the top one hundred craftsmen, without this patriarchal handicraft, they are not able to take something as a model, and have nowhere to take orders from. It has five respected qualities: first, it can teach every craftsman various machines, secondly, it can demonstrate the usage of the machines, thirdly, it can make clear the reason for the machines, fourthly, it can invent new machines in the field where there was always no machine. Fifthly, it can use the established method to assist in what the work falls short of. So, it is called the military office.
It can broaden the fine source of advantages
(Things concerning) people’s lives and daily use, diet, clothing, palaces, all kinds of advantages, are things in urgent need, none of which does not result from machines. If tilling the field to produce food, one must use such machines as the mechanical cable plough; if irrigating the dry field, or if draining water from a paddy field, such machines as the suction lift-pump, water-screw, windlass with a crank must be used; if pressing alcohol or oil, such machines as the screw must be used; in weaving or cutting clothing, such machines as the loom, spinning wheel and scissors must be used; If (one) wants to transport clothing, food and other goods from far away, (one) must use ships, vehicles or other machines; if (one) wants to build a palace, (one) must use weight-hoisting machines, weight-hauling machines and other machines (to move) metal, stone, soil, wood and things in need. For all necessary things in the land of the living, what is not obtained from the learning of the art of force? Therefore, it could be regarded as the source of all fine (advantages). Not only that, even in providing disaster relief and fighting calamities, just like guarding against floods, (one) should transport big stones to build dikes；in fire protection, (one) should use the water cannon to sprinkle water; when (one) encounters a beast of prey, (one) should use bow, crossbow, sword, and spear; if (one) meets a strong enemy, (one) should use the fu lang big-gun. The wonderfulness in conquering the many by the few cannot be completely narrated. Would a good man who is acquainted with this learning not dredge this wonderful versatile source? To extend it further, by exploiting a mine, (one) can excavate gold and iron to provide the funds for trade and weapons; by making an organ, (one can) play music to assist in the prosperity of quiet temples and palaces; The automatic striking clock gives the correct time automatically to make up the inefficacy of the sundial on cloudy days. All these wonderful machines not only enrich the management of things people use in their daily lives, but also benefit important affairs of state politics, its advantages are inexhaustible, scholars should know to adopt them.
Common use is always the same in all countries
In a centuries-old civilized country, it is sure that no machine is of no use. Barren places and remote frontier fortresses, for example, in green countries where there are people, are at a latitude of less than 70 degrees north. (the position of the country, where the heads of people are green, is latitude less than 70 degrees north.) There is no city, no canton, no county (in the barren land). It is really the most remote place, and the most savage land. But people there also know how to use skin-boats to catch aquatic animals, and how to use the bow and arrow to fetch birds and animals. So, the use of machines is common throughout the world, how widespread it is?
If man bequeathes creations to posterity, then they will be unchanged (honoured?) for a thousand years.
After God created heaven and earth, until the Flood, there were plenty of people. There was a king, a female king, her name was Semiramis. She built a huge city, named Babylon. The circumference of the city was 60 thousand bu, the height of (its wall) 20 zhang, the thickness (of the wall) 5 zhang, 250 city gate towers were built, one million and 300 thousand laborers worked for one year to finish the construction. At that time, every kind of machine existed, and no machine had not been used. The machines have been handed down to today, being improved again. Does it always remain the same through the ages?
The ancestors of human beings made a start on making machines.
God, assists in creating heaven and earth, then it is said he created the first ancestors of human beings (then created the first ancestors of human beings), named Adam and his wife Eve, placed them in a nice peaceful region on di tang (earth). At the beginning, people did not catch any disease, and did not get old or die. All the five cereals, fruit trees and other (living things) grew from the earth by nature, manpower was not needed. All the birds and animals were obedient to humans, and they did not poison (humans). Since Adam and Eve disobeyed the order from God, and got sin by not respecting the commandments, then the cereals became difficult to cultivate, birds and animals became harmful, there were famine and cold, there were illness and death. Man was punished to engage in farming and hard work, and woman was punished to give birth to children. Then, Adam began to make machines, such as a cultivator, and produced clothing and food by himself. So, all machines were created by the first ancestor, and God’s will was received and the highest norm was set too. They came half from human power and half from the ingenuity of nature
The marvelousness of establishing methods corresponds to the natural.
All things under heaven emerge and ripen of themselves naturally. But the methods of machines emerge and ripen because of the reason of things. That is just the so-called parlance that whenever there are things there must be rules. However, although methods come from making, compared with the resultant things, the methods are somewhat simple, some of them are similar, some help one another, some exceed each other, some ridicule one another. For example, celestial bodies circulate by themselves day and night, such kinds of machines as self-running mill (weight-driven geared mill), self-moving quadricycle and automatic striking clock always resemble celestial bodies completely. Human ears, eyes, hands and feet can see, hear, move and hold automatically. When a machine is made in the shape of a human being, its hands can hold and lift something automatically, its feet can walk and stop automatically, the eyes can close and open automatically, every thing is similar to a real human being. Could they not be called articles that skillfully imitate natural exquisiteness? Sometimes, there is work that is not within human or natural power. Armed with screw, windlass, wheel, or using wind (power), water (power), or hollowness, one can complement their deficiencies. That means they help each other. The so-called assisting in planning something must have that meaning! As for hoisting, transporting and turning a great weight with small force, they are sufficiently competent for (moving) the heaviest object without any difficulty. Between heaven and earth nothing has an advantage over these machines. And the quality of weight is originally underneath, and the machines can not only be competent for it, but can also make the heavy object ascend automatically without awareness. Just like using a screw to lift water, the water only knows that itself has been descending, but not knows that it has been ascending. Is it laughable? With these causes, it could be said that the marvellousness of method-establishing corresponds to the natural. Or say that the thing which is worth seeing in an unorthodox school is actually an urgent affair of the highest learning. Here its bare bones are especially gathered up, detailed account will be given in the following text.
The illustration of the exterior virtue (goodliness) of the craft of force.
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| Comment: | Four Explannations of the Craft of Force, the end of the first "chapter one". |
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| Translation: | The craft of force*
Four explanations*
The above inner quality and exterior virtue are only the general outline of this learning. The detailed explanation has four main threads, they are listed as four chapters as below.*
Chapter one: explanations of weight
--This learning is set up in order to move weight. If there were no weight, why must it be moved? And what would be moved? Therefore, explanations of weight are arranged as one chapter.*
Chapter two: explanations of the simple machine
--Weight could not be hoisted, it must be hoisted by a machine. Machines are too many to be enumerated. Among machines, we seek the most ingenious ones. Therefore, explanations of machines are arranged as one chapter.*
Chapter three: explanations of force
--The ingenious machine is surely used to hoist weight, to haul weight and to hoist weight by rotating. However, the machine must rely on power to move (weight), for instance, on manpower and horsepower, or on wind power and water power, or on power of heavy object. Therefore, explanations of power are arranged as one chapter.*
Chapter four: explanations of movement
--There is a heavy object. (We) want to raise it, or to make it (move) far away, or make it endlessly turn and move back and forth alternately. These all are moving methods, including lifting, or prising, or pushing, or hauling, or turning by hand, or treading by food, and all different kinds of (movement). Therefore, explanations of movement are arranged as one chapter.
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| Comment: | Section 2: • Ocean and Earth form a sphere •
Look at: Klaus Vogel's dissertation, Clavius' commentary on Sacrobosco (see James Lattis)
As in section 1: heading contains consideration on weight, body contains only geometry
Pattern: Make a mechanical claim in the cosmological realm (heading) and proof it geometrically (body) |
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| Translation: | Section 2: The second heaviest thing could not be heavier than the oceans. The oceans are attached to the earth, and they combine to form a sphere.
Let’s look at the above figure: a denotes the sun and e denotes the earth and the ocean, i denotes the moon and o denotes the shadow of the sun. The sun is under the earth while the moon is in Heaven. The shadow comes into being when the sun passes the earth, and a lunar eclipse occurs when the shadow falls across the moon. Only when the earth and the ocean unite into a sphere, the shadow of which is also circular, then the lunar eclipse appears gradually like half of a circle. Look at the second figure: it is naturally clear. If the shape of the earth were square, its shadow would also be square, and the lunar eclipse would appear completely linear, instead of a semicircle. This is described in detail in books on astronomy.
in the books of astronomy. |
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| Comment: | Section 3: • Calculation of the diameter of the Earth using the distance and the difference in degree between two places • (extends to next facsimile page)
Relation between angles at which heavenly bodies are observed and distances known in China since 15th century (or earlier). But in connection with the idea of a flat earth.
Compare numerical values given with western ones (Al-Biruni) |
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| Translation: | Section3: No heavy object could be bigger in size than the earth. The distance from the surface to the center of the earth is more than ten thousand li.
Every circle’s circumference has three hundred and sixty degrees, so the circumference of the earth also has three hundred and sixty degrees. Every degree (of the circumference of the earth) is two hundred and fifty li, so, multiplied (by 360), ninety thousand li is obtained. Because the boundary a i o u has ninety thousand li, the diameter from o to i is 28,633 li, according to the ratio of 22:7. The distance from a to e is half of this, namely, more than fourteen thousand and three hundred and sixteen li. Therefore it can be said that the distance from the surface to the centre of the earth is more than ten thousand li. How to know that a degree (of the circumference of the earth) is two hundred and fifty li? For example, Hangzhou is at latitude thirty degrees and thirteen minutes north, and Shanghai is at latitude thirty-one degrees and thirteen minutes north, the distance (between the two cities) is one degree. Although Shanghai is northeast, it faces Suzhou and Lake Taihu directly to the west, so they lie at the same degree (of latitude). The curved route amounts to more than three hundred li, while the straight route amounts to only two hundred and fifty li. This is made clear in Figure 2.
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| Comment: | Section 4: • The definition of weight in Aristotelian and Archimedean senses •
Last sentence: attempt to bring together Aristotelian (go down) and Archimedian (balance) tradition (by the Jesuits), This is an old distinction in the Arabic between wazn and thiql.
Commentary:
Tartaglia mentioned: “the heavy body does the same thing in going toward its proper home, which is the center of the earth;”(Nova Scientia, p.75) However, he did not agree to the idea: “…the body when it arrived at the center of the world would immediately stop there.”(Nova Scientia, p.76) Tartaglia’s figure is quite different from WT’s.
Jordanus: “the motion of every weight is toward the center [of the world]” (The Medieval Science of Weights, p.129). |
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| Translation: | Section 4: What is weight? It means that every object falls vertically, and must desire to get to the center of the earth.
Let’s look at the above figure: the circle denotes the earth, a denotes the center of the earth. e, i and u all denote heavy objects. Every object desires to fall vertically and does not desire to stop until it reaches the center of the earth. The quality of weight is to move downwards, while the center of the Earth is its natural place. It seems like a magnet attracting iron. The quality of iron is to move towards the magnet. No matter if the magnet is above or under or left or right, iron surely moves towards it, it is because of its inherent quality. A heavy object has two (qualities): one is a natural tendency to move downwards; the other is that its body has weight.
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| Comment: | Section 5: • Explanation of specific weight •
First occurence of a term for specific gravity (benzhong) in the Chinese tradition although the concept was already present in the Nine Chapters of the Art of Calculation.
Look at western tradition of science of weights for example of gold and silver etc.
Look at Menelaos and Philon of Byzantine
Commentary:
Tartaglia mentioned: “a body is said to be specifically heavier that another when its material substance is more ponderous than the material substance of the other, as is lead than iron, and similarly other materials.” (Tartaglia, Quesiti, p.114)
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| Translation: | Section5: Ben zhong (inherent heaviness) of an object
Ben zhong, such as that gold is heavier than silver while silver is heavier than iron. When the volumes sof the gold and silver are the same, then gold is heavy and silver is light, because the nature of gold is originally heavier than that of silver, so (we) do not compare the weight of one liang of gold with that of ten liang of silver. Therefore it is called ben zhong.
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| Comment: | Section 6: • geometrical discussion of heavy body including the different dimensions and the geometrical center • Definition of shape as a boundary between inside and outside is Aristotelian.
Euclid translated into Chinese in 1607.
Archimedean relation of weight and shape (this plays a role in discussing specific weights, center of gravity etc.)
Check if this is a paraphrase of Archimedes!
Commentary:
Pure mathematical talk? |
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| Translation: | Section 6: A body with weight surely has the point, line, surface and shape of itself.
What has volume inside and boundary outside is called shape, in which the midpoint is the center of this shape. The straight line that passes the center and does not exceed the boundary at two sides is the diameter (radial line). There are two kinds of shape: one is plane shape, the other is solid shape. For example, among the above figures, besides points and lines, a is a plane circle, e is a rectangle, i is a triangle and o is a square: they are all plane shapes. Solid shape has three dimensions: length, width and thickness. As above, figures u, e and so on are also solid shapes.
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| Comment: | Section 7: ?? Definition of center of gravity ?? Center of gravity from Heron and Pappus (probably from Commandino's edition and commentary on Pappus). Stevinus' "The Elements of the Art of weighing" (from the 1580) has the same definition (First Book, definition 4, p.99 in Dijksterhuis edition).Z
Commentary
It is the same as definition IV of First Book of Stevin (p.99). However, explanation is quite simpler than Stevin’s. Additionally, two figures of rectangle are used by W &T. Stevin used one figure of circle.
It is the same as the definitinion repeated by Guido (Guido, Mechaniche, 259). |
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| Translation: | Section 7: The center of gravity. If a heavy object is hung at its center (of gravity), it doesn’t move.
Supposing there is a heavy object here, hung by a thread. If it is hung at its center, as a, it neither inclines nor moves. If it is not hung at the center, as e, it must incline and fall vertically.
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| Comment: | Section 9: •Transfer of concept of diameter from geometrical to mechanical meaning • This is not in Stevin! The section continues the parallelism between geometrical and mechanical notions. In some of the former sections, mechanical propositions were proven geometrically, while here a geometrical concept is transferred to mechanics. The application of abstract discussions of centers of gravity to the center of gravity of the Earth combining Aristotelian and Archimedean approaches. Also in "Biao Du Shuo". In the Arabic tradition a discussion about center of gravity including a deductive structure developed independently. |
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| Translation: | Section 9: A line that passes through the center of gravity, but does not exceed two boundaries, is the diameter of the weight.
Suppose the center of gravity of a triangle a is at the midpoint. The straight line from e to i passes the midpoint. So (the line) is the diameter of the weight. All heavy objects are like this. For instance, in the above cubic figure, three diameters all pass through the center of gravity, therefore the diameters of a weight are infinite (countless).
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| Comment: | Section 10: • The vertical diameter of the weight coincides with the plumbline ("line of the weight") • The plumbline (thongxian, line of the weight) is a new term in the Chinese tradition. Maybe from the practical tradition in which plumblines were uswed? In Celiang Fayi (a book on measurements and surveying translated from from Jesuit sources) the plumline is called "quanxian" ("line of the counterpoise/small weight?") Look at Clavius' Practical Geometry.
Look up: Guldin on centers of gravity.
In the Arabic tradition, geometry is not explained in mechanics books, but reference is made to the geometrical standard works.
Commentary:
It is somewhat similar to definition V in The Principal Works of Simon Stevin (p101), but its explanation is more complicated than Stevin’s. Its figure is also much different from Stevin’s althoght they are all spheres. |
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| Translation: | Section 10: There is a line of weight passing through the center of the earth, which intersects the horizon and makes two right angles. This line is the vertical diameter of the weight.
For example, in the above figure, the circle is the earth, in which there is the center of the earth and (on which) there is a horizon breadthways. There is a square heavy object whose line passes through the center of the earth and intersects the horizon, making two right angles. Therefore, the erect line is the vertical diameter of weight.
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| Comment: | Section 11: • Definition of the Radial plane of weight (zhong zhi jing mian) • Definition 6 in Stevin (op cit.). it is a surface rather than a plane (finite rather than infinite).
Commentary:
WT’s definition here is quite similar to definition VI of The Principal Works of Simon Stevin (p101), but W & T used two figures (cubic solid, shpere), while Stevin used one figure. Explanation of W & T is more complicated than Stevin’s.
WT’s explanation is somewhat similar to Commandino’s (Guido, Mechaniche, 259). |
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| Translation: | Section 11: There is a heavy object. It has diameters, no matter it is upright or oblique. Separate this object along a diameter and the profile is a diametral plane of weight.
For example, in the above round figure, a e is a diameter. Separate it along the diameter, namely, make two hemispheres. The planes of the hemispheres are diametral planes of weight. Withal, for another example, in the above cubic figure, i o u is the outer edge. Two half-cubes are obtained after this cube is separated along a diameter. The two inside separating planes are diametral planes of weight. If it is divided along the diameter c ch, the two profiles are the diametral planes of weight. Because the diametral plane always passes through the center of gravity, the two separated parts are equal.
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| Comment: | Section 12: • The center of gravity of a triangle is on the line running from the one angle to the subtense and bisecting the subtense • Notion of center of gravity seems not to figure in Clavius' edition of Euclid's elements. The theorem is in Stevin's second book on the Elements of the Art of Weighing, Theorem 2 Proposition 2. Stevin's second book deals with centers of gravity of plane figures and solids. It contains very similar theorems as the following ones of Qiqi Tushuo and further contains proofs of these theorems.
Sections up to now: mere definitions. From this section on: concrete examples. Stevin's first example in Book 2 of his Art of Weighing is the equilateral triangle, as it is the triangle in this section.
Commentary:
WT's theorem is either a summary of the Example I of Theorem I (Proposition I) of Stevin’s book (p.227) or Theorem II (Proposition II) of Stevin’s (p.229). In Theorem II, there are many sentences for proof. WT’s explanation is simpler than Stevin’s. The direction of a bisector in WT’s figure is different from that of a bisector in Theorem I of Stevin’s book. |
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| Translation: | Section 12: There is a triangle. Make a line from a corner to the midpoint of its diagonal, and the center of gravity must be on this line.
If (we) make a line from the angle a to its diagonal e i and separate it into two equal parts at o, the center of gravity must be at (the line) a o. The situation from e to u is the same.
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| Comment: | Section 14: • The center of gravity may be found by constructing the intersection point of two lines bisecting the side of a triangle and running through the opposite angle •
**Commentary:
WT’s problem and method are the same as Problem I (Proposition III) and Construction of Stevin’s book (p.233). The figure is the same as Stevin’s. |
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| Translation: | Section 14: To find the center of gravity of triangle.
The method says: there is a triangle, bisect each side. Draw a straight line from (the middle points) of the lines to their (opposite) angles. The center of gravity is the point where the lines intersect as a cross. For example, the above (side between) a and e is bisected and i is obtained, draw a straight line from i to o. Then, bisect (the side between) o and e and u is obtained: draw a straight line from u to a. Two straight lines intersect as a cross at the center, namely, what we wish to find is obtained.
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| Comment: | Section 15: • The intersection point divides these lines in the proportion 2 to one. • Question what is the rationale behind the order of sections 12 to 15:
suggestion 1: order emerges from conversation about centers of gravity which raises the question how such center is found geometrically.
suggestion 2 : argumenmt proceeds from how center of gravity was introduced (lying on the vertical bisecting a figure) to the geometrical point (since the only point lying on more than one line is their intersection point)
The argument proceeds from mechanics (section 12) to geometrical justification or elaboration (sections 14 and 15) via the claim that geometrical and mechanical center are identical (section 13).
**Commentary:
WT’s theorem is the same as Theorem III (Proposition IV) of Stevin’s book (p.233). WT’s figure is similar to Stevin’s. WT’s explanation is a summary of Stevin’s. |
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| Translation: | Section 15: There is a triangle. Every line which begins from a corner and passes through the center of gravity to its opposite side is divided into unequal parts which are in duple ratio.
For example, in the above figure. line a e passing through the center from an angle to its diagonal u i is divided into two parts. The line a c is twice as long as the line c e. The line i c is twice as long as the line c o.
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| Comment: | Section 17: • The center of gravity of any regular polygon is identical to its geometrical center. •
**Commentary:
It is an example on the basis of the last two sentences of Example III of Theorem I (Proposition I) of Stevin’s book (p.229). It is quite possible for WT to make a special theorem and to add an example to it.
There are a similar figure, proposition, which show and demonstrate the centre of a regular hexagon, in Propositio XXI of De Centro Gravitatis Solidorum, Liber Primus (p.46).
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| Translation: | Section 17: (For) a regular polygon, its center of gravity and center of figure are located at the same point.
For example, the above hexagon, its angles are equal, and its sides are also equal, so, it is named as regular polygon. Its center of gravity is always the same center as its center of figure.
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| Comment: | Section 18: • The center of gravity of a circle or ellipsis is identical to its geometrical center. • Explanation by analogy to polygon. See Commandino Theorem 2 Proposition 2. (Is it also in Archimedes?)
**Commentary:
It is an example on the basis of the last two sentences of Example III of Theorem I (Proposition I) of Stevin’s book (p.229). It is quite possible for WT to make a special theorem and to add an example to it.
There are the same proposition and two similar figures, which show and demonstrate the centre of a circle and the centre of an ellipse, in Propositio XXIII of De Centro Gravitatis Solidorum, Liber Primus (p.50).
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| Translation: | Section 18: “The center of gravity and the center of figure of circle and egg-shaped circle are also at the same point.
A circle’s boundary is similar to a polygon, therefore, its centers are all the same. An egg-shape is also similar to a circle, so its centers are the same, too.
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| Comment: | Section 21: •The center of gravity of a regular solid is identical to its geometrical center • Compare Stevin's second Book, Theorem 9 POroposition 14.
**Commentary:
It is identical with Theorem IX (Proposition XIV) of Stevin’s book (p.261). Their difference is: Stevin said “any solid”; WT said “regular mult-edge body” or “regular octagonal prism”.
We wonder whether there is any relationship between WT’s representation and some Jesuits’ translation of European books, such as Yuan Rong Jiao Yi and Ji He Yuan Ben. For instance, the term Leng zhu (Ping xing leng ti, leng zhui ti, zheng si mian ti, Ji He Yuan Ben, Tonghui, Vol.5, Appendix, 5-p.1420) You fa xing (regular shape, Yuan Rong Jiao Yi, SKQS,789-p.930), Ba leng zhu (octagonal prism). |
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| Translation: | Section 21:For every regular mult-edge body, its center of gravity and center of figure are at the same point.
Take the above regular octagonal prism as an example. Line a e i is its inner axis, e is both its center of gravity and center of figure.
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| Comment: | Section 22: • Finding the center of gravity of an arbitrary solid by hanging it in three directions • Compare Stevin's Third Book Proposition 1, Example 1
**Commentary:
WT’s proposition and figure are selected from Proposition I and figure of Stevin’s book (p.300-301). Stevin also said “by practice its centre plane of gravity, centre line of gravity”. The second figure is much simpler than Stevin’s.
WT’s explanation is identical with Stevin’s (p.301).
Actually, Stevin clearly explained the procedure to find the centre of gravity: firstly, to find a centre plane of gravity; secondly, to find a centre line of gravity; thirdly, to find the center of gravity. WT followed Stevin, but did not emphasize the steps of the procedure.
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| Translation: | Section 22: There is an object. How to find its center of gravity?
Take the above irregular plane (body) as an example. (We) desire to find the center of gravity. Firstly, make a horizontal line above (the plane), tie it to a. Secondly, make a line hang vertically from e closely at one side (of the plane body). Thirdly, also make a vertical line from i close to the (other) side. Then make a broken straight ink line from a down. The two lines, from e to o and from i to u, constitute a diametral plane. After that, turn the connected body (horizontally). Make two lines as the above-mentioned e o and i u again, (and) so obtain the second diametral plane. Look at the two lines upwards and downwards, obtain a diameter of weight at the intersection as a cross. Then turn the connected object sidewise, tie it from point c to a, find a diameter (from c) to ch. Look at them towards the intersection, too, so obtain k, which is the center of gravity.
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| Comment: | Section 23: • Objects that are not on its proper place move down to the center of the Earth along a vertical line • Characteristic of statements in De Caelo or the Sphere |
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| Translation: | Section 23: Every heavy object is not at its (natural) place, so it cannot but go down to the center of the earth, and make a straight vertical line.
Each object under Heaven has its own natural place. The quality of objects is that each of them is fond of getting its natural place. If any object is not at its (natural) place, it is certainly contrary to its quality, so it can be attacked by other objects. Therefore, to move towards its natural place respectively is what each object likes. For instance, fire originally flames upwards. As soon as it is put enter water, which is not its natural place, it goes out. The quality of weight is to go down, water and soil are its natural places. Moreover, the quality of objects is straightness and directness, a heavy object comes down vertically instead of acting deviously. Moreover, the quality of all things under Heaven is the most artful. The route of a straight line must be short. The route of a devious line is very long. The object is fond of the convenience of shortness and directness therefore, it does not like to move deviously disobeying its quality.
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| Comment: | Section 27:*the constant distance between two perpendicular lines*
**Commentary:
Its postulate is almost the same as Postulate V in the First Book of Simon Stevin (p111). However, W&T’s figures and explanations are similar to and simpler than Stevin’s. W&T used two figures, one of which is not found in Stevin’s book.
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| Translation: | Section 27: The distance between two vertical lines seems always constant.
Lengthen every straight line of gravity, it would certainly arrive at the center of the earth, therefore, the end of each vertical line certainly comes into conjunction with the center of the earth. This is clear in the figure of the above Section 3. These vertical lines are not parallel lines. But as the following sideward figure (shows), among such four long or short triangles, the ends of two straight lines converge the most when one line is closest to another line; the ends of two straight lines converge the least when one line is farther from another line. Straight lines are originally separated, (man) only feels they are parallel, (but) cannot see that their ends converge. Therefore, (he) thinks the distances are similar.
Only the reason for one heavy object is expounded hereinabove, now the reason (of weight) will be explained comparing one heavy object with another.
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| Comment: | Section 28:*A radial plane divides a heavy object fifty-fifty.*
**Commentary: definition of ‘jing mian’
Its definition is very close to Definition VI of the First Book of Stevin’s (p.101), but Stevin said only “dividing” instead of “equally dividing”. W&T’s definition is almost the same as the first sentence of the explanation of Stevin definition VI. W&T’s explanation is almost the same as Stevin’s.
#Quite identical with Latin verson of Stevin’s book. equal affectively heavy (in weight): equilibrium, postional gravity: zhundeng (See: section 17 of chapter 2). Translation is probably wrong.#
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| Translation: | Section 28: The diametral plane of every heavy object bisect (the object).
As for bisection, namely, (if an object) is divided through its diametral plane of the center of gravity, the weight of the two parts are naturally equal, so, it means bisection.
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| Comment: | Section 30:*The proportion between weight and volume of congeneric objects is constant*
**Commentary:
Benedetti mentioned: “for bodies of one and the same material, the ratio between their volumes [quantitates] is the same as the ratio between their heaviness (or lightnesses).” (Benedetti, Demonstraio, 156)
Tartaglia mentioned: “the ratio [of the volume] of one body to another (it being assumed that they are homogeneous and uniform) is the same as the ratio of their respective forces [weights]” (Tartaglia, Quesiti, 148), but he drew no figure.
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| Translation: | Section 30: Among congeneric weights, there is (the theory that) the ratio between weight and volume is equal.
For example, the above big cubic figure is eight times (the size) of the small cubic figure, it weighs 16 jin, (then) the volume of the small cubic figure is naturally eight times less than the volume of the big cubic figure, and its weight should be two jin.
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| Comment: | Section 31:*Two objects with the same weight and different volume are not congeneric.*
**Commentary:
WT’s meaning is similar to a supposition of Tractatus Balasii de Ponderibus, Part III (The Medieval Science of Weights, p.273).
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| Translation: | Section 31: There are two heavy objects. Their volumes are equal, (but) their weights are not equal. (Then) they are not congeneric in weight.
For example, there are two objects above. (Their) shapes are equal. However, one is (made of) gold, the other is (made of) silver. Their weights are naturally not equal. Why? The substance of gold is nearly twice as much as silver’s, so they are not congeneric in weight. Perhaps somebody asks: “Why does gold weigh almost twice than silver?” Say: the substance of gold is the most dense and thick. Let’s try to observe the goldbeater: one liang of gold can be made into tens of thousands of gold foils, while silver fails to equal (gold). This is the reason.
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| Comment: | Section 32:* There are two kinds of heavy things, namely dry and waterish.*
#Four elements or four possibilities in Aristotle. dry or wet: it seems that there some things like this in Galileo’s discourse on bodies in water. See: Stevin’s book, p.393.# |
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| Translation: | Section 32: There are two kinds of weight: one is dry and the other is wet.
The dry, such as metal, stone, soil and wood, is what can’t flow. The wet, such as water, oil, alcohol, thick liquid or mercury, is what can flow.
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| Comment: | Section 34:* movement of a heavy object and its relation with perpendicular line*
**Commentary:
WT’s proposition, explanation and figure are very close to Proposition I of Guido (Guido, Mechaniche, p.260).
#similar picture propositon 6 of first section in Guido Ubaldio’s book---- bei Matteo, archiv, inner library of MPIWG#
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| Translation: | Section 34: There is a weight，which is inserted at a straight line, or in a high place, or in a low place. Only the weight at a vertical line does not move. Otherwise, it cannot but move and turn downwards.
For example, in above figure, a is one motionless end of a straight line. If the weight is at e, which is just located at the top of a vertical line and at the center, (it) does not move. If the heavy object is at i, which is just located at the foot of the vertical line and at the center, it does not move. (If it is) at o or at u, it cannot but move and turn downwards, making an arc.
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| Comment: | Section 36:*horizontal plane on the Earth*
**Commentary:
WT’s theorem is almost the same as Postulate VI in Stevin’s book (p.397). At least a part of WT’s explanation is close to Explanation of Postulate VI in Stevin’s book.
#general geographical knowledge, in Stevin’s book#
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| Translation: | Section 36: Surface of water is flat.
Water floats along with the earth. The earth is a large circle. Water adheres to the earth, so water’s surface is circular too.
It has already been said in Section 2 above, but why is it now said again that the surface of water is flat? As for a large circle, its circular shape can’t be seen, only its length can be seen, so only its flat surface can be seen.
For example, there is a concave place on the horizon. Water comes from all sides and certainly fills the concavity. After water is level with the surface of the earth, it will overflow. Therefore, water adapts itself to the earth and becomes round, it becomes flat adapting to the earth too.
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| Comment: | Section 39:* How to calculate water’s volume according to its weight*
**W&T’s question is the same as Problem VIII (Propostion XXI, figure) of Stevin (p.479). W&T added another cubic figure of water, and replaced 5 lbs with 13 jin, replaced 65 lbs with 65 jin, emphasized so-called “rule of three”. W&T deleted Stevin’s proof.
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| Translation: | Section 39: The weight of water is known, to find its largeness (volume).
For example, there is 13 jin of water in a pot. Man does not know how many dou or sheng or he is its largeness.
The method says: one cubic chi can contain 65 jin of water, now the rule of three is used.
the first, 65 jin , water contained in a one cubic chi pot
the second, 10 cun, equals to one cubic chi in volume
the third, 13 jin, water in the pot
the fourth, 2 cun, the largeness of the original pot
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| Comment: | Section 40:*specific gravity of an object and its position in water: rest in water*
**Commentary:
W&T’s theorem is close to Theorem IV of Stevin’s Book (p.405) except W&T emphasized the surface of the body is level with the surface of water instead of “in any place”. In Stevin’s figure, the body is in the middle of water, while the body is level to the surface of water in W&T’s book. Stevin gave his proof.
Stevin: vessel; W&T: reservoir.
#Aristotle did not use specific gravity, must be in specific part of Stevin’s book. Galileo’s idea corresponds to Stevin’s) (a little dfferent from Stevin’s explanation, probably from Galileo’s book, Yan Dunjie’s paper#
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| Translation: | Section 40: There is a definite object. (If) its inherent heaviness is equal to (the inherent heaviness) of water, it will neither float nor sink in water, its top is level with the surface of water.
As the above figure (shows), e is the volume of a reservoir, a is the weight of a definite object. Since the inherent heaviness of the definite object is equal to the inherent heaviness of water, the top of the object is certainly horizontal and is level with the water surface.
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| Comment: | Section 41:*specific gravity of an object and its position in water: float*
**Commentary:
W&T’s theorem is the same as Theorem II (Propostion II, figure) of Stevin’s book (pp.401-403), but their explanation is much simpler that Stevin’s, and deleted proof. W&T drew cube.
#in Stevin’s book: Problem is order!#
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| Translation: | Section 41: There is a definite object. If its inherent heaviness is lighter than (the inherent heaviness) water, (if) it is in water, it will not totally sink; one part of it will be above the water surface, another part will be under the water surface.
As the above figure (shows), e is the volume of a reservoir, a is the weight of a definite object. Since the definite object is lighter than water, part of it sinks and part of it floats. Because water is heavier, it forces the definite object to rise a little.
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| Comment: | Section 42:*specific gravity of an object and its position in water: sink*
**Commentary:
W&T’s theorem is almost the same as Theorem III of Stevin’s book (pp.403-405). W&T’s explanation is quite different from Stevin’s.
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| Translation: | Section 42: There is a definite object. If its inherent heaviness is heavier than water, it will not stop until it sinks to the bottom in water.
For example, it is naturally clear in the above figure. There is a thin and wide dry board, which is made of either gold or lead. So long as it is put slowly and flatly on the surface of water, it also will not sink. Why? (It is) thin and wide, so the qi (gas) on the board unites with the body of board, and qi and the surface of water approach each other, therefore, though both of gold and lead are essentially heavy, they do not sink. But if there is any small crack where water goes up, then (the board) will certainly sink.
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| Comment: | Section 45:*proportion of weight between two congeneric objects in different kinds of water* See Stevin Preamble to the practice of hydrostatics book 1, Proposition 1 p. 487 in Dijksterhuis edition <br>
look at latin translation or Dutch original for clarifying the terminology translated as "specific gravity" in the English translation of Stevin
**Commentary:
WT’s theorem is the same as Theorem VI of Stevin’s book (p.409).
What WT’s explanation means is identical with Stevin’s explanation, but simpler than the latter. WT used sea water and river water instead of water AB and water CD.
Additionally, WT said “two congeneric objects”; Stevin said “a solid body”.
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| Translation: | Section 45: There are two kinds of water, one is heavy and the other is light. There are two objects that are congeneric and equal. The ratio of the heavy water to the light water is the inverse ratio of the volume submerged in them respectively.
Suppse one is seawater and the other is river water, the seawater is naturally heavier than the river water. By only seeing that the above two objects are entirely equal, but a submerges more and e submerges less, the ratio of the weight of (the two kinds of water) will be known. If the submerged part of a is twice as much as the submerged part of e, then seawater must be twice as heavy than river water.
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| Comment: | Section 46:*less weight of solid in water than in air*
See Stevin Elements of Hydrostatics Theorem 7 proposition 8 (numerical example in Stevin Problem 2 proposition 9, different from example in Qiqi Tushuo)
**Commentary:
WT’s theorem is the same as Theorem VII of Stevin’s book (p.409). WT’s calculation is the same as Stevin’s explanation. But WT used a few number to show how to calculate. WT added another water figure so that they make explanation clear. WT assumed the solid body is copper.
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| Translation: | Section 46: A solid in water is lighter than in emptiness (air). The amount of water (of the volume equal to) that is occupied (by the solid) is the amount of its reduced weight.
For example, the above copper cube in the air weighs 16 liang. If comparing it with a cube of water of the same size, water should (weigh) two liang. So a submerged cubic copper object is lighter than the object in the air, 16 minus two, for 14 liang in weight.
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| Comment: | Section 48:*How to calculate weight of liquid according to weight of solid while the liquid and the solid are equiponderant*
Look at Stevin Elements of hydrostatics, Theorem 7, problem 2 proposition 9 example 2.
**Commentary:
Stevin’s Problem II (Proposition IX) and its Example (p.411) are only the first step of WT’s. Stevin desired to find the apparent weight of a solid body in water. WT’s figure is very similar to Stevin’s (p.412). WT’s numerical values are different from Stevin’s.
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| Translation: | Section 48: There are two objects, which are equal in size. However, one is solid and the other is liquid. Find the weight of the liquid if the weight of the solid is known.
For example, there is a lead ball that weighs 23 jin; a water ball is the same (size) as the lead ball. How much does (the water ball) weigh?
The method says: hang the lead ball with a horsetail thread at one end of a balance, and sink it into water. Add weights at the other end of the balance, and do not stop adding until equilibrium (is achieved), then, the lead ball weighs only twenty-one jin. From twenty-three jin, the weight (of lead ball) in the air minus twenty-one, the weight (of the lead ball) in water, two jin is remained, viz. the weight of the water ball. See its proof in the above Section 46.
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| Comment: | Section 56:*An axis of the lighter globe in water must be a vertical line*
Look at Archimedes on floating bodies proposition 8 (look at commandino's translation, where a proof is given) See also Galileo dicourse on bodies in water Theorem 11, but only for material heavier than water.
# (quite close to Archimedes proposition 8, from Commendino’s commentary, figure is similar to Galileo’s) (Stevin said in Dutch: specific lightness本轻?, or specific heaviness/gravity本重)# |
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| Translation: | Section 56: if a segment of a ball is inherently light and floats on water, its bottom will be up. The axis of the ball must be in a vertical line.
For example, there is a wooden ball as above. If its flat bottom is in water, it will be up and is certainly not deflective; its axis a i must be in a vertical line, as a i is in e o. It must naturally return to the right position if it is forced to deflect.
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| Comment: | Section 57:*pressure of water on the upper surface of an object in water*
**Commentary:
WT’s meaning in this section is the same as Theorem VIII (Proposition X) in Stevin’s book (p.415). However, representation and figure that WT used are obviously different from Stevin’s.
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| Translation: | Section 57: When force of water presses an object, the weight is only the water column. Other water around does not press weight (on the object).
Finding the place where water presses on the object, (it) is only the bottom plane of the pressed object. Make the vertical lines around (the bottom plane) on water, (it forms an object) as a column in water. The column is the weight pressed on the object. Just as the above figure of the column in water. The bottom side underneath is very small. (Make) vertical lines from the bottom to the top. The (weight of) water inside the column is pressing weight. Other water around is not concerned with it.
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| Comment: | Section 58:*pressure of water on the side surface of an object in water*
**Commentary:
WT’s meaning in this section is the same as Example I of Theorem IX (Proposition XI) in Stevin’s book (pp.421-423). However, representation and figure that WT used are obviously different from Stevin’s and simpler than Stevin’s. Stevin did not mention such terms as impact and rushing tendency. WT took a water gate as a practical example to explain their theorem.
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| Translation: | Section 58: Water comes and impacts a gate horizontally. Find the weight of the rushing tendency.
According to the above method of making a water column, make a vertical line ae only according to the height of the impacted gate’s surface. Move the vertical line equally to i. Then, going arrisways from a, the upper end of the vertical line, to i, that is the weight of the half-column of rushing water. All the other water around is not concerned with it.
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| Comment: | Section 59:*How to calculate weight of one object according to weight of another object, proportion between their volume and proportion between their specific gravity*
**Commentary:
WT’s problem is the same as Problem IX (Proposition XXII) of Stevin’s book (pp.479-481). Stevin gave a corollary after the explanation.
WT’s calculation and numbers are the same as Stevin’s explanation. In WT’s book, one body and another body were replaced by gold and silver.
Comparing WT’s group of figures with Stevin’s group of figures, we find that WT added some concrete numbers of the volume and the weight to the figures, and used the broken line instead of a part of Stevin’s real lines.
Representation like “fa yue” (method says) can be found in a traditional Chinese book, namely Suan Fa Tong Zong. Jiu Zhang Suan Shu says “shu yue” (procedure says).
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| Translation: | Section 59: Ratio of the volumes of two objects and ratio of their inherent heaviness are known. Find that weight if this weight is known.
For example, two volumes, a and e, their ratio is a being three times e. The inherent heaviness: a is silver, e is gold, the ratio of them is one to two. Find how much e weighs if a weighs six jin is already known.
The method says: as one third of silver is equal to e. Three parts of silver totally weigh six jin, so one third weighs two jin. Using the proportional method: the ratio of one to two is the ratio of two jin to four jin, so e is found to weigh four jin.
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| Comment: | Section 60:*a calculating example “rule of three”*
**Commentary:
WT’s problem seems to be a variation of Problem IX (Proposition XXII) of Stevin’s book (pp.479-481). The weight is to be found in section 59, while the volume is to be found in section 60. Here, WT did not mention gold or silver.
It is possible for WT to make a variation on the basis of Problem IX (Proposition XXII) of Stevin’s book (pp.479-481). |
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| Translation: | Section 60:
the first, three, the big number of the ratio
the second, one, the small number of the ratio
the third, twenty-four, number of the volume of a
the fourth, eight, number of the sought volume e
There are two objects. The ratio of their inherent heaviness are known, and their weights are known (also). Find the volume of that (object) if the volume of this (one) is known.
For example, a weighs 6 jin and its volume is twenty-four (cubic) chi, e weighs four jin. The ratio of their inherent heaviness is one to two. Now it is desired to find the volume of e.
The method says: the ratio of the volume of a to e should first be sought, then the volume of e can be found. Multiply the ratio of six jin to four jin with the ratio of the inherent heaviness of a to e, This ratio is one to two. Use the method of cross multiplication as X-shaped frame instead of direct multiplication to multiply (one ratio by the other ratio). Six multiplied by two makes twelve, and four multiplied by one makes four. Therefore, the new achieved one is the ratio of twelve to four, then, reduced to the ratio of three to one. So a is treble e. Now rule of three is used.
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| Comment: | Section 61:*How to calculate the proportion of specific gravity and volume between two objects and their weight*
**Commentary:
WT’s problem seems to be another variation of Problem IX (Proposition XXII) of Stevin’s book (pp.479-481). WT did not mention gold or silver too.
It is possible for WT to make a variation on the basis of Problem IX (Proposition XXII) of Stevin’s book (pp.479-481).
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| Translation: | Section 61: There are two objects. Their weights are known, and the ratio of their volumes is known (also). Now find the ratio of their inherent heaviness.
For example, (the ratio of) the two weights a to e is six to four, (and) the ratio of their volumes is three to one. Find the ratio of silver to gold.
The method says: use cross multiplication to multiply the two known ratios, so the ratio of two numbers is the ratio of the inherent heaviness. Six multiplied by one is six, and four multiplied by three is twelve. Therefore, the ratio of six to twelve is obtained; reduce it, is one to a half. So compare the weight of silver object with the gold object, the difference is naturally a half.
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| Comment: | Chapter 2, Section 1:*the name of machine, the force-moving-weight machine* |
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| Translation: | Section 1: Craftsmen originally have many utensils. If one desires to explain (the reason) of these utensils for moving weight, such things as nails and ropes are of use. However, the original use of them is to assist in the convenience of moving weight: they are not helpful in the function of utensils. Therefore, the reason for nails, rope and other things would not be explained.
All the tools used in the art of force are collectively called forcibly-moving-weight machines. The implements used in the learning of the art of force are all devised for moving weight. Weight is originally underneath, but it is forced to move upwards. Therefore, they (the implements used) are commonly named forcibly-moving-weight machines. |
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| Comment: | Chapter 2, section 2:*three usages of the machine*
**Commentary:
This section is probably an extract of Galileo’s narrative (On Mechanics, pp.272-274). Galileo did not emphasize windpower.
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| Translation: | Section 2: Machines have three uses: first, to move great weight with small force; second, in all conditions in which people have difficulty in using their own strength using machines is convenient; third, (using) weight of an object, waterpower and wind power to subustitute for manpower.
For example, there is a heavy object, it can be moved by one hundred persons. Nevertheless, the machine needs only one person to move it, so this is to move a great weight with small force. Additionally, suppose a seagoing vessel has a small crack at its inner bottom, water seeps into it (the vessel) day by day. If man does not take out (the water), the vessel would certainly sink. So, a windpipe must be used and reaches downwards to take it out. Then water is taken out through the pipe. (The pipe) takes out what the bucket and scoop cannot do, (and) these machines can be used really conveniently. As for using the power of weight of objects, waterpower and wind power to substitute manpower, it is clearly recorded in every machine. It is unnecessary to go into details.
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| Comment: | Chapter 2, Section 3:*different materials of the machine* |
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| Translation: | Section 3: The substances of machines are multifarious. Wood, copper and iron are in the majority.
The wood be used must be hard, such as elm, Chinese scholartree, mulberry, sanders and hippocastanum. In short, it is good (to use wood), including fibre and transverse force, that resists change. While painting wood, it is suitable to use walnut oil or sesame oil, rapeseed oil, or cotton oil, which is better, (but) tallow oil cannot be used. Tallow oil is hot-natured, so it is easy to burn wood and to make sound because of friction. Iron should be smelted adequately, and for copper, the red one is the best, as the yellow (brass) is brittle-natured
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| Comment: | Chapter 2, Section 8:*machines are divided into six kinds* |
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| Translation: | Section 8: There are six general categories of machine: the first, balance; the second, steelyard; the third, lever; the fourth, pulley; the fifth, round wheel; the sixth, helix.
The balance, steelyard and lever all belong to the straight line category; pulley and wheel all belong to the category of round roller; the helix is similar to a snake coil, and belongs to the category of screw and water-screw. All of the above five categories pertain to the appearance of machines for weighing. If (man) uses his hand at one end and exerts his force, for example, in the figure, the hand acting on the small sliding weight of a steelyard, all the five kinds also have the appearance of machines for moving. The helix can also weigh things, but it has more uses if it is used to move something by turning, so no sliding weight is arranged (on it).
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| Comment: | Chapter 2, Explanations of balance, Section 9:*three parts of a balance*
**Commentary:
WT’s figure is close to figures of Proposition III & IV in Stevin’s book (p.310, 314), but is simpler than them. The last sentence’s meaning of WT’s explanation can be found out in Stevin’s book (p.309). However, Stevin wrote many sentences to dicribe how to construct a most perfect balance (the title of Propostion II) in detail.
If it is possible that WT wrote Section 9 and Section 10 on the basis of Stevin’s propositions, why they used such terms as pointer and chui zhun (vertical datum line) which are different from Stevin’s terms, for instance, tongue, hook, fork?
Guido gave the definition of “the center of the balance” (Guido, Mechaniche, p.260).
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| Translation: | Section 9: A balance consists of three parts: a crossbeam, a pointer and a vertical datum line.
The crossbeam is divided into two parts: the left and the right. Its middle is called the center. The center is what is linked to the crossbeam and doesn’t move. The extremities of left and right are called ends. The pointer is: if two ends are level, the pointer is always a vertical line. The vertical datum line is the line of weight-hanging. Being level means being equal. If one end is a little lighter or heavier than the other, the pointer must incline towards the left or to the right, (this means) not equal.
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| Comment: | Chapter 2, Section 11:*three positions of the pointer of a balance*
**Commentary:
Benedetti discussed the problems in WT’s sections 11, 12, 13, and 14, which had been discussed by Aristotle’s Questions of Mechanics 2 and 3 (Benedetti, Speculationum, p.182).
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| Translation: | Section 11: The center of the balance’s pointer has three positions: above the beam, or under the beam, or inside the beam, as in the following three figures.
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| Comment: | Chapter 2, Section 13:* the turning of the beam of a balance when its pointer is under the beam*
**Commentary:
WT’s proposition and its figure are very similar to Proposition III of Guido’s book (Guido, Mechaniche, p.261)
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| Translation: | Section 13: (Concerning) the beam of a balance, (if) its center is under (itself) and equal weights are appended to its ends. While the beam is parallel with the horizon, it does not move. If one end rises aslant, the descending end must turn up and over once and then stop.
As per the above first figure, the beam with the characterst tian ping (horizon) is parallel with the horizon, so it is always stays horizontal and does not move. If the beam is inclined upward as in the second figure, it must turn over once, and its pointer’s center must be above it. The reason why it must turn over is that the center of gravity is underneath.
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| Comment: | Chapter 2, Section 15:*the beam of a balance in horizontal position and upright weight-hanging line*
**Commentary:
WT’s figure is close to the first figure of a group figures in Stevin’s book (p.104). WT’s definition of ‘zheng li zhong’ probably corresponds with ‘vertical lowering/lifting weight’ in Stevin’s Definition XIV and its Explanation (pp.103-107).
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| Translation: | Section 15：The balance suspends the weight upright.
The vertical thread at the right end of a balance is linked to the middle diameter of a heavy board as e, the board is supported underneath by a (pyramidal) supporting angle as i. The board does not move at the top of i. Because a weight is added to the left end of the balance, the board and the vertical thread rise automatically till (the board) becomes level and parallel with the horizon. This is called the balance suspending the weight upright. The so-called “upright” is named because of the vertical thread.
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| Comment: | Chapter 2, Section 17:*definition of “zhundeng” (equal in the state of balance)*
**Commentary:
WT’s definition can be regarded as an extract of Definition VIII and its Explanation as well as Definition XI and its Explanation (pp.103-105). In examples, WT’s numerial value is different from Stevin’s (p.105). WT’s figure is quite similar to Stevin’s (p.102). Definition XI explained what is “to be equal apparent weight”.
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| Translation: | Section 17: There are two different weights; (they) are hung at the left and right (side) of the crossbeam of a steelyard. If the crossbeam is level with the horizon, the two weights are called “being effectively equal in weight.”
For example, a weight of one jin is hung at the right ; e weighs four jin and is hung at the left . The crossbeam is level. Two weights are called being effectively equal in weight. Because it is different from “be equal to.”
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| Comment: | Chapter 2, Section 18:*different postures of heavy objects at the beam in balance*
**Commentary:
This section is very similar to Tartaglia’s explanation, but Tartaglia gave a proof (Tartaglia, Quesiti, pp.134-135). WT’s figure is almost the same as Tartaglia’s (p.135).
WT’s narrative and figure are also similar to Jordanus’ (The Medieval Science of Weights, p.140-141). Jordanus said “… the suspended weights will be of equal positional gravity.” (p.141)
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| Translation: | Section 18: There are two equal and similar weights. One is hung underneath one end of the crossbeam, the other is horizontally attached to the beam. (Concerning) the weight attached to the beam, its center of gravity must be at one extremity of the crossbeam, and the crossbeam is level.
For example, weight a is hung underneath one end of a crossbeam, its heaviness is equal to that of the weight o, its shape is similar to that of the weight o. Nevertheless, the weight o is horizontally attached to the crossbeam, its center of gravity is i. The portion i e is equal to the portion e u, so the beam of the steelyard is naturally level. The reason for this is that the center of gravity of a is upright under u, the center of gravity of o is horizontal under i, so (they are) effectively equal to each other.
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| Comment: | Chapter 2, Section 19:*the law of lever*
**Commentary:
It is possible that WT added the first sentence to this section in order to empahasize its importance. The second sentence, WT’s theorem is the same as Theorem I and (Proposition I) in Stevin’s book (p.117). Numerical values in WT’s explanation are different from Stevin’s. Stevin made a long mathematical proof. Among the figures in Stevin’s book, two figures at least are close to WT’s figure.
Jordanus: “If the arms of a balance are proportional to the weights suspended, in such manner that the heavier weight is suspended from the shorter arm, the weights will have equal positional gravity.” (The Medieval Science of Weights, p.183).
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| Translation: | Section 19: This section is the foundation of “science of weight,” on which various methods are based.
There are two hanging weights that are effectively equal in weight. The ratio of the great weight to the little weight is the same as the ratio of the long part to the short part of steelyard’s beam, (the four numbers) are also in propotion.
For example, great weight e weighs 8 jin, (it) is effectively equal to small weight a, which weighs 2 jin, their ratio is fourfold. So, the long portion of the beam, from lifting cord to point u, consists of 4 sections, (and) the short portion, from lifting cord to point i, is only one section, the ratio is also fourfold. Therefore, the two ratios are equal, and these two ratios are also in proportion.
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| Comment: | Chapter 2, Section 20:*weight of a heavy object is proportional to its falling speech at the beam of lever*
**Commentary:
In the opinion of Aristotle, those balances which have longer arms are more exact than others because of the greater speed of the extremities of those longer balances. (Benedtti, Speculationum, 180)
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| Translation: | Section 20: The weight is at the end of the long part of the lifting cord (actually the beam), the farther (from the lifting cord) it is, the heaver it weighs, the faster it falls.
For example, the above a weighs two jin, its weight is eight jin. If the beam increases by two jin, then o should weigh 14 jin.
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| Comment: | Chapter 2, Section 21:* concept of “equal in effective weight” & calculation of proportion between weights or between distances *
**Commentary:
WT’s proposition and its figure are close to Proposition V and VI of Guido (Guido, Mechaniche, p.296).
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| Translation: | Section 21: There are two equal weights, which are hung on the (beam of) a steelyard. They are effectively equal to the sliding weight (respectively). The ratio of their heaviness is equal to the ratio of the distances (between the weights and the lifting cord).
For example, kp is the beam of a steelyard, its length is 12 sections. The lifting cord i is at the third section. Weight e is hung under ch, it weighs six jin. It is effectively equal to a, which is under k. Weight c weighs 6 jin, it is under e, and effectively equal to o. The ratio of weight a to o is equal to the ratio of ip to ich on the beam of the steelyard. If ip is nine sections, ich is two sections, it is named 4.5-fold ratio. o, which is 18 jin and a four jin, also have the 4.5-fold ratio.
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| Comment: | Chapter 2, Section 22:*calculation of weights or distances when one weight is equal to another in effective weight*
**Commentary:
WT’s proposition and its figure are close to Proposition V of Guido (Guido, Mechaniche, p.296).
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| Translation: | Section 22: There are two unequal weights, which are hung on (the beam of) a steelyard and are effectively equal to the sliding weight. The ratio of their weights is equal to the ratio of the distances (between the weights to the lifting cord).
For example, the beam of the steelyard is 16 sections. The small weight i is 3 jin, (and it is) hung under o. The distance between i and the fulcrum is 12 sections. The great weight a is 18 jin, (and it is) hung under e. The distance between e and the fulcrum is two sections. The small weight i is effectively equal to ch, which is six jin. The great weight a is effectively equal to k, which is 9 jin. The ratio of the weight a and weight i is six; the ratio of ou, which is 12 sections, to eu, which is two sections, is also six.
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| Comment: | Chapter 2, Section 23:*calculation of distances or weight (including weight of the beam)*
**Commentary:
WT’s problem is the same as Example II of Problem I (Proposition II) in Stevin’s book (p.125), but Stevin did mention the rule of ratio, and Stevin used two numerical values. WT divided the beam into 10 equal parts, while Stevin divided ‘prism’ into six equal parts (above figure on p.126).
#Why did WT use ‘san lu fa’ (rule of three) and componendo, which are in Tong Wen Suan Zhi (tale of content)? Stevin did not mention componendo although he mentioned ratio.#
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| Translation: | Section 23: There is the beam of a steelyard, which is a heavy body (itself), and there is another weight which is hung under one end (of the beam). The lifting cord is not fixed and can be (moved) closer or farther. When the beam is effectively equal in weight to the weight, the ratio (of the beam to the weight) is equal to the proportion of the following 1, 2, 3 and 4.
1 the weight is 60 jin 60
2 the whole beam is assumed to weigh 40 jin 40
3 the difference between (the length of) the longer part on the left, which is eight sections, and the shorter part on the right, which is two sections, is six sections 6
4 the shorter part on the right, which consists of two sections; double of it consists of four sections 4
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| Comment: | Chapter 2, Section 26:*how to request the position of the fulcrum (when there are two heavy objects)*
**Commentary:
WT’s problem is the same as Problem I (Proposition II) in Stevin’s book (p.125). Its figure and conclusion are close to Stevin’s. But calculation process and numerical value are different. WT used componendo, viz. so-called ‘he shu cha fen fa’ in Tong Wen Suan Zhi by Matteo Ricci and Li Zhizao. Stevin’s explanation is identical with Section 19. Stevin did not mention how to find the position of the lifting cord in detail.
WT’s problem is also identical with Proposition VII of Guido (Guido, Mechaniche, p.297), but Guido gave a more general proposition. Guido’s proposition actually corresponds with sections 27, 28, 29 and 30 because he said “given an indefinite number of weights on balance,…”. WT’s figure is somewhat simpler than Guido’s.
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| Translation: | Section 26: There are two weights which are hung on the two ends of the beam of a steelyard. (Suppose the two weights) are effectively equal, find the position of the lifting cord at which the two weights are effectively equal.
a weighs six jin, (it is) on one end, o., one end. e weighs two jin, and (it is) on one end, u. The whole beam consists of four sections. (We) desire to know at which section the lifting cord should be located? The method says: a plus e is eight. Take the method of proportional computation.
1 8, is the sum of two weights
2 2, is the weight of e
3 4, is the number of (sections of) the whole beam
4 1, is the numberof (sections of) part oi. The lifting cord should be located at point i.
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| Comment: | Chapter 2, Section 27:* how to request the position of the fulcrum (when there is one heavy object, taking the beam’s weight into account)*
**Commentary:
The problem and supposition are quite similar to those in Section 23, but calculation here is different from that in Section 23. Here, WT used componendo again. WT used broken lines to draw a suppositional equivalent of the beam like a ball.
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| Translation: | Section 27: There is a steelyard, which is a heavy body (itself). Give its weight and the numberof sections into which its (beam is divided). There is also a weight that is hung under one end. (If the steelyard is) effectively equal (to the weight), find the position of the lifting cord.
The weight of the steelyard is 12 jin. The whole beam is divided into six sections. The hung weight a weighs 24 jin. It is desired to be known at which section the lifting cord should be located? The method says: divide the beam of the steelyard into two equal parts. From e to u (is one part), and u is the center of gravity of the steelyard. Now, assuming the weight of u is 12 jin, add (it) to(the weight of) a, 24 jin, is 36 jin. Take the method of proportional computation.
1 36 jin, is the sum of two weights
2 12 jin, is the weight of the beam of the steelyard
3 3 sections, is the number of sections contained in iu
4 1 section, is the number of sections contained in io. The lifting cord should be located at point o.
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| Comment: | Chapter 2, Section 28:* how to request the position of the fulcrum (when there is one heavy object, taking the beam’s weight into account)*
**Commentary:
The problem and supposition are quite similar to Example III of Problem I (Proposition II) in Stevin’s book (p.127), but calculation here is different from Stevin’s. WT used componendo again. WT used broken lines to draw a suppositional equivalent of the beam like a ball. |
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| Translation: | Section 28: There is a steelyard, which is a heavy body (itself). Give the weight and the numberof the sections into which its (beam is divided). There is also a weight being hung at (a point), which is slightly closer to one end (of the beam). (, find the position of the lifting cord at which the (steelyard) is effectively equal (to the weight).
The weight of the steelyard beam is 24 jin and the beam is consists of 18 sections. The hung weight a weighs 12 jin, it is hung under section i. It is desired to be known at which section the lifting cord should be located? The method says: It is obtained that the center of gravity of the beam is directly at point u. Assuming there is a weight of 24 jin hung under point u. Between the two weights, from i to u, there are six sections. The sum of the two weights is 36 jin. Take the method of proportional computation.
1 36 jin, the total amount
2 12 jin, the hung weight
3 6 sections, the part of the beam between the two weights
4 2 sections, from i to c. The lifting cord should be located at section c.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=27 |
| Comment: | Chapter 2, Section 29:*how to request the position of the fulcrum (when there are two heavy objects, taking the beam’s weight into account)*
**Commentary:
WT’s problem is the same as Example IV of Problem I (Proposition II) in Stevin’s book (p.127). Stevin’s figure is on p.128. However, WT’s componendo is different from any of Stevin’s calculations.
Stevin indicated this example’s relationship with Example III of Problem I (Proposition II), viz. Section 28 of WT. Likewise, there is relationship between Section 28 and Section 29.
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| Translation: | Section 29: Give the weight of a steelyard and (the numberof) sections (into which its beam is divided). However, two weights are hung in the inner side of beams, not at the two ends. (If the weights are) effectively equal, find the position of the lifting cord.
The weight of the steelyard is 12 jin and the whole of (its beam) consists of 18 sections. The heavier weight a weighs 18 jin, (and) the lighter weight e weighs 6 jin. It is desired to be known at which section the lifting cord should be located. The method says: According to the method in section 28, take the method of proportional computation.
1 18, the number of the sections contained in the whole (beam)
2 6 is the weight of e
6 is the numberof sections from i to t
2 is the numberof sections from i to u
Take the method of proportional computation again.
1 36 is the sum of the two weights
2 18 is the weight being hung under u
3 10 sections is the numberof sections (contained) from o to u
4, 5 sections is the number of sections (contained) from o to c
Therefore, c should be the lifting cord. Then all the two weights are effectively equal to the weight of the body of the steelyard.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol2+28+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=28 |
| Comment: | Chapter 2, Section 30:* how to request the weight of one object according to weight of another object*
**Commentary:
WT’s problem, figure and explanation is the same as Problem II (Proposition III), figure and Example I in Stevin’s book (pp.131-133) except numerical values.
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| Translation: | Section 30: There are two weights, which are effectively equal. Give the decided position of the lifting cord, and the heaviness of this weight is already obtained. Find the heaviness of that weight.
a weighs 8 jin, the beam of the steelyard is divided into six sections. The lifting cord is at the second section, point i. Find the weight of e. The method says: Take the method of proportional computation as the one in section 19.
1 4 sections, (the numbert of sections contained in) the longer part of the beam
2 2 sections, (the numberof sections contained in) the shorter part
3 8 jin, the weight of a, should be 8 jin
4 4 jin, the weight of e, should be 4 jin |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=29 |
| Comment: | Chapter 2, Section 31:* how to request the position of the fulcrum according to weight of one object, taking the beam’s weight into account*
**Commentary:
Problem and calculation are quite similar to those in Section 27. The weight of the beam is replaced by the hung weight. Numerical values are different.
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| Translation: | Section 31: There is one hung weight, give the weight of the beam of steelyard. (If the weight is) effectively equal (with the beam), find the position of the lifting cord.
For example, the weight of the beam of the steelyard is 40 jin, (and the beam) consists of 10 sections. The hung weight weighs 60 jin. Find at which section the lifting cord should be located. The method says: the center of gravity of the beam is at o, and from o to e contains 5 sections. Take method of proportional computation.
1 100 jin is the total amount of the weight of the beam and the hung weight
2 60 jin is the heaviness of the hung weight
3 5 sections is the (the numbert) of sections (contained) in oe
4 3 sections the (number) of sections from o to u, which is the section where the lifting cord is located.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=30 |
| Comment: | Chapter 2, Section 32:*how to request one distance according to another distance*
**Commentary:
WT’s problem and calculation are the same as Problem III (Proposition IV) in Stevin’s book (p.133-135). WT’s figure is similar to Stevin’s (p.134). Length’s numerical values are equal, but weight’s numerical values are different.
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| Translation: | Section 32: There are two weights which are effectively equal. Given the length of this side of the beam, find the length of that side of the beam.
Suppose a weighs 9 jin, (and) e weighs 3 jin. They are hung under the two ends of (the beam). It is already obtained that the length from i to u contains two sections. Find the number of sections contained in the part from u to o in length. The method says: according to the method of proportional computation in section 19.
1 3 jin is the lighter weight
2 9 jin is the heavier weight
3 2 sections is (the number of sections contained in) the shorter side of the beam
4 6 sections is the number of sections of the longer side of the beam.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol2+30+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=30 |
| Comment: | Chapter 2, Section 33:*how to request weight of object according to weight of beam without moving weight*
**Commentary:
It is a variation of Section 23. Numerical values and figures are equal. It is almost the same as Problem IV (Proposition V) in Stevin’s book (p.135), but their calculations are different. Likewise, Example III of Problem I (Proposition II) is a variation of Example II of Problem I (Proposition II) in Stevin’s book (p.125) that is the origin of Section 23.
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Pappus in Alexandria made a thorough and brilliant investigation of the five primary machines, that is, the lever, pulley, wheel and axle, wedge and screw (Guido, Mechaniche, p.244).
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| Translation: | Section 33: Give the weight of the beam of steelyard, weigh the weight of object without a sliding weight.
The weight of the beam is 40 jin, divide it into 10 sections. The heaviness of the hung weight is unknown, but move the lifting cord to the position by which (the weight and the beam) is effectively equal, thus, the location of the lifting cord is determined.
Suppose that there are two sections from the weight to the position of the lifting cord, then, the longer part should contain 8 (sections). Minus with each other, (result) is 6. This is namely the difference. Take the Rule of Three.
1 4 sections, is the double of the (numberof sections contained in) the shorter part.
2 6 sections, is the difference between the (numberof sections contained) in the long and the short side.
3 40 jin, is the the weight of the beam.
4 60 jin, is the weight of the hung object.
the fourth, 60 jin, the weight of the object hung on the beam
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=32 |
| Comment: | Chapter 2, Section 35:*three kinds of the lever: “jie” (fulcrum is in the middle of a lever), “tiao” (object and power are respectively at both ends of a lever), “ti” (power in the middle o a lever)* |
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| Translation: | Section 35: There are three kinds of lever, they commonly serve to lift objects. The first, fulcrum is in the middle (of lever); force is applied on its handle; (and) the heavy object is at its head. Its name is the lever for prising, jie. The second, fulcrum is at its head; the heavy object is in the middle; (and) force is also applied on the handle. Its name is the lever for raising, tiao. The third, fulcrum is at its head; force is applied on the middle; (and) the heavy object is on the handle. Its name is the lever for lifting, ti. |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=32 |
| Comment: | Chapter 2, Section 36:*calculations of proportions between weight and power or between distances at a “jie’ lever*
**Commentary:
WT’s proposition and its figure are very close to Proposition I of Guido’s On the Lever (Guido, Mechaniche, p.298). Guido did not show any example with numerical value, but tried to give a proof.
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| Translation: | Section 36: Jie gang (the lever for prising) stays horizontally on the fulcrum. There is a weight is at its head. A force is acted on its handle. The ratio of the weight to the force is equal to the ratio of the length of two side of lever. For example, a lever for prizing consists of nine sections in length, its fulcrum is at u. The short side consists of three sections, (and) the long side is consists of six sections. The weight of a is 40 jin, the force e must be 20 jin. According to the method of proportional computatioon in section 19, (the ratio) of a to e is two, (the ratio of) the long side to the short side is also 2. |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=33 |
| Comment: | Chapter 2, Section 37:* calculations of proportions between weight and power or between distances at a “tiao’ lever *
**Commentary:
WT’s theorem and figure are very similar to Galileo’s narrative (On Mechanics, pp.284-285). The first sentence of WT’s explanation is the same as Galileo’s narrative (p.285). There is no calculating example of WT in Galileo’s book.
WT’s theorem and figure are also close to Proposition II of Guido (Guido, Mechaniche, 299), The last sentence of WT’s explanation is almost the same as Corollary I of Proposition II of Guido (p.299). Guido said this type of lever is second mode. Guido did not make any example with numerical values.
WT’s figure is closer to Guido’s than to Gelileo’s.
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| Translation: | Section 37: Tiao gang (the lever for raising) stays horizontally on the fulcrum. Its head is at the fulcrum. There is a weight in the middle (of the lever). A force acts on its handle. (This section is concerned with) the proportional relationship (among the factors envolved).
The ratio of the part of the lever from weight a to the fulcrum to (the length) of lever for raising is just equal to the (ratio of) force to weight. Suppose that from i to o (contains) nine sections, from u to o (contains) 3 sections, this is one third. Therefore, the weight weights 60 jin, the force is only 20 jin. The reason is that the closer to the fulcrum the raised weight is, the smaller force is used. So, the lever for raising can usually save strength. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol2+34+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=34 |
| Comment: | Chapter 2,Section 38:*how to request power according to weight of lever and weight of a heavy body*
**Commentary:
WT’s problem derived from Example IV and its figure of Proposition VII in Stevin’s book (pp.329-330). Their “method” and numerical values are the same as Construction of Stevin’s Example IV (p.331).
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| Translation: | Section 38: The length of a lever for lifting, 10 chi, and the weight of its own body, 400 jin, are given. There is another object of 1,000 jin on (the lever). The diameter of weight of the lever and the middle diameter of the weight are obtained. Find the force for lifting.
The method says: the ratio of ou to oi should be equal to the ratio of 400 to 1000. Suppose that (the length of) eo is 2 chi, take the method of proportional computation. The ratio of 10 chi to 2 chi is equal to the ratio of 400 jin, the sum of two weights, to 280 jin.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=35 |
| Comment: | Chapter 2, Section 39:*how to request power at a “ti” lever*
**Commentary:
WT’s proposition is close to Proposition III of Guido (Guido, Mechaniche, p.299). There is no example with numerical values in Guido’s book.
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| Translation: | Section 39: The head of ti gang (the lever for lifting) stays horizontally on the fulcrum. There is a weight on its handle, (and) a force was acted at the middle (of the lever). (This section is concerned with) the proportional relationship (among the factors envolved).
The ratio of the number of sections contained in the whole lever ou to the number of sections from the fulcrum to the force ei is equal to the ratio of the force to the weight. Suppose ou consists of 12 sections, ei consists of 4 sections, the ratio (of them) is threefold. The force 60 jin to the weight 20 jin is threefold, too. The force for lifting the weight is usually several times the weight, so (lever for lifting) is seldom used.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=35 |
| Comment: | Chapter 2, Section 40:*the proportion between power and weight is equal to the proportion between two distances at a “tiao” lever* |
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| Translation: | Section 40: Force is acted on a lever to raise a weight. The ratio between them is equal to the ratio of one part to another part of lever. One part is from the fulcrum to the perpendicular broken line that reaches from the center (of the weight) to the position of the lever; the second part is from the fulcrum to the (position where) the force (is acted).
Suppose (ea) is the lever, i is the fulcrum. The power exerted at e is 300 jin, ao weighs 900 jin. So the ratio between them is one third. Now make a perpendicular line from o, the center (of weight), to the lever, and (the line) reaches point u. The ratio of the length from u to i to the length from i to e is also one third. If ui contains 2 sections, then ie contains 6 sections. (The ratio) is obviously one third.
In the second figure, the weight ao is hung under the lever. At the two positions a and c, only the perpendicular line uo is used, two points a and c are not used. After this, all the method is the same (as the method above).
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=37 |
| Comment: | Chapter 2, Section 41:*the influence of three positions of an object on power when its center of gravity is over a “jie” lever*
**Commentary:
WT’s proposition is the same as Proposition VIII of Guido (Guido, Mechaniche, pp.301-302). WT’s figure is a simplified figure of Guido (pp.301-302, first figure).
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| Translation: | Section 41: A power is (acted on a lever) to raise a weight, the center (of the weight) stays above the horizontal lever. The higher the weight is raised, the smaller the power used; the lower the weight is raised, the bigger the power used.
For example, lever ea stays horizontally on (point) i, its perpendicular line is oa. The weight is raised higher, and the power is exerted on (point) e. (Draw) a perpendicular line from point o to point u , the length from u to i is shorter than the length from a to i, therefore, the smaller power is used according to section 40. If the weight is below the horizontal (lever), (draw) a perpendicular line from o to f, (f)i is longer than ai. As the force acts on g, according to the last section, a bigger force is needed.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=38 |
| Comment: | Chapter 2, Section 42:*the influence of two positions of an object on power when its center of gravity is over a “jie” lever*
**Commentary:
WT’s proposition is regarded as another corollary of Proposition VIII of Guido (Guido, Mechaniche, pp.301-302). WT’s figure is much simpler than figure of Guido (p.302, first figure).
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| Translation: | Section 42: Jie gang (the lever for prising) stays horizontal, and the center of the weight is above. The higher the center of the weight is prised, the smaller the power (needed).
As the above figure, the center of the weight is prised upward, (and) a perpendicular line reaches point a. Look at the horizontal weight below, the closer it is to the fulcrum, the smaller force is used.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=39 |
| Comment: | Chapter 2, Section 44:*the proportion between the arm of the force is equal to that between two parts of a lever* |
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| Translation: | Section 44: There is a weight that is hung at the head of a lever, the fulcrum is in the inner side, (and) force is applied to the handle. The ratio of the distance (the handle of lever moves) from level to the lower position to the distance the weight hung at the head of the lever moves to the upper position is equal to the ratio of the (length of) the two sides of the lever.
For example, in above, (the ratio of) the distance at the shorter side before the fulcrum to the distance at the longer side at the back of the fulcrum is one third, thus (the ratio of the length of) the short side to the long side is also one third. It is also true for the lever for lifting, as the latter figure.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=40 |
| Comment: | Chapter 2, Section 45:*how to request the fulcrum according to weight, power and the length of a lever*
**Commentary:
WT’s problem and its part of numerical values are the same as Proposition XI of Guido (Guido, Mechaniche, pp.302-303). WT’s figure is almost close to figure of Guido (p.302, fifth figure).
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| Translation: | Section 45: Given theweight, given thelever (and) given the force to move the weight,find the position of the fulcrum.
For example, a weighs 100 jin, the force is 10 jin, and the lever consists of 22 sections, find the position of the fulcrum. Take the method of proportional computation.
1 110 jin, is the amount of (the sum) of the force and the weight
2 22 sections, are the number of sections contained in the lever
3 10 jin, is the number of sections of the force
4 2 sections, is the position of the fulcrum
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=40 |
| Comment: | Chapter 2, Section 46:*how to request power when there are the weight of several objects are hung at lever*
**Commentary:
Except given length of the lever, WT’s problem and its figure are almost the same as Proposition XIII of Guido (Guido, Mechaniche, p.303). Guido did not mention numerical values in example.
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| Translation: | Section 46: Give several weights, give the fulcrum, (and) give the length of lever. Find how much power (is needed)?
For example, there are three weights: a weighs 48 jin at the head, e weighs 24 jin at the bound of the ninth section, i weighs 12 jin at the bound of the 38 sections. The fulcrum is at the bound of the 21st section. The total length of the lever is 60 sections. Find how much power should be used. The method says: the lever within a e, consists of nine sections. Find the position of fulcrum between (these) two weights. It is found that the short side contains three sections, (and the fulcrum) is at (point) u. The lever from u to c,contains 35 sections. Take the method of proportional computation, five sections are obtained, and (the fulcrum) is at (point) ch. The third time (to use the method of proportional computation), from the fulcrum to the force, (point) o, contains 39 sections; from the fulcrum to (point) ch contains 13 sections. The ratio (between them) is three. (The ratio of) the weights, 84 jin, to the force (should also be 3, so the force) shoud be 28 jin.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=42 |
| Comment: | Chapter 2, Section 47:*how to request the fulcrum according to power, the weight of several objects and the length of a lever*
**Commentary:
Wt’s problem is very close to Example V of Problem I (Proposition II) in Stevin’s book (p.129), but their numerical values are different.
Commentary:
WT’s problem is almost the same as Proposition XIV of Guido (Guido, Mechaniche, p.303). Numerical values in Guido’s problem are those of WT in example.
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| Translation: | Section 47: Givenseveral weights, given the length of the lever, and given the amount of the force, find the position of the fulcrum.
The method says: make use of the figure in section 46. First, find (the postion of the fulcrum) at which(the weights are) effectively equal. Suppose that (from the head) to ch contains 8 sections, from ch to the position of force contains 52 sections. Take the method of proportional computation.
1 120 jin, is the number of (the sum) of a, e, i and o, which are the three weights and the force
2 28 jin, is the amount of the force
3 52 sections, are the sections of the length of lever
4 13 sections, are the sections contained between ch, the center of gravity, and the positon of the fulcrum
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=42 |
| Comment: | Chapter 2, Section 48:* how to request power when the weight of a lever is taken into account*
**Commentary:
WT’s problem derived from Example II and its figure of Proposition VII in Stevin’s book (pp.325-326). Their “method” and numerical values are the same as Construction of Stevin’s Example II (p.327).
Section 38 and Section 48 are respectively Example IV and Example II in Stevin’s book.
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| Translation: | Section 48: Given the weight, given the heavy lever, given the position of the fulcrum, find the amount of the power.
For example, ch weighs 2000 jin, its center (of gravity) is i. The two ends of the lever are o and c. The weight of its (the lever) body is 400 jin, and its center of gravity is at g. The lever is obliquely raised on the fulcrum e, ae is its fixed place. The diameter of the weight is ik. kg contains 6 sections, and fc contains 12 sections. How much power shoud be used at c? The method says: first, find the centers of gravity of the weight and the lever’s body. Take the method of proportional computation.
1 2,400 jin, is (the sum of) of the heaviness of the weight and the lever
2 400 jin, is the amount of the weight of the lever
3 6 sections, is (the number of sections) from k, the center of gravity (of the weight), to g, the center of gravity (of the lever),
4 1 section, is the numberof sections from k to u. Therefore, ug consists of five sections.
Take the method of proportional computation again.
1 12 sections, is the numberof sections contained from (the positon of) force, c, to the fulcrum, f
2 1 sections, is the number of sections contained in uf
3 2400 jin, the total amount of two weights
4 200 jin, the amount of power. |
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| Comment: | Chapter 2, Explanations of the pulley, Section 49:*the definition and structure of a pulley* |
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| Translation: | Section 49: Pulley, the entire body is a wheel. On the side of circumference of the wheel, the twosides are high, (while) the middle is concave. (The pulley) has not spoke, teeth or shaft, but it has a hollow hole for a shaft.
The wheel is small; and its thickness is not too much. Its two sides are high and the middle is concave, which allows rope to revolve in the middle. The wheel has no shaft itself, (it) only has hollow hole to hold shaft. There is a frame to fix the shaft as well, and the shaft runs through the (hole of the) wheel. The smoothness of (the slot) is maximally beneficial to the revolving of rope. Therefore, it is named pulley. What is called yang tou gu lu (wheel with the shape of the head of a sheep) in the middle south is this (pulley). As (in the) above (figure), a is a small wheel, in the middle of which there is a hole. e is the revolving rope, which goes up and down through the slot. o is its frame, and i is the shaft which runs through (the wheel). |
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| Comment: | Chapter 2, Section 50:*why are a balance and a pulley congeneric?*
**Commentary:
This section seems to be an extract of Gelileo’s narrative (On Mechanics, pp.284-286). WT’s figure is somewhat similar to Gelileo’s (p.286).
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| Translation: | Section 50: Pulley is also of the same kind as balance, so power is equal to weight.
For a balance, if the two weights are equal, then, it is in level; if one is heavy (and) the other is light, the (balance) must lean and descend. This is why the power (applied) to a pulley is usually equal to the weight. Somebody may say, wheneverei turns, (the pulley) would not be level. Why do (you) say that (it is) a balance? Say: ei is the diameter and all the lines around it are also (diameters). So, no matter how the wheel revolves, the pulley is still a balance. (Even the pulley) is not named as balance, but (it) has the essential of balance. Therefore, it is said that pulley is of the same kind as balance.
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| Comment: | Chapter 2, Section 54:*a moving pulley’s characters*
**Commentary:
Meaning of WT’s theorem is close to Galileo’s narrative (On Mechanics, p.287). Galileo gave a proof, rather than calculation with numerical values.
Commentary:
WT’s proposition and its figure are very close to Proposition II and figure of Guido (Guido, Mechaniche, p.306; figure: left on p.306).
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| Translation: | Section 54: (If) the two ends of the rope of a pulley are all upwards, a weight is hung at one end, the force is used at one end, (then) the whole weight could be lifted by half force.
For example, the rope fastened at a, a force was used from i and o to e. A weight, which weighs 100 jin, is hung under the frame. Exert force from (point) e to raise it, with a force of 50 jin, (one) can raise the weight of 100 jin. Why? The rope ai does not move, so, oi acts like a lever for raising, (and) i acts like a fulcrum. As the hung weight is under the middle (of the wheel) u, taking the method of proportional computation concerning the lever for raising, the ratio of iu to io is always equal to the ratio of radius to diameter, therefore, with half force one can raise the whole weight
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| Comment: | Chapter 2, Section 55:*a moving pulley’s characters*
**Commentary:
WT’s proposition seems to be a compound of Proposition II (p.306) and Proposition XI of Guido (Guido, Mechaniche, p.311).
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| Translation: | Section 55: (If) the two ends of the rope of a pulley are all upwards, a weight is hung at one end, the force is exerted at the other end. Although half force is used, the time needed must be doubled. And, the distance, across which the rope goes upwards, must be the double of the distance across which the hung weight rises. Seeing the above figure, it is self-explanatory.
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| Comment: | Chapter 2, Section 57:*numerical relations among weight, power, shaft’s radius and wheel’s radius when weight is hung on the shaft and power is added to the wheel’s edge*
**Commentary:
WT’s theorem is an extract of Proposition IX and its Theorem in Stevin’s book (pp.341-343). WT’s figure probably is a variation of Stevin’s stereograph (p.342).
WT’s theorem is close to Proposition I of Guido (Guido, Mechaniche, p.318). WT probably transformed Guido’s figure of a wheel with handles into figure of a wheel.
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| Translation: | Section 57: There is a wheel. Its shaft extends outside its two sides, (and) sticks with the wheel. A weight is hung under the shaft. Man exerts force horizontally beside the rim. (The ratio of) the weight to the force is equal to the ratio of the radius of the wheel to the radius of the shaft.
As the above figure, the radius of wheel is ai, the radius of shaft is ae. ai should be horizontal. Under i there is a force or a weight as o. A rope twines round the shaft, by which a weight u is hung. As ai consists of 4 sections, (and) ae consists of 1 section, the ratio between the two radii is fourfold. Therefore, (if) u weighs 800 jin, only 200 jin of force is used to be effectively equal (to it). By adding a little force, the weight is raised.
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| Comment: | Chapter 2, Section 60:*the influence of power’s acting point at the edge of a wheel on efficiency*
**Commentary:
WT’s theorem is close to the first paragraph of Corollary of Proposition I of Guido (Guido, Mechaniche, p.318). WT probably transformed Guido’s figure of a wheel with handles into figure of a wheel.
Galileo also discussed this theorem in detail, and drew a figure (Galileo, Mechanicks, p.281). Galileo’s figure is close to and more complicated than WT’s.
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| Translation: | Section 60: If the radius of wheel is not horizontal, when a weight is hung on it, the proportional raltionship (among the facters concerned) is also not the same.
As the above figure, ao is a radius that is not horizontal. Its handle is at o, the hung weight below is c. Its perpendicular line is from o to u, (and u) is on the horizontal line ai. The weight hung on the shaft weighs 300 jin, as ch. The ratio of (it) to force c is equal to the ratio of au to ae. As au is three, (and) ae is one, so, 300 jin (could be raised) by a force of 100 jin. If hands are used instead of weight, then, the saved force is always the same whether (the force acts) at o or i. This is because that by drawing downwards, (the wheel must) obliquely descend, (and) its perpendicular line is always on the circumference of wheel. If (man) desires to use a weight (to apply force), then, set a pulley on the circumference of the wheel, the rope by which the weight is hung turns with the pulley. So, force is also saved.
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| Comment: | Chapter 2, Section 61:* the proportion between moving distance of an object and clambering distance of a man is equal to the proportion of radius between a wheel and its shaft*
**Commentary:
If the wheel is transformed into the lever, WT’s proposition is the same as Proposition IV of Guido (Guido, Mechaniche, 299). WT’s figure is close to Guido’s that contains two circles. Is it possible that WT drew their figure on the basis of Guido’s?
Commentary:
WT’s theorem is close to the last paragraph of Corollary of Proposition I of Guido (Guido, Mechaniche, p.318). WT probably transformed Guido’s figure of a wheel with handles into figure of a wheel.
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| Translation: | Section 61: The ratio of (the length, along which) the rope on the circumference of wheel being drawn down to (the height, along which) the weight hung on the shaft being lifted, is equal to the ratio between the two radii.
For example, ae is four zhang, (and) is equal to io. Man stays at the position e, and draws the rope a downwards. (When the rope) reaches e, (its length) is four zhang. But the weight o can only be lifted to u, (the height) is only one zhang. As ac contains four sections, ci contains one section, so the ratio is fourfold.
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| Comment: | Chapter 2, Section 62:*using characters of a wheel*
**Commentary:
WT’s theorem is very close to Corollary III of Proposition I of Guido (Guido, Mechaniche, p.319). There is no example following Corollary III of Guido.
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| Translation: | Section 62: By using a wheel, (man) saves strength but spends more time, pro rata.
Suppose without using the wheel, for raising a weight of 1,000 jin, (man) spends only one ke. If (he) uses this wheel, four ke should be spent. As (by using wheel), although strength is saved, more time is spent.
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| Comment: | Chapter 2, Section 63:*how to request the radius of a wheel according to the radius of its shaft, the weight of object and power*
**Commentary:
WT’s theorem and numerical values in example are very close to Proposition II and tis example of Guido (Guido, Mechaniche, p.319). WT probably transformed Guido’s figure of a wheel with handles into figure of a wheel. WT used componendo.
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| Translation: | Section 63: Given the force and given the weight. (Man) desires to lift (the weight) with a wheel. Find the structure of the wheel.
There is a weight weighing 60 jin, and a force of 10 jin. Take the straight line ae to be the two radii of the shaft and the wheel. Take the method of proportional computation.
1 60 jin is the total amount of the weight and the force
2 10 jin is the amount of the force
3 14 sections is the number of sections contained in straight line ae
4 2 sections is the number of sections contained in ec. Radius of shaft is then obtained. So, ca consisting of 12 sections is the radius of the wheel. According to scection 58 above, the force a is effectively equal to the hung weight e. Therefore, the structure is obtained.
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| Comment: | Chapter 2, Section 69:*the whole wheel, partial wheels, crank, balance’s beam and capstan*
**Commentary:
Guido said: “this type of instrument includes the windlass, the capstan, the brace and bit, the wheel with its axle whether the wheel is geared or smooth and others.”(Guido, Mechaniche, 319) This sentence is similar to a part of Section 69 of WT’s book.
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| Translation: | Section 69: As for the categories of wheel, there are complete ones, there are incomplete ones. As to the incomplete ones, some lack one part; some lack two parts.
(Some wheels) only have rims, but no shaft and no body, such as a. For (the wheel) with shaft, some have a rim with the shape of a semicircle, such as e; or with the shape of one fourth (of a circle), such as i; or only with the shape of an arc, such as o. (Some wheels) are only lines, either having a handle outside the shaft, such as u, or a crank inside the shaft, such as c.
There are also many types of (wheel) with shaft and body but without rim. (Among them), is the balance, on its shaft there is one diameter, such as f; or windlasses, with several diameters, as ch; or some have only one radius, (or some) have several (radii), such as k.
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| Comment: | Chapter 2, Section 70:*relative positions of two wheels* |
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| Translation: | Section 70: As for the body of wheels, (if the parts) are combined together, (then) (the wheel) could be of use.
There are two kinds of combination. There are two complete wheels, (one) is inside, and (the other) is outside, such as a. there are two incomplete wheels, but (they) share the same shaft, they have two radii, but no rim, such as e. All of these (parts) are required to (be with each other) for the use of (a wheel).
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| Comment: | Chapter 2, Section 71:*eight kinds of wheels in common use* |
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| Translation: | Section 71: There are eight kinds of wheel in common use:
1,drum-treadmill (men or animals walk inside the wheel, in order to turn other weights)
2,capstan (men or animals push or drag outside the rim)
3,treadwheel (only men tread on it)
4,climbing wheel (only men scale it with hands)
5,water-wheel (water power impacts the wheel and makes it rotate)
6,wind-wheel (wind power blows the wheel and makes it rotate)
7,gear wheel (the gears rotate with gears of other wheels successively)
8,flywheel (the former seven wheels receive power, but add no power. The flywheel receives power and also strengthens the power by its own weight.)
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| Comment: | Chapter 2, Section 74:*three kinds of spiral implement, namely spiral respectively on cylinder, sphere and cone* |
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| Translation: | Section 74: There are three kinds of helical implements: one, the column screw; two, the sphere screw; three, the cone screw.
As there are three kinds of round body: one, column; two, sphere; three, cone. As the helical thread leans against (the round body) and creeps upward, so it turns into three kinds: the column is employed to lift weights; the sphere is necessary to astronomers; as for the cone, (it) is the instrument for boring hard substances and digging deep, (and) is often used by craftsmen. While in this science of weight，only the column screw is usually used.
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| Comment: | Chapter 2, Section 75:*the use of a spiral (screw)*
**Commentary:
Comparing the beginning of this section with that of Galileo’s narrative (On Mechanics, p.292), there are some similarities, for example, WT and Galileo all emphasized the importance of screws among instruments. WT used more concrete examples to explain the usage of the secrew.
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| Translation: | Section 75: All of the implements above have wonderful uses, while the usage of this implement is greater and more ingenious.
How to know that this implement is more ingenious than the instruments above? Because (comparing with the others) it has the widest usage and greatest capability. For instance, the timber used for a water gate is heavy and long, it could not be lifted by manpower, (but) it is not difficult to hoist it with a screw. For another (instance), a long great timber, whose tip is made of iron, enters very deeply into the earth, (so that) it cannot be lifted by manpower. If the screw is used, it can be lifted. Or if man desires to squeeze a thing with water and juice, with any other heavy thing, (he) can not squeeze it, even if (it is) squeezed, its juice and water cannot be exhausted. For this, only with a screw, (he) can exhaustedly squeeze it, and even pumice could not be drier than the draff and dreg remaining. In Western schools, the screw is also used in printing books, therefore the books have suitable shades of colours which can even reach perfection in printing of characters and drawings. As for fixation of various things, no matter the device is made of copper, iron, gold or wood, once the screw enters, (the device) will be steady and firm. Not only that, (fixation of things with screw) is not laborious, and (the device to be fixed) can be disassembled. Moreover, other machines with great capability must be long and large, but for this machine, even the shortest and smallest one, (with it) nothing can not be managed. The (size) of the implement is smaller (than other ones), but its capability is greater (than them), it is fantastic. Observe the celestial phenomena, for instance, the sun, one year is one cycle (of its movement), from midwinter to the Summer Solstice, it is nothing but a sphere screw. Another instance, when the rainy wind encounters a whirling attack, even large wood and large stones can be carried upwards. Another instance, the whirling water in a wave can suck person and things downwards. Hundreds of different kinds of plant, for instance, vine, melon, bean, and grape, all have the appearance of (screw). Aquatic animals in the oceans that have a screw-like appreance are innumerable. In the past, these things were very precious. Southerners used them to make cowries to substitute for gold and silver. This is (the sign) that Heaven and earth give to show the great and wonderful usage of it, by using the appearance of things to show people to use (the screw). It is not only that the science of weight-moving could not absent itself from these (screws). Without their rotation and connection with each other, even the various usages of such little things as rope, and the string of a bow, crossbow and musical instruments in peoples’s daily life, could not be realzed. Therefore, comparing the six implements above, the virtue of this implement is more ingenious. In addition, its manufacture is simple and convenient. It is not necessary to say anything about the consistency of the long and large ones, even the tiny ones are also very solid and absolutely not risky. Therefore, Ya xi mo de (Archimedes) frequently used this implement, as he aimed at its wonderfulness. If (man) can understand the subtlety of reason for its (wonderfulness), it will not be difficult for (him) to make every implement under heaven. For the scrupulous person, it is not difficult to understand.
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| Comment: | Chapter 2, Section 76:* two balls, which are joined by a thread respectively on two inclined planes, are equal in effective weight*
**Commentary:
WT’s theorem should be a variation of Theorem XI (Proposition XIX) in Stevin’s book (pp.175-177). Stevin did not mention solid triangle, triangular prism and hook.
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| Translation: | Section 76: There is a solid triangle; its bottom is parallel to the ground. On each intersecting side, there is a ball that is tied parallel (to the side) on a hook. The two balls are equal to each other. The ratio of the (length of) the right intersecting (side) to the left intersecting (side) is equal to the ratio of (the height) of the right ball to the left ball.
For example, if the (length) of the right intersecting (side) is half of the left intersecting (side), therefore, (the height of) the position of the right ball is also half of the position of the left ball. The two sides of a (solid) triangle are an inclined plane. (Its shape) is just like the shape of a triangular prism.
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| Comment: | Chapter 2, Section 77:*two balls, which are joined by a thread respectively on two decussate inclined planes, are equal in effective weight*
**Commentary:
WT’s theorem should be an extract of Corollary I & II of Theorem XI (Proposition XIX) in Stevin’s book (pp.178-179). WT’s figures are the same as Stevin’s (p.178). Stevin did not mention solid triangle, triangular prism and hook.
Wang Zheng added the following Chinese representation to this section: “The upright side is called gu, the inclinded one is called hypotenuse, and the bottom is called gou. If [the vertical [side] intersects the bottom, [the triangle] is named as gou gu (right angled triangle).”
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| Translation: | Section 77: There is a solid triangle, its bottom is parallel to the ground. The right intersecting side is half of the left intersecting side. On each side, there is a ball tied parallel (to the side) on a hook. As long as (the height of) the right ball is half of (the height of) the left ball, the two balls must be effectively equal to each other.
Suppose the (solid) triangle below is a right angled (solid) triangle, (the ratio of) its right side to its left side is the ratio of gu to hypotenuse, which is equal to the ratio between the two balls. The upright side is called gu, the inclined one is called hypotenuse, and the bottom is called gou. If ( one side) intersects the bottom vertically, (the triangle) is named gou gu (right angled triangle).
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| Comment: | Chapter 2, Section 78:*two balls, one of which is on a inclined plane, are joined through a pulley by a thread and are equal in effective weight*
**Commentary:
WT’s theorem and its figure are the same as Corollary III and figure of Theorem XI (Proposition XIX) in Stevin’s book (pp.180-181).
Wang Zheng made use of Chinese terms gou and gu, and explained similarities and differences in function between pulley and hook.
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| Translation: | Section 78: There is a (solid) triangle that is the same as the one in above (section), but (the balls) are not tied on hooks. They depend on a pulley and (the rope) passed through it. The vertically hung weight is downward. The ratio of the vertically hung weight to the inclined weight is also the ratio of the gu (the vertical side of the right angled triangle) to the hypotenuse.
It seems that hook and pulley do not belong to the same kind (of implement), but the weight passing through the inside of a hook is in accordance with the weight passing outside the pulley. So their ratios are also the same.
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| Comment: | Chapter 2, Section 79:*definition of “xie li zhong” (a heavy object supported slantways)*
**Commentary:
WT’s figure is close to the second figure of a group figures in Stevin’s book (p.104). WT’s definition of ‘xie li zhong’ probably corresponds with ‘oblique lowering/lifting weight’ in Stevin’s Definition XIV and its Explanation (pp.103-107). [See: Section 15 in chapter 2]
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| Translation: | Section 79: There is one weight hung at one side of a pulley, and (another weight) at the other side is hung in air. The hung weight stays at the point of a fulcrum, and is named as inclined standing weight.
For example, a heavy board o has an inclined diameter of weight, a motionless point is fixed on the fulcrum i. One point, for instance, (point) p is tied to a rope, and (the rope) passes slantways upwards and through a pulley. There is a vertical hung weight a. The hung heavy board moves neither upward nor downward. As the straight line pu is inclined, weight a is named as inclined standing weight.
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| Comment: | Chapter 2, Section 81:*hoisting weight and moving weight on a inclined plane follow the same principle* |
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| Translation: | Section 81: The principles of moving weights on an inclined plan or lifting weights by the inclined plane are the same.
There is an inclined plane, (man) desires to move a weight on its surface. Or (he) moves the weight on the plane from below and makes it (go) upward, or (he) lifts the weight on the plane from above and makes it (go) upward. In these two (circumstances), the inclined plane does not move. Or there is a heavy sphere on the ground, make the tip of the inclined plane slantways enter under the sphere, and move (the plane) forward to make the weight go upward by itself, this is a method of moving the inclined plane for lifting weight. The principle is the same as the one of the former two (circumstances). For example, in the second figure above, the heavy sphere a is on the ground, there is an obstacle e in front of it. Let the tip of the inclined plane enter under the sphere, like i. Push the (inclined plane) forward forcibly, then the sphere rises to (point) o by itself.
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| Comment: | Chapter 2, Section 82:* an inclined plane turning along a cylinder forms a spiral shape*
**Commentary:
The figures of this section are a little similar to Galileo’s (Mechanicks, p.299). Galileo explained the form of a screw (p.297). In order to explain how to make a screw, WT used obliqued plane, rather than Galileo’s triangle.
WT’s proposition is similar to Proposition I of Guido (Guido, Mechaniche, 324). Guido used the trem “wedge”, while WT used the term “inclined plane”.
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| Translation: | Section 82:An inclined plane climbsaround a cylinder, this forms a helix.
Using the inclined plane shape to lift weight is inconvenient, the reason is that its body must be long. Therefore, wind the length of the inclined plane on a cylinder to make a helical implement, in order to reduce its length. For example, aoi is the hypotenuse of the inclined plane above, its body is very long and is equal to the helix (around) the cylinder. The gu au is equal to the height of the cylinder, (and) the gou ui is equal to the circumference of the cylinder. So, it is known that for an inclined plane, a long body must be used, but for the helical line winding upwards, it need not be long.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=73 |
| Comment: | Chapter 2, Section 85:* the bigger the radius of a cylinder with spiral is, the more capably it works* |
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| Translation: | Section 85: The two cylinders are unequal, the heights of their helixes are equal. If the cylinder is bigger, the power is also greater.
For example, cylinder a is smaller, and cylinder e is bigger. The heights of the helixes (around them) are equal. But the hypotenuse of the big cylinder is four times the gu, and the hypotenuse of the smaller cylinder is double the gu. Therefore, for the bigger cylinder, a weight of four jin needs only (the power) of one jin. Comparatively, it is different from the situation of the smaller cylinder that a weight of four jin needs the power of two jin. The reason (of this section) is the same as the one concerning the thickness of helix.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=74 |
| Comment: | Chapter 2, Section 86:*the spiral makes man save labour, but makes him spend more time * |
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| Translation: | Section 86: With a helix, (one can) save strength the most, but the spent time must be inversely (longer).
The hypotenuse of a helix is double the gu, (so, with it), using half power is enough, but the time spent must be double (the time used for lifting the weight) vertically. For instance, in the above figure, the force is exerted at o. One vertical weight is at u, (and) one weight slantways reaches a. Exert force for one period of time, the weight u reaches o, while the weight a can only reach p. Spend the same one period of time once more, (the weight a) now arrives at o. However, for (lifting) the weight a needs only the power of two jin, for (lifting) the weight u, the force of four jin must be used. The reason why half power is used is that the distance must be doubled, so the spent time and the saved force are inverse. |
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| Comment: | Chapter 2, Section 87:*spiral-implement-making materials* |
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| Translation: | Section 87: There are three kinds of materials of which the helical implement (are made): one, steel; one, wood; one, copper, in order to prevent the implement from being bent. The steel, if it is used, should be even and smooth uniformly, and it would be better that there is no obstruction. If (one) desires that it runs without a hitch, it is suitable to use oil. Oil could make the material not shrink. For the small helical implement, the male one (outside screw) should be made of steel, while the female one (inside screw) should be made of red copper. The reason is that the engagement of the copper and the steel doesn’t induce shrinking and roughing. However, for the big implement, it is feasible that it must be made of steel. The wood used must be hard, (the reason) has been explained in the former section.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=75 |
| Comment: | Chapter 2, Section 88:*how to make a spiral implement according to the radius of a cylinder and inclined angle of the spiral* |
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| Translation: | Section 88: Give the diameter of a cylinder, and also give the gradient of the helix. Make a helical implement.
Suppose ai is the diameter of the cylinder aei, and the angle (of the helix) is also given. Decide the assurgent shape of the helix to make the helix implement. The method says: First, use compass and rule to select ai, the length of the cylinder from straight line a to e. As the straight line, ai is equal to the diameter, three and one seventh of it is uo, then the circumerence of cylinder aei is obtained. Use the compass and rule again to make an angle shape from ai equal to the inclined angled shape. Set a vertical line on o, which meets the inclined line of the angle at p, then, a triangle is obtained. ao is one circumerence of the bottom of the cylinder, and ap is one circumference of the helix. Move the vertex of the angle a to point p, (the helix) turns upward continuously, (the helix) could be endless.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=77 |
| Comment: | Chapter 2, Section 89:*how to request the angle of a spiral according to the known length and height of the spiral* |
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| Translation: | Section 89: Given the ratio of (the length of) helix to (the height of) vertical line, Find the angle.
For example, the length of the helix is eight fen and its height is one fen. To find the angle, there is the arithmetical method and the geometrical method. The arithmetical method makes use of theof proportional computation.
1 eight sections the length of the helix
2 one section the height of the helix
3 100,000 half of the diameter of the circle
4 12,500 half of the hypotenuse, its angle is seven degrees and eleven minutes. Thismeets the requirement.
Geometrical method: there is a straight line ae, which is bisected at (point) i. Take i as the center, and a as the boundary, make one semicircle, as aue. As ae consists of eight sections, take one section from a to o, make the straight line ao at the circumference of the circle. Make a straignt line through o and e, so the angle aeo meets the requirement.
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| Comment: | Chapter 2, Section 90:*how to request the angle of a spiral according to structure of the spiral* |
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| Translation: | Section 90: Give a helical implement, find its angle.
There is a cylinder, its diameter (consists of) three sections, and its height consists of eight sections. The inclined running angle of the helix is desired to be known. The method says: Find the circumference of the circle, ei, based on the diameter of the cylinder, make a vertical line that is equal to the height of the cylinder, namely eight sections. eo is one section. Make a straight line from o, so the angle eio is obtained, (this) meets the requiement.. In addition, there is a simple method: suppose making a vertical line on line ei, its height is equal to the length of one round of the helix, namely eo. Join (it) with i, (one) also obtains what is required.
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| Comment: | Chapter 2, Section 92:*how to construct a spiral implement according to known weight and power* |
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| Translation: | Section 92: Given the weight, (and given) the power, find the helical implement to move (the weight).
For example, there are a weight of 1,000 jin, and manpower of 100 jin. With what kind of helical implement, can man move (the weight)? The method says: take the (method of) proportion of ten sections. For instance, the above vertical line ao consists of 10 sections, take one section as ai from (it). Use the compass and rule to get ten sections. Set a straight line on it, from i to u, then, a triangle aiu is obtained. Use this triangle to make a helical implement. (With it, man) can raise the weight of 1000 jin by the manpower of 100 jin.
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| Comment: | Chapter 3, The First Diagram of Weight-hoisting
The Explanation of the First Diagram:
**This diagram shows us a typical Chinese steelyard.
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| Translation: | The First Diagram of Weight-hoisting
The Explanation of the First Diagram
Weight Hoisting
Explanation
Suppose there is a rock which weighs 500 jin that is going to be hoisted. First, use a vertical rack a as is shown in the diagram. Then, on the crossbeam e is tied the lifting rope of a steelyard i. At the head of the steelyard, there is the rope o with which the weight can be lifted; at the end of the steelyard, there is a rope u which a person can pull down. The length of the beam of the steelyard is eleven chi; it is one chi from the head of the steelyard to the point c, and it is ten chi from the head of the steelyard, through point c, to point ch. k expresses manpower, and p is the weight of the rock. Because it is one chi from o to c, (the interval) between them can be regarded as one portion; and it is ten chi from o to ch, therefore, this (interval) includes ten portions. Because the ten portions can lift up one portion, the power of one person can lift (the weight of) 500 jin. |
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| Comment: | Chapter 3, Explanation of the Third Diagram of Weight Hoisting:
**WZ made a copy of plate No.XI before p.89 in Zeising’s book (Part I). However, WZ did not draw pulley block, and omitted deleted three persons so that they simplified the original plate. In addition, they misunderstood two pulleys and transformed them into simple parts which could also be found on this page below. In the diagram, a lifted weight was transformed into a stone. The action of two persons is the same as those in Zeising’s book, but the westerners were transformed into Chinese.
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| Translation: | The Third Diagram
The Explanation of the Third Diagram
Explanation
If there is a rock that has a certain weight, it is about to be hoisted. Firstly, make a three-legged vertical rack with the upper end gathered and the lower end apart. At the binding place of the upper end fix a short iron bar horizontally, on which is tied a pulley. Another pulley is tied below, and is tightly affixed to the stone. Pass an end of a rope through the upper pulley and down, then around the wheel of the lower pulley and up, again through the upper pulley and (then) down. Then, it is indeed possible to lift it with human power. If the stone is quite heavy, add one pulley to the upper and lower pulleys separately, or add two, which isn’t impossible. The more (pulleys), the lighter, (and) less human power is (needed). If the rock is still too heavy to lift, then, on two vertical racks (actually, any two legs of the rack), fix a windlass between (them). At the two ends of the windlass are separately set four wooden sticks as a cross. Human power is used to roll the rope, which is rolled around the pulley. This is more convenient. Furthermore, the power is greater. These two methods are included in the drawing above. |
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| Comment: | Chapter 3, Explanation of the Fifth Diagram of Weight Hoisting:
**WZ made a copy of plate No.XII after p.94 in Zeising’s book (Part I). However, WZ simplified the original plate, and deleted a few persons who did not operate the machine. In addition, they misunderstood the pulley block below and transformed it into a part which could also be found in the 5th diagram. A lifted weight was transformed into a stone. The action of two persons is the same as those in Zeising’s book, but the westerners were transformed into Chinese.
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| Translation: | The Fifth Diagram
The Explanation of the Fifth Diagram
The Explanation
If a stone is so heavy that it is difficult to hoist, and even if six pulleys are used and the windlass has been replaced with a big wheel. If the stone can’t be lifted up. So, set another rack at the side, (on which) a big cross wheel is fixed horizontally. Let four people in order turn the rope which is rolled around the big vertical wheel on the rack. Its power is far greater. There is absolutely no reason why the stone cannot be hoisted [it can absolutely be hoisted]. |
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| Comment: | Chapter 3, Explanation of the Sixth Diagram of Weight Hoisting:
**WZ made a copy of plate No.XIIII after p.98 in Zeising’s book (Part I). However, WZ simplified the original plate, and deleted a few persons who did not operate the machine. In addition, they drew two pulley blocks unclearly. A lifted weight was transformed into a stone. The action of two persons is the same as those in Zeising’s book, but the westerners were transformed into Chinese.
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| Translation: | The Sixth Diagram of Weight-hoisting
The Explanation of the Sixth Diagram
Explanation
Suppose there is a four-legged rack as before, on which a pulley is used to tie the weight. At the two sides of the rack are fixed two separate windlasses. But the cranks with which the windlasses can be turned are out of the rack. The two ropes tying the weight turn around the pulley and droop to roll separately around the two windlasses, which are each turned with human power. The weight will be hoisted naturally. |
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| Comment: | Chapter 3, Explanation of the Seventh Diagram of Weight Hoisting:
**The diagram is very close to figure 35 in Besson’s book (p.111). However, there are obvious differences between Bessson’s figure and WZ’s diagram. The projectional direction of two beams in WZ’s diagram is different from that of Besson. WZ simplified the machine and background in the original figure, and transformed the style of the skep or bucket, made some of them similar to the Chinese style. He transformed a part of wall into the top of Chinese-styled city wall. He kept only one operator who drives a crank, but omitted other persons in the original figure.
Plate No. NXI before p.95 in Zeising’s book (Part I) is quite similar to figure 35 in Bessons’s book.
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| Translation: | The Seventh Diagram
Explanation of the Seventh Diagram
The Explanation
If a wall or a house is built, bricks, stones, clay, soil and the like will be carried up. If (they are) not so heavy, then, with barrels or baskets, one person can carry five or six baskets or barrels (at once/ once). The method (is): a horizontal rack of wood poles inserted firmly is used above; at either end (of the rack) is fixed a pulley. A long rope runs through each pulley; one end of each of the two ropes is tied to a long pole. All baskets, barrels and so on are hooked on the pole. Below are two windlasses, to each of which the other end of each hanging long rope is linked, and (which) are set on a rack. If the things are not so heavy or so many, then it is enough for one person to turn the windlasses. Provided that the things perhaps are too many (and) too heavy, then, between the two windlasses is also installed a big wheel. The big wheel has another rope bound to another windlass aside. The windlass is (fixed) on another rack. One person turns the single windlass which draws the rope around the big wheel. Then the two windlasses will turn naturally; all the things will be carried up. |
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| Comment: | Chapter 3, Explanation of the Eighth Diagram of Weight Hoisting:
**The diagram is a copy of figure 39 on p.115 in Besson’s book. WZ simplified the background, and moved the sprocket wheel, worm and worm gear to the middle of the general figure. Although he correctly drew the worm and worm gear as an independent group of parts, he transformed the worm and worm gear in error into a simple crank at the top of the device so that he drew the incorrect transmission mechanism.
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| Translation: | The Eighth Diagram of Weight-hoisting
The Explanation of the Eighth Diagram
Explanation
A long rack with crossbars, like a ladder, is used. At the two ends (of the rack) are set two vertical poles separately. At the lower end is fixed a big pulley-style wheel; at the upper end is fixed a windlass. However, the structure of the windlass is divided into four sections, like the segments of a pumpkin. According to the length of the propped ladder (the ladder-shaped rack), bailing buckets are made (placed) inside, the number of which is not limited, and the form of which is just like that on a water-lifting device. The bailing buckets are full of soil, clay and the like. One person exerts his strength to turn the pumpkin segment-shaped windlass above. Thus, all the bailing buckets can move upward (successively) as flowing water. |
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| Comment: | Chapter 3, Explanation of the Tenth Diagram of Weight Hoisting:
**This diagram is a copy of Plate 170 in Ramelli’s book. WZ changed the structure of the rim of driving wheel by omitting the board of the rim. Except person in the wheel, other persons and background in Ramelli’s plate are omitted by WZ. A lifted weight was transformed into a stone. WZ’s explanation is similar to Ramelli’s Chapter 170.
Plate No.13 before p.41 in Zeising’s book (Part IV) is very close to Ramelli’s Palte 170 except the background of the machine. |
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| Translation: | The Tenth Diagram of Weight-hoisting
The Explanation of the Tenth Diagram
Explanation
At first, a drum-treadmill is made. A drum-treadmill is the wheel that a person treads inside on the wheel without stopping in order to drive other wheels. On the shaft of the drum-treadmill is set a copper wheel with teeth as a to turn a big wheel with teeth as e. There is an iron or copper screw on the shaft of this big wheel as i. What this screw i is close to is still a screw, as o. But screw o is several times bigger than screw i, which is the female (worm gear); while i is its male (worm). At either side of the worm gear o is tied a weight-hoisting rope, as u. The (two) ropes are separately tied upward to pulleys on a rack aside, as c. The pulleys above are hung one beside the other and in two tiers. The total is four pulleys, as ch. The lower two pulleys are hung side by side, as k. There is a heavy rock, as p, which is fastened to the pulleys. (The ropes) run directly to the two sides of the worm gear. Then, with one person walking in the big wheel, as f, the rock is certainly lifted. |
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| Comment: | Chapter 3, Explanation of the Eleventh Diagram of Weight Hoisting:
**This diagram is a copy of Plate 174 in Ramelli’s book. Except two persons who drive a capstan, other persons and background in Ramelli’s plate are omitted by WZ. A lifted weight was transformed into a stone. WZ’s explanation is similar to Ramelli’s Chapter 174.
Plate No.16 after p.51 in Zeising’s book (Part IV) is very close to Ramelli’s Palte 174 except the background of the machine.
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| Translation: | The Eleventh Diagram
The Explanation of the Eleventh Diagram
The Explanation
Firstly, a big rack is made as a; then, a cross-shaped capstan is made as e (shows). Above (it) is set a small wheel around which there are long teeth, as i, and which is fixed at a side of the rack. On the opposite side of the rack is set a big horizontal wheel with teeth around, which engage the long teeth of the small wheel, as o. On the upper part of the vertical shaft of the big horizontal wheel, a small wheel is also set, with its teeth fixed transversely, as u. Then, on the crossbeams of the top of the rack is set a big wheel with teeth, which engage the transverse teeth of the small wheel on the vertical shaft, as c. Then, on the shaft of the big wheel on the crossbeam is tied one end of the weight-hoisting rope, as ch. The other end turns through a pulley, as k, which is also set on a rack, and (runs) straight to the weight as p. By means of human power, the capstan is rotated, as f. Thus, the weight is raised. If the pulley is set horizontally on a rack far away, (this device) can be used as a method to haul weight. |
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| Comment: | Chapter 3, Explanation of the First Diagram of Weight Hauling:
**This diagram is a copy of Plate 178 in Ramelli’s book. WZ omitted background and one subsidiary person in Ramelli’s plate. The bracket was changed a little. WZ’s explanation is similar to Ramelli’s Chapter 178.
Plate No.20 after p.62 in Zeising’s book (Part IV) is very close to Ramelli’s Palte 178 except the arrangement of subsidiary persons. The background of the machine was omitted by Zeising too.
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| Translation: | The First Diagram of Weight-hauling
The Explanation of the First Diagram
Explanation
Firstly, make a cubic rack as a; then use a windlass, which a person turns, as e (shows). However, this windlass is like the segments of a pumpkin, having six teeth. Close to the teeth of the windlass is vertically set a big wheel, around which there are teeth to engage with the teeth of the windlass, as i. On the shaft of the big wheel is obliquely set an iron screw (worm), as o. Close to this screw is erected an upright shaft. On its lower part is horizontally set an oblique iron screw (a worm wheel), too, as u. Above it is set a small wheel with teeth, as c. Close to the small wheel, there is a horizontal big wheel, as ch, around which there are teeth to engage with those of the small wheel. On the lower part of the shaft of this big wheel, there is a small pulley, (the form of) which is like a windlass. A rope winds on to it three times, as k. With one end (of the rope) attached to a weight; with the other end, a person is used to pull it, as p. Thus, the weight is moved. |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=26 |
| Comment: | Chapter 3, Explanation of the Second Diagram of Weight Hauling:
**This diagram is a copy of Plate 180 in Ramelli’s book. WZ omitted the background of the machine in Ramelli’s plate. WZ’s explanation is similar to Ramelli’s Chapter 180.
Plate No.22 after p.67 in Zeising’s book (Part IV) is very close to Ramelli’s Palte 180.
WZ drew only one person who drives a crank. This person’s action is very close to that drawn by Zeising, rather than by Ramelli. |
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| Translation: | The Second Diagram
The Explanation of the Second Diagram
The Explanation
First, make a cubic rack as a. In the front of the rack is fixed a vertical shaft, as e. In the middle (of it) is a big wheel, as i. Around the wheel, there are helical teeth, as o. On its upper surface are upright teeth, as u. On the lower end of the vertical shaft, there is a star-shaped wheel (toothed wheel), as c. Close to each side of it is an upright pole, on both of which is also set a star-shaped wheel apiece, as ch. Above these two star-shaped wheels aside are two (pulley-style) wheels, as k, for ropes to wind up. Close to the big worm wheel is set a vertical wheel, as p. Its teeth engage with the upright teeth of the big wheel. The shaft of the vertical wheel has a long screw (worm), as t. Close to this long screw is a big vertical wheel, which also has helical teeth, as j. On the two sides of it are tied ropes attached to a weight, as a. There is a crank of the screw (worm), as f, in front outside of the big wheel on the vertical shaft. With one person turning it, the weight is moved. Beneath every weight, there are long wooden rollers, as g. (The weight) moves forward with the rollers rolling and supporting successively. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+28+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=28 |
| Comment: | Chapter 3, Explanation of the Third Diagram of Weight Hauling:
**This diagram is a copy of figure 30 on p.106 in Besson’s book. WT simplified the original figure by omitting one person and background, and by transforming the heavy object into a large rock. |
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| Translation: | The Third Diagram of Weight-hauling
The Explanation of the Combined Diagram
Explanation
Firstly, make a big flat vehicle, beneath which are set removable long wooden rollers, as a. At the two sides of the front of the vehicle are set oblique (side) poles. On (the two poles), there is a shaft. At each end (of it), are cross wooden sticks, as e. In front of it, make another two vehicles. Each of them is like its own style, as i and o (show). However, the front two empty vehicles, when used, stay unmovable temporarily and wait for the loaded vehicle to approach. Then carry and move them forward. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+30+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=30 |
| Comment: | Chapter 3, Explanation of the Fourth Diagram of Weight Hauling:
**This diagram should be a copy of Plate 48 in Verantius’ book (1615). WZ drew the rims and spokes of two wheels thicker than those in Verantius’ book. Comparing WZ’s diagram with Verantius’ plate, WZ added a short rod which is held by a person. He made another person see back.
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| Translation: | The Fourth Diagram
The Explanation of the Fourth Diagram
The Explanation
Make big wheels; two wheels are set on one shaft one by one. At the middle of the shaft is tied a big barrel or other weights. With a long rod attached to the shaft, the shaft doesn’t turn, while the two wheels do. One person shoulders the rod and draws it. Or set a crossbar on the top of the rod, and one person pulls it. Both are feasible.
Explanation
Make two small wheels, between which there is a shaft with a rod attached. At the middle of the rod is hung a big barrel or other weights. One person shoulders it and draws. Or pulls it by the means of a crossbar. Both can (work). |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+32+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=32 |
| Comment: | Chapter 3, Explanation of the First Diagram of Weight Hoisting by Rotating:
**This diagram is a copy of Plate 85 in Ramelli’s book. WZ’s explanation is similar to Ramelli’s Chapter 85. WZ made an unclear copy of the cutaway ground where the mechanism is showed.
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| Translation: | The First Diagram of Weight hoisting by Rotating
The Explanation of the First Diagram
Weight hoisting by Rotating Explanation
First of all, make an upright pole. In the middle (of it) is made a square crank with the shape marked a. The upper and the lower part of the pole should be aligned straightly. The vertical branch of the crank at the side is the place for one’s hand to turn. Inside is a small (thin) shaft; outside is a wooden or bamboo pipe. Thus (it) can be turned easily. Either make a wheel below or make a wheel above in order to make a machine to hoist other weights by rotating. (How) to make it depends on people. At each of the two farthest ends of the upright pole is made an iron drill, which is installed in iron mortar in the rack. Then it can rotate without obstruction. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+34+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=34 |
| Comment: | Chapter 3, Explanation of the Second Diagram of Weight hoisting by Rotating:Chapter 89 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 89 in Ramelli’s book. WZ’s explanation is partly similar to Ramelli’s Chapter 89. WZ thought the big gear wheel can be regarded a flywheel that can help manpower. |
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| Translation: | The Second Diagram
The Explanation of the Second Diagram
The Explanation
First of all, make a big wheel with teeth (around), as a, which is installed between two poles. Then, make a windlass, around which there are teeth that engage the teeth of the big wheel, as e. One person turns its crank outside of the pole. Then the weight can be lifted by rotating. If human power can’t manage, at one end of the windlass, (which is) close to the pole, is set a flywheel, as i. A flywheel, itself seeming useless, however, is one that can actually add power to the person with its weight. Therefore, (if) the windlass insufficiently turns it (the big wheel), add a flywheel. Then, human power must surpass (the need) a lot. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+36+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=36 |
| Comment: | Chapter 3, Explanation of the First Diagram of Water Lifting:Chapter 45 of the Various and Ingenious Machines of Agostino Ramelli.**This diagram is a copy of Plate 45 in Ramelli’s book. WZ omitted majority of the background in Ramelli’s plate, especially the above half background. WZ’s explanation is similar to Ramelli’s Chapter 45. |
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| Translation: | The First Diagram of Water Lifting
The Explanation of the First Diagram
Water Lifting
Explanation
Firstly, make a big vertical wheel, in which a noria is hidden, as a. It turns (lifts) water into a trough, as e. On the same shaft of the big vertical wheel, there is a second vertical wheel with teeth, as i. Secondly, make three screws which are settled upward in proper order, as o, u and c. At the lower end of the first screw, there is a small drum wheel (lantern) which also has teeth, as ch, and with its teeth engages the teeth of the second vertical wheel. At the upper end (of it), there is another small wheel with teeth on one side, as k. Then, (with its teeth) (it) meshes the teeth of the wheel on the lower part of the second screw. The teeth of the wheel at the upper end of the second screw mesh properly with those of the wheel on the lower part of the third screw. Thus, water naturally goes upwards.
Screw-making is described in detail in Taixi Shuifa (Hydraulic technology of the Far West) |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+38+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=38 |
| Comment: | Chapter 3, Explanation of the Second Diagram of Water Lifting:Chapter 47 of the Various and Ingenious Machines of Agostino Ramelli.**This diagram is a copy of Plate 47 in Ramelli’s book. WZ omitted most of the background in Ramelli’s plate. WZ’s explanation is similar to Ramelli’s Chapter 47. |
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| Translation: | The Second Diagram of Water Lifting
The Explanation of the Second Diagram
Explanation
First of all, make a big vertical wheel. Make three wheels with teeth, which are set upward one above another. (They) separately mesh with the teeth of gears at the upper ends of three screws. At the lower end of the pole, there is a horizontal wheel. Each tooth of the wheel is made of a piece of vertical board, whose outer part is curved like a spoon set against where the flow of water rushes. Water rushes against its spoons, and the spoons are pushed one after another. Then the big vertical pole rotates naturally and the three screws can naturally lift water in turn. However, each screw rotates in its trough, which means the worry of a leak causing inconvenience. Therefore, in advance, in each trough is made and fixed tightly an empty pipe, whose upper part and lower part are beyond (the height of) the trough. The screws rotate in the pipes so it won’t let the stored water leak, which is very subtle. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+40+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=40 |
| Comment: | Chapter 3, Explanation of the Third Diagram of Water Lifting:Chapter 61 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 61 in Ramelli’s book. WZ omitted the background in Ramelli’s plate. WZ were not good at the copy of detailed mechanism and the cutaway ground where the mechanism is showed. Ramelli drew a nozzle as a pipe held in mouth of a human head, while WZ drew the nozzle as the head of dragon.
WZ’s explanation is similar to Ramelli’s Chapter 61, but it is simpler. WZ emphasized heng sheng che in Tai Xi Shui Fa.
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| Translation: | The Third Diagram
The Explanation of the third Diagram
Explanation
Firstly, make a frame for a flywheel. Secondly, at both ends of the shaft of the flywheel is fixed an iron crank. But one (crank) end points up and the other down. (Their directions) must be made opposite. Therefore, by one (crank) end (the shaft) is joined to a wood (rod) that can move up and down at the top of the water-lifting rod of a suction lift-pump. At the other (crank) end, human power is used to turn it. Thus, water can be lifted. The flywheel is the wheel that can help a person exert strength.
The making of a suction lift-pump is also described in detail in Taixi Shuifa (Hydraulic Technology of the Far West). |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+42+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=42 |
| Comment: | Chapter 3, Explanation of the Fourth Diagram of Water Lifting:Chapter 61 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 73 in Ramelli’s book. WZ omitted the background such as field in Ramelli’s plate. WZ almost did not draw the cutaway ground.
WZ’s explanation is similar to Ramelli’s Chapter 73.
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| Translation: | The Fourth Diagram
The Explanation of the Fourth Diagram
Explanation
The water in a well can’t move up. First of all, make a windmill to take the place of persons and animals. The windmill is one that has a shaft which is just above the well to rotate the bailing buckets to lift water in the well. However, in this drawing, the structure of the bailing bucket is not that of the bailing bucket which is often used in this (well). Instead, it is a long pipe going through down to the bottom of the well. There is a shaft at the bottom of the pipe. In the pipe, there is a rope stringing many leather balls like eggs. Both the up and down ends (of the ball) are small, so as to move up and down in the pipe. The shape (of the bailing buckets) is like a string of pearls. Their number is not limited, and only depends on the extent to which the rope can hang down into the water at the bottom, then turn backward in the pipe up to the pool at the top of the well and the rope can circle endlessly. The shaft is turned by means of the wind-wheel, and the shaft rotates the rope of leather balls from (around) the shaft at the bottom of the pipe and upward successively, filling it (the pipe) with water in proper order, and (making water) directly stream up continuously from the pipe and then pouring it (water) down into the pool at the top of the well. The methods to make the balls and the pipe are shown in detail as in the separate figure besides the drawing. The structure of a windmill has many styles, which are later described in detail in other drawings on grinding mills.
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=44 |
| Comment: | Chapter 3,Explanation of the Fifth Diagram of Water Lifting: Chapter 112 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 112 in Ramelli’s book. WZ had their understanding of the operation of the device and changed the action of some persons in diagram, for example, two left persons below. WZ omitted a part of background in Ramelli’s plate, and drew the water wave outside pool in different styles. WZ’s explanation is similar to Ramelli’s Chapter 112. |
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| Translation: | The Fifth Diagram of Water Lifting
The Explanation of the Fifth Diagram
Explanation
Make a long trough with wide front and narrow back. At its middle is settled horizontally a shaft. At its front end is fixed a wooden spoon. There are rings on the spoon, which are linked to a thwart wood (shaft) at the upper side of the front of the trough. There is a small long board under the front end of the trough, as a. The spoon is plunged into water and filled. Up at the high place, (the spoon) has to empty and pour (the water) out depending on the small long board alongside (the spoon) below.
Formerly, I myself even made an instrument to channel water. One name (of it) is heyin, the flume-beamed swape; the other name is huojiegao, moving counterweighted bailer bucket. Its structure is completely identical to this (machine). However, a spoon is used at the front end of this (machine), which is cleverer. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+47+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=47 |
| Comment: | Chapter 3, Explanation of the Sixth Diagram of Water Lifting:Chapter 45 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of figure 46 on p.122 in Besson’s book. WZ changed the projectional direction of the top of Besson’s machine and simplified partly the bracket and the background of the machine. |
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| Translation: | The Sixth Diagram of Water Lifting
The Explanation of the Sixth Diagram
Explanation
First of all, make a square vertical rack. (Its height) depends on the extent, to which the water barrels at the two ends of the beam of a balance can rise to a high place to pour water, as a. Under this (beam), in the center of the rack in water, a square stone is used to settle an iron pit (in), as e. In the pit is set an upright pole, at the lower end of which is an iron drill. On the lower part of the upright pole is fixed a big wheel with vertical boards, as i. A little above it, settle an obliquely cut semi-conical cam, one oblique part of which gradually goes down while the other gradually goes up, as o. On the semi-conical cam, there is another pivot in the center of the shaft of the semi-conical cam below, as u. A little above the pivot, cut a long aperture in the middle (of the pivot), (in which) a shaft is horizontally fixed, as c, running through the center of the beam of the balance to make it (the beam) up and down. The upper end of the pivot is settled to the upper beam of the rack and is not allowed to be moved, as ch. Then, (the exterior of the beam) at the two sides of the beam of the balance, which are close to the sliding face of the first quarter (the contour rod) of the semi-conical cam, are protected with round wooden (rods) or sawali to make them smooth and lustred without sticking, as k. At each of the two farthest ends of the beam of the balance is installed a bailing barrel, as p. However, lower rods must be fixed transversely beside (the ends of) the beam for a bucket to link with, as t, then, without bringing any obstacles to the body of the beam. Moreover, it is convenient to pour water into a trough. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+50+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=50 |
| Comment: | Chapter 3, Explanation of the Seventh Diagram of Water Lifting:
**This diagram is very similar to plate No.17 before p.52 in Zeising’s book. The structure of the spoon is closer to that of the device on p.112 in Zonca’s book, but in Zonca’s plate there is only one operator. There is no rope in both Zonca’s device and Zeising’s device. The background of the device WZ drew is different from both Zonca’s and Zeising’s. We wonder whether WZ selected the diagram from another western source or he rearranged the background on purpose. |
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| Translation: | The Seventh Diagram of Water Lifting
The Explanation of the Seventh Diagram
Explanation
Firstly, make a two-upright-pole rack as a. Between the upper ends of the upright poles, there is a shaft. Secondly, make a big wooden spoon, as e. At the edge (of it) there are two ears (ear-like rings), through which a thwart wood (piece) passes, as i. The handle of the spoon is the channel for water to run out, which is just passed through by a shaft between the upright poles and can turn upward and downward, as o. The thwart wood (going) through the two ears is linked to the front end of the swape (boom), which stands aside, with a rope. At (its) back end, there is a hanging wooden (bar), in which many holes are cut in order to insert a wooden handle according to the convenient height for a person (who draws the handle down) to exert strength. This machine can lift much more water. Changing the beam of the swape is another clever approach, according to the intention of the people. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+52+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=52 |
| Comment: | Chapter 3, Explanation of the Eighth Diagram of Water Lifting:
**This diagram is a copy of plate No.16 after p.51 in Zeising’s book or the plate on p.110 in Zonca’s book. Zeising’s device is very close to Zonca’s device. Some parts of WZ’s machine were drew unclearly or in error. In particular, WZ had misunderstanding of the crank, the piston and the rod of piston. He also omitted the background of the machine.
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| Translation: | The Eighth Diagram of Water Lifting
The Explanation of the Eighth Diagram
Explanation
First of all, make a drum-treadmill, in which a person treads, as a. At each end of the center shaft of the drum-treadmill attach a crank. One side (of crank) bends upward while the other bends downward, as e. On the rod which is (inserted) in the square hole of each crank attach a pulley, as i. At the place where the pulley passes through is a vertical circle, whose lower end is fixed to the top of the water-lifting rod of a suction lift-pump, as o. When the drum-treadmill is rotating, one (crank) naturally falls while the other rises, and water can be lifted up successively. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+54+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=54 |
| Comment: | Chapter 3, Explanation of the Ninth Diagram of Water LiftingChapter 109 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 109 in Ramelli’s book. Ramelli drew only the head of the second person who drives a crank of the machine, but WZ changed the figure of this person and drew his whole body. WZ’s explanation is similar to Ramelli’s Chapter 109, and more complicated than Ramelli’s.
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| Translation: | The Ninth Diagram of Water Lifting
The Explanation of the Ninth Diagram
Explanation
First, make a star-shaped wheel, as a. A star-shaped wheel is a wheel along the rim of which big round teeth are made. The distance between two teeth is as long as the width of each tooth; and round holes are also made (so that the wheel) is similar to a big shining star with rays of light, therefore it is named star-shaped wheel. Out of the star-shaped wheel is made a drum casing, as e. The drum casing is a box, the upside and downside of which are combined into a circle, and the two sides of which are covered with wooden board. Its shape is like a drum, therefore it is called a drum casing. In the middle of the bottom of the drum casing is cut a small hole to let water enter, as i. On the top of the drum case is cut a square aperture, as o, in which is inserted a square wedge with a square upper end and a round lower end. At both sides of the square wedge is fixed a small pulley, as u, which makes the square wedge easily rise and fall. The rack is shown as c, where the drum casing is fixed and the square wedge is set to move up and down. In front of the square hole with the square wedge (inserted in) is cut a hole facing up, to which a pipe is fixed obliquely, as ch, in order to let the water run out. Firstly, set the star-shaped wheel in the drum casing. Make sure the standard is that the two sides of the star-shaped wheel and the round parts of the gear at the rim of the wheel are close to the circle and the (side) board of the drum casing. The shaft of the star-shaped wheel directly reaches out of the rack at its two sides (which is used to fix the star-shaped wheel) with cranks, as k. It is convenient for people to turn. Or make another water-driven wheel to turn this star-shaped wheel. It is not impossible, because the rack of the drum casing is set in water, water enters naturally from the small hole below. Therefore, (the water) is turned upwards successively by the star-shaped wheel to the place where the round end of the square wedge is hanging, and the water can’t go on passing and move forwards, but only flow out from the oblique pipe. |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=56 |
| Comment: | Chapter 3, Explanation of the First Diagram of Grinding-mill:Chapter 123 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 123 in Ramelli’s book. WZ’s explanation is similar to Ramelli’s Chapter 123. However, WZ paid attention to the construction of the machine, and added their own understanding of it to the diagram. The last sentence was added to the explanation by WZ.
Plate No.3 after p.23 in Zeising’s book (Part III) is very close to Ramelli’s Palte 123 except the background of the machine.
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| Translation: | The First Diagram of Grinding-mill
The Explanation of the First Diagram
Grinding-mill
Explanation
Make a big wheel with teeth along the rim, and spokes inside, as a. Only the shaft (of the wheel) is set obliquely so that the wheel naturally turns obliquely. Then, on the top of the upright rack at the two sides of the inclined wheel is set a transverse beam, as e. One person, with his hands to hold the beam and his feet to tread on the spokes, wants to step up but cannot. Therefore, the wheel has to turn naturally, as i. Beyond the wheel, set another small wheel which engages with its teeth those of the big wheel. The shaft of the small wheel is linked to the pivot of a grinding-mill with their teeth engaging each other. Then the millstone has to turn. This is one of the (methods) in which strength is exerted less and the person can’t be too fatigued. |
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| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=58 |
| Comment: | Chapter 3, Explanation of the Second Diagram of Grinding-mill:Chapter 124 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is almost a copy of Plate 124 in Ramelli’s book. Obviously, there are some differences between WZ’s diagram and Ramelli’s plate. Firstly, the projectional direction of WZ’s diagram is contrary to that of Ramelli’s. Secondly, the rim of driving wheel in WZ’s diagram is open. Thirdly, the action of the operator is different from that in original plate. Some detailed parts and background had been changed by WZ. WZ’s explanation is a simple summary of Ramelli’s Chapter 124.
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| Translation: | The Second Diagram
The Explanation of the Second Diagram
Explanation
Make a big drum-treadmill. The explanation of a drum-treadmill has been introduced before. But this drum-treadmill is so large that it can contain two people to tread side by side. At either side of the drum-treadmill is settled a small wheel with teeth apiece to revolve the pivot (of a millstone) successively. Then, the two millstones can turn together. One look and it is naturally clear. Therefore, there is no need for detail. |
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| Comment: | Chapter 3, Explanation of the Third Diagram of Grinding-mill:Chapter 128 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 128 in Ramelli’s book. There are some errors or misunderstanding in WZ’s diagram. The person on the left side acted a little differently from Ramelli’s. In WZ’s diagram, the connecting rod on the left side seems to pass a vertical pole, the position of the rocker on the right is different from that in Ramelli’s. WZ’s explanation is similar to Ramelli’s Chapter 128. However, WZ did not repeat how to raise or lower the upper stone of the millstone.
Plate 128 in Ramelli’s book is the same as plat No.1 after p.11 in Zeising’s book (Part III).
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| Translation: | The Third Diagram
The Explanation of the Third Diagram
Explanation
An iron crank is fixed on the lower (side) of the pivot of a millstone, as a. Again, on the lower part of the pivot (crankshaft) is set a cross of wooden poles. At each end of both poles is fixed a lead weight, as e. At the end of the pivot (crankshaft) is fixed an iron drill which is in an iron pit, as i. To the middle of the crank (crankshaft) is linked a wooden rod, at either end of which there is a turning ring, as o. One turning ring is linked to the rod which a person pulls by hand, as u. This rod pulled by the person is linked with its upper end to a rack. The vertical rod also has a shaft, as c. One person pulls the wooden rod in his hand obliquely, which can be (swung) forward or backward. And, the lead weights at the cross on the lower part of the pivot are the helpers. Then the millstone can rotate naturally. If the stone is heavy, add another crank at the opposite side and another person is needed to pull it face to face as in the above method (the first person did). And there is still surplus power. |
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| Comment: | Chapter 3, Explanation of the Fourth Diagram of Grinding-millChapter 130 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 130 in Ramelli’s book. WZ’s explanation is very similar to Ramelli’s Chapter 130. But WZ emphasized counterweight less than Ramelli. WZ added the last paragraph to the translation of Ramelli’s explanation.
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| Translation: | The Fourth Diagram
The Explanation of the Fourth Diagram
Explanation
A millstone is entirely like a common one. Only is there an upright pole at one side, on which is set a big vertical windlass wound with a rope to hang a weight, as a. Above the windlass is settled a horizontal wheel with vertical teeth along the rim (on the lower surface), which is to turn the vertical wheel that turns the pivot of the millstone, as e. Below (the windlass) there are cross poles (capstan). Wait until the weight hangs down to the ground, push the poles with human power. Thus, the weight can move up again, as i. Beside the upright pole, there is another vertical rack with a crossbeam on the top, as o. In the middle of the crossbeam is cut a long aperture, in which are fixed three small pulleys, as u. Above the falling weight, there is a small vertical frame with two small pulleys set in, as c. The rope to wind on the big windlass on the upright pole turns horizontally and passes through under the pulley that is set on a small rack standing aside, as ch, and sequentially goes up above it. (It) passes through the first pulley on the left on the crossbeam and turns downwards; then (goes through) under the lower pulley in the small vertical frame and turns upwards, passes through the second pulley, the one on the right, on the crossbeam and turns downwards; again, it goes through under the upper pulley in the small vertical frame and then turns upwards, passes through the third pulley, the middle one, on the crossbeam and turns downwards, then is tied onto the small beam at the top of the small vertical frame, as k. There is a ring on the small beam at the lower end of the small vertical frame. On the top of the falling weight there is a hook, which hooks the ring, as p. While the weight falls, the millstone rotates naturally. So many small pulleys must be used in order to make the falling weight always fall down so slowly and not easily touch the ground so that the millstone can rotate more times. The falling weight with another small weight added below is in order that people can increase or decrease (the amount of the small weight) depending on their number (how many people there are).
This self-turning mill that I expected to make and try before is very convenient. Today, (I) get this one. In fact, it is the same as that I thought of before. However, this slowly-falling-weight method couldn’t be dreamed of before. |
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| Comment: | Chapter 3, Explanation of the Fifth Diagram of Grinding-mill:
**This diagram should be a copy of a plate in Zonca (between p.88 and p.89), but WZ simplified the plate and selected merely the main content. For example, he drew only one horse by canceling at least two persons and the other horse that drives the mill, and omitted the background of this type of field mill. In addition, spokes of wheels in WZ’s diagram are less than those in Zonca’s plate.
It is worth while noticing differences of the 5th diagrams among editions of QQTS. There is the head of a person outside the left mill room in Lai Lu Tang edition. There is no person or his head outside the left mill room both in the edition with the preface of Wang Yingkui and in Shou Shan Ge Cong Shu edition. Some lines were transformed into ropes in Shou Shan Ge Cong Shu edition. This indicates that new compiler misunderstood the structure and transmission mechanism of the field mill.
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| Translation: | The Fifth Diagram
The Explanation of the Fifth Diagram
Explanation
If many people travel far away, these millstones are carried in a carriage as in the above drawing. The two pgass of millstones are set at the two ends (of the carriage), between which is set a big upright pole. Under it is set a horizontal wheel with teeth, as a. At the lower end of its shaft, there is an iron drill, which is set in the iron pit in the center of the even wood in the carriage. At each of the two sides of the teeth of the (toothed) wheel is set a small wheel with teeth, which horizontally revolves the pivot of each pgas of millstones at either side. On the upright pole over the horizontal wheel, set horizontally a wooden crosspiece, in the middle of which a hole is cut and (the pole stands) upward. Set a crossbeam on top of it, as e. The two ends of the crossbeam are beyond the carriage and each is linked to a hanging vertical pole, as i. With a horse turning the two vertical poles, the two millstones can revolve naturally. When the carriage goes, it can concurrently carry other baggage. Therefore, it is very convenient.
I think that if the crossbeam is made into a cross, then four fans can be used. Either set them up on the carriage or hang them outside around the carriage. They can work as windmills. |
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| Comment: | Chapter 3, Explanation of the Sixth Diagram of Grinding-mill:
**This diagram is a copy of the driving wheel in Plate 23 in Verantius’ book (1615). WZ omitted the rooftop, the wall and mills on the right side of the original plate. The driving wheel is the power of two mills.
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| Translation: | The Sixth Diagram
The Explanation of the Sixth Diagram
Explanation
Make a big wheel, along the outer rim of which are fixed cross bars, as a. There is a long shaft inside. At the two ends are set two vertical wheels, which have their own teeth to revolve the teeth (rundles) of the lantern wheels on the upright pivots of two pgass of millstones, as e. Three people are arranged to hold a crossbeam with their hands and tread, with their feet, the cross bars along the rim of the wheel. Thus, the two pgass of millstones turn. If only one pgas of millstones is used, then one person is enough. It depends on how people consider (it) and then act. |
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| Comment: | Chapter 3, Explanation of the Seventh Diagram of Grinding-mill:
**This diagram is quite similar to Plate 8 in Verantius’ book (1615). WZ simplified the stand, and changed the detailed structure of the fan a little.
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| Translation: | The Seventh Diagram
The Explanation of the Seventh Diagram
Explanation
A big wheel turns the pivots of the lantern wheels of two pgass of millstones, as a, which always use a general method. Only the shaft of the big wheel is a large upright pole. At the lower end of the pole, there is an iron drill which is in the mortar (shaped hole) on the ground. In the middle of the pole is set a big flat wooden rack, in the center of which is cut a round hole. The pole passes through the hole and goes up. (The size of the hole) depends on the extent to which the pole turns conveniently, as e. On the upper half of the pole, set two crossbars in two layers, each of them has a vertical bar, as i. Outside each of the four vertical bars, hang a big square frame with cloth, as o. These cloth frames can spread out and retract. Facing the place (from) where wind blows, they naturally spread out, and retract naturally after the wind. They spread out one by one and are gradually blown by wind. Therefore, the two pgass of millstones can turn naturally. On each surface of a cloth frame, there are two ropes tied obliquely, as u, for fear that the wind is so strong that the cloth won’t endure it, and tends to be damaged. |
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| Comment: | Chapter 3, Explanation of the Eighth Diagram of Grinding-mill:
**This diagram is almost a copy of Plate 9 in Verantius’ book (1615). In the aspect of the concrete structure of the wind-wheel, large gear and stand, there are some obvious differences between the diagram and the plate. For example, Verantius did not draw the whole wind-wheel, while WZ drew the whole wind-wheel with longer fans.
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| Translation: | The Eighth Diagram
The Explanation of the Eighth Diagram
Explanation
Its lower part completely follows a general method, except that the teeth of a big wheel can’t immediately reach the teeth of the lantern wheels on the pivots of millstones. Therefore, add another two lantern wheels separately. On the vertical shaft is set another wheel with teeth so that it is easy to touch the pivot of a millstone. The fan on it is a long triangle, as a. Two sides (of the fan) are made of thin wood board so that (the fan) is easier to be blown by wind and its power is especially strong. |
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| Comment: | Chapter 3, Explanation of the Tenth Diagram of Grinding-mill:
**This diagram should be a copy of the right part of Plate 10 in Verantius’ book (1615). WZ added pivots respectively to two end of the vertical shaft. He drew fans that are much like cloth. At least a part of working fans should be fell flat, but all the fans in WZ’s diagram are stand-up.
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| Translation: | The Tenth Diagram
The Explanation of the Tenth Diagram
Explanation
The others are completely the same except that on the upright pole is set a cross horizontally, whose rim is made like a wheel, as a. Along the rim of the upper surface of the wheel, wooden boards are used to make square fans, as e. One side of each fan has its own rope to tie tightly. When wind is blowing, the boards stand upright and turn naturally. But being tied by the ropes, (the boards) can’t move forward. Facing leeward, (the boards) naturally droop a little again, and can’t resist wind. |
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| Comment: | Chapter 3,Explanation of the Thirteenth Diagram of Grinding-mill :
**This diagram is very similar to Plate 22 in Verantius’ book (1615). There are still some differences of such detailed parts as the flywheel and the spokes of the vertical gear between. WZ simplified the background of the machine.
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| Translation: | The Thirteenth Diagram
The Explanation of the Thirteenth Diagram
Explanation
The others are completely as usual. Only on the vertical wheel which revolves the lantern wheel on the pivot of a pgas of millstones, set a long iron shaft, which is made into a square crank outside the rack, as a. At the farthest end of the iron shaft is securely fixed a wooden cross. Two ends (of each bar) are lead bobweights which make (the cross) heavy and easy to turn to add power to a person, like a flywheel. An iron ring is used to encircle the turn of the square crank. The two sides (of the ring) are both tied with a rope. One end of the rope is linked to the ring in the middle of a wooden bar, as e. The lower end of the bar is settled on the ground, where there is a ring which can turn, as i. Two persons pull their own bars face to face, which come and go alternately. With the flywheel to add power, the turn of the millstone is more convenient and saves labor. Compared with a person walking around outside the millstone (and pulling), (it can) save labor more than several times. |
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| Comment: | Chapter 3, Explanation of the First Diagram of Saw-will for Wood:
**This diagram is a copy of plate No.17 in Zeising’s book (Part III).
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| Translation: | The First Diagram of Saw-will for Wood
The Explanation of the First Diagram
Saw-will for Wood
Explanation
First of all, make a waterwheel and a rack, as a. One end of its shaft is outside the rack and is connected with a crank, as e. A vertical iron rod is linked to the crank; each end (of the rod) has a ring. The ring at the lower end encircles the farthest end of the crank while the ring at the upper end encircles the lower crosspiece (connecting rod) of a saw. The teeth of the saw are set in the middle. At its two sides, the upright poles linked to the crosspieces (of the saw) are in two vertical grooves from top to foot, as i. The outside waterwheel rotates, and then the crank goes up and down, and the teeth of the saw also follow it up and down. This is the method to saw wood. If (it) can make wood come close to the saw, then there are especially ingenious techniques in it, which must be explained in detail. Wood is laid on a rack, at the two ends of which there are four vertical upright poles to clamp wood, as o. And the rack is always set in a long trough, underneath which there are several small wooden rollers, as u. At the left extremity of the wood which is not sawed, there is a rope tied to the shaft of an iron wheel with inclined teeth under the rack, as c. At one side, there is a long rod, the tine of which has an iron blade to drive a tooth of the oblique-toothed (wheel), as ch. And (the long rod) is fixed at the lower part of a big revolving wooden pole far away as k (shows). At the upper part of the big revolving wooden pole, there is a small rod, which is also linked to the lower part of the lower (actually upper) crosspiece of the saw, as p. As soon as the saw moves up, (then it) will also carry upward the small rod on the upper part of the revolving wood (shaft), and the revolving wood (shaft) must obliquely turn a little, too, so that the long rod with an iron blade is bound to drive an inclined tooth and then come out above it naturally. Once the saw moves down, the revolving wood (shaft) must also turn downward a little obliquely, then, the edged rod enters below the next tooth at the same time. Drive the teeth by means of this while wrapping the rope on the shaft in this way. Therefore, the wood will come close to the saw. At the same time, worry that the inclined teeth of the wheel move up and back again, and then use a short edged iron rod again to follow closely and prevent it quickly, as t. All these are ingenious mechanisms which are too subtle to easily explain. |
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| Comment: | Chapter 3, Explanation of the Second Diagram of Saw-will for Wood:Chapter 136 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is a copy of Plate 136 in Ramelli’s book. WZ drew a part of detailed mechanism and background less clearly than Ramelli did. WZ’s explanation is similar to Ramelli’s Chapter 136. WT moved a small part of Ramelli’s explanation to the explanation of the first diagram of saw-mill for wood.
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| Translation: | The Second Diagram
Explanation of the Second Diagram
Explanation
Firstly, make a rack with upright poles and set a big waterwheel, as a. At the same shaft of the waterwheel is set another toothed wheel, as e. Its teeth on one side turn a lantern-wheel which is assisted by a flywheel, as i. The flywheel and the lantern-wheel are on the same shaft. At one end of the shaft, there is an iron crank, which is linked to the wood above, which pulls a saw, as o. The toothed wheel of the waterwheel also turns a little lantern-wheel at another side. At the same shaft, there is another little lantern-wheel turning successively, beside which is set a small toothed wheel, as u. This small toothed wheel successively rotates a small lantern-wheel above. At the same shaft of the small lantern-wheel, there is a sawtoothed iron wheel, as c. Then the shaft of the sawtoothed iron wheel is the one to which a rope is tied to turn wood and make it close to the saw. That blade, which prevents the teeth from coming back by means of the wooden piece at the upper end of the saw, swings aside and moves up and down, as ch. Its mechanism is somewhat the same as the first diagram. |
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| Comment: | Chapter 3, Explanation of the Third Diagram of Saw-will for Wood :
**WZ’s diagram is the same as pl.13 on page 89 in Besson’s book. WZ cut right narrow side of plate and a little part of its top.
WZ’s diagram is also quite close to Plate No.15 on p.39 in Zeising’s book, but there is another person at right side in Zeising’s plate. There are some small differences between WZ’s and Zeising’s.
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| Translation: | The Third Diagram
Explanation of the Third Diagram
Explanation
The rack on which a saw is set and wood is laid needn’t be explained in detail. The diagram itself is clear. Only in this rack, at each of its two sides, there is a big wheel with long spokes, as a. The extremity of each spoke must get close to and enter the rim of the wheel a little, which is moved by a person. Let a person move the little wooden bar that is set on one side of the wheel, which is easy to hitch (to the spoked wheel) and to rotate it. The two (spoked) wheels are connected with one shaft, around which a rope is wrapped to move the wood and make it close to the saw. These two wheels moved by people are also linked together with one shaft. But in the middle of the shaft is an iron crank, to which two long iron rods are linked. And they extend straightly to the long crossbars that move the saw up and down, as e. Outside each of the two shafts is symmetrically set a crank. Two people turn them and the saw can move naturally. And every time the wheel turns one circuit, the wooden bar rotates one spoke and the wood comes close to the saw. |
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| Comment: | Chapter 3, Explanation of the Diagram of Saw-will for Stone:Chapter 134 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is almost a copy of Plate 134 in Ramelli’s book. WZ simplified the rooftop. WZ’s explanation is similar to Ramelli’s Chapter 134, but he did not mention that a man always helps by throwing water and sand into the cuts.
Plate No.28 after p.14 in Zeising’s book (Part III) is very close to Ramelli’s Palte 134 without the rooftop.
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| Translation: | The Diagram of Sawmill for Stone
Explanation of the Sawmill for stone Diagram
Sawmill for Stone
Explanation
Provided there is a stone to be sawn into several pieces, then there is a rack, as a. Near one end in the rack, set a vertical shaft on which is settled a horizontal toothed wheel, as e. The horizontal wheel revolves a lantern-wheel at one side, as i. The lantern-wheel revolves the upper (part) of a small vertical wheel again, as o. Outside the shaft of the small vertical wheel, there is a crank, as u. The end of the crank is linked to a straight iron bar, at the two ends of which there are rings, as c. The ring at one end encircles the end of the crank; however, the ring at the other end encircles the lower end of a long wooden rod which pulls the saw. At the upper end of the long wood rod, there is a shaft which can rotate. (Two) wooden rods join the saw upright to the mobile pulley-styled rollers at the two sides, as ch. (The number of) saws can be two or three, all of which are made of excellent iron, but have no teeth. The lower ends of the two long wooden rods which pull the saw are connected with an iron bar, at the two ends of which there are rings, as k. One horse is used to turn the horizontal wheel on the vertical shaft. Then the crank will go and come and the saw will therefore move. |
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| Comment: | Chapter 3, Explanation of the Diagram of Vertical Trip Hammer:
**This diagram is a copy of figure 25 on p.101 in Besson’s book. There are only small differences between the copy and the original figure.
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| Translation: | The Diagram of Vertical Trip Hammer
Explanation of the Vertical Trip Hammer Diagram
Vertical Trip Hammer (Stamp Mill)
Explanation
Firstly, make a rack and set perhaps one, two, three or four pestles, as a. Below, mortars are used to hold each of them, as e. Secondly, make flywheels, the bigger one in the middle and the smaller ones outside, altogether are three, as i. The two ends of the long shaft of the flywheels stretch out of the rack separately and are fixed to cranks, as o. (Along) the two sides of the shaft are set little iron bars which are staggered up and down, as u. These iron bars correspondingly face every pestle, which has its own small swape-styled rod to catch the handle of the pestle, as k. (As to) one pestle or two pestles, one person turns the wheel from one side and then the pestles move up and down naturally. If there are more pestles, then it is naturally enough for two persons to turn them at two sides. |
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| Comment: | Chapter 3, Explanation of the Diagram of Revolving Bookcase Chapter 188 of the Various and Ingenious Machines of Agostino Ramelli.
**This diagram is almost a copy of Plate 188 in Ramelli’s book. WZ simplified the background of the bookcase and some detailed parts of the mechanism in Ramelli’s plate, example, he did not uncover the side of the bookcase, and omitted a group of small gear wheels in the right figure below.
WZ’s explanation is somewhat similar to Ramelli’s Chapter 188. But WZ’s explanation mainly described the construction of the bookcase, while Ramelli paid more attention to the usage and advantage of this device.
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| Translation: | The Diagram of Book Shelf
Explanation of the Revolving Bookcase Diagram
Revolving Bookcase
Explanation
First of all, make a big wheel, whose shape is the same as a drum casing, as a. Inside are toothed wheels, which are equal (in size) and nine in number. One wheel is (arranged) in each of eight directions, and another wheel is in the center. At the same time, in the interior encircled by the eight wheels, separately set eight equal small wheels, all of which have teeth. The wheel in the center revolves, then the eight small wheels turn naturally and the eight bigger wheels follow them (to turn). Its details are (depicted) in a partial diagram at one side, as e. The books are laid on the side shafts of the eight bigger wheels, and there are stands and shafts (for the books). Its details are (depicted) in the partial diagram at one side, too, as i. The big wheel is settled on a rack, as o. (If one) wants to read a certain book, then the book will naturally get close to the person as soon as the big wheel rotates. However, the other books, although having been turned, still freely rise and fall separately, and never turn upside down along with the wheel. |
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| Comment: | Chapter 3,Explanation of the Diagram of Anaphoric Water-clock:
**This diagram should be a copy of Plate 6 in Verantius’ book (1615). WZ changed the projectional direction of the rooftop, and deleted a dial plate. Numbers of the scale on dial plates were transformed into Chinese characters.
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| Translation: | The Diagram of Anaphoric Water-clock
The Explanation of Anaphoric Water-clock Diagram
Sundial (actually Water-clock)
Explanation
First of all, a small vat is used to contain water. Drill a little hole at its bottom and water flows out slowly. Set a small wheel above with a long shaft stretching out of a wall. A rope is wrapped on the wheel, at whose lower end is tied a heavy wood block, as a. However, it shouldn’t be too heavy. At its upper end is tied a small weight, as e. At the end of the shaft outside the wall is fixed a “sundial” (a calibrated dial and a hand), as i. As (the level of) the water slowly goes down, the heavy wood block must also slowly drop slowly, and (the hand of) the “sundial” rotates in accordance with time. This is a convenient method. |
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+108+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=108 |
| Comment: | Chapter 3, Explanation of the Diagram of Mechanical Cable Ploughing :
**This diagram is a copy of figure 33 on p.109 in Besson’s book. But WZ partly changed the figure. He omitted the farm cattle that draw the plough. He also cancelled the original background, but drew a Chinese styled farm field, including paddy field, tree and farm tools. He switched the projectional direction of the bracket on the right side. He made the side rim of wheels black. We can find such style of drawing in ancient Chinese books on machines (Xin Yi Xiang Fa Yao, and so on).
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| Translation: | The Diagram of Mechanical Cable Ploughing
The Explanation of t Mechanical Cable Ploughing Diagram
Mechanical Cable Ploughing
Explanation
First of all, make two racks with windlasses, as a. The two windlasses are tied with two long ropes, which thread through a plough, as e. Two persons rotate the ropes around the windlasses successively and another person operates the plough forward and back. The field can be ploughed naturally.
In the past, when I was engaged in political affgass at the Board of Revenue and Population, I used to make this thing according to my own imagination. It is unexpected that it and this diagram coincide so much. It may be said that it is the same as what I thought of before.before.
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| link | http://nausikaa.mpiwg-berlin.mpg.de/docuserver/digitallibrary/digilib.jsp?lib2/china/QiQi/Vol3+111+1++0/0 |
| link2 | http://nausikaa2.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.x.cgi?dir=schre_qiqit_X03_zh_1627&step=thumbpage&page=111 |
| Comment: | Chapter 3, Explanation of the Diagram of Water Shooter :
**The 1st diagram of water cannon
This diagram is a copy of Plate No.24 after p.72 in Zeising’s book (Part II).
**The 2nd diagram of water cannon
This diagram is a copy of Plate No.23 before p.71 in Zeising’s book (Part II).
**The 3rd diagram of water cannon
This diagram is a copy of Plate No.22 after p.70 in Zeising’s book (Part II). |
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| Translation: | The First Diagram of Water Cannon (Shooter)
Second Diagram
Third Diagram
Fourth Diagram
Explanation of Water Cannon Diagram
Water Cannon
Diagram
Explanation (Make the explanation from the partial diagrams)
First of all, find two copper cylinders, as a, A. The width of its section ranges from two cun to perhaps ten cun, which rests with people’s intention to make it. Its height is perhaps at least one chi, or at most one and a half chi. Its inside section must be equal from top to bottom. Its bottom should be the firmest and thickest and its gas holes, b and B. There is a valve either alongside or at the bottom or at the side near the bottom a little. However, it is more convenient at the bottom. Alongside (each cylinder) is settled a tube, which is bent a bit upward, as i and I. Each has small valves, o and E. Above (the tube), there is a trunk tube with two branches, as u, which tightly covers and joins with the tops of two bent tubes. Not (even) a tiny leaking crack is the criterion. There are four gas holes on the valves, two of which are at the water intakes and the other two at the outlets or intakes of the bent tubes. In addition, there are two pistons. c and M, whose handles are made of iron and whose disk, copper. The disk uses two layers of copper. The rim of the disk should be to the extent that (the disk) fills in the section of a copper cylinder. A criterion is that between the two layers of the copper disks, layers of soft leather are used to jam them. Both of the two copper cylinders are installed in a copper tank, the criterion is that they should be extremely stable and immovable. The bottom of the tank should be flat. If there is no copper tank, a big firm wooden barrel is acceptable. Above the two copper cylinders is set a crossbeam, as ch and e. In the middles of the two parts are set two iron holes, through which the two pistons pass and move up and down. At the center, there is an upright iron balance strut, at the top of which there is a small round hole for a turnable shaft. On (the shaft) is set a long wooden balance bar horizontally. The two pistons are linked to the bar with rings at the place where they move up and down. At the two parts (of the long wooden bar) are horizontally fixed more wooden poles so that more people can draw and lift. Furthermore, there is a small right-angled tube, as k and v, which is linked together with the outside of the water outlet of the trunk tube. It should be the tightest and can be circularly turned and to take itself to four sides and eight directions, all directions. Close to the middle (of the small tube), there is a small groove around. Insert short nails (into the groove) and be sure to make (the small tube) turn and not move upward. It must use the groove and nails because waterpower is the most powerful; otherwise, it will be driven away (by water). On this tube, there is another right-angled tube. But its spigot, pH, is a bit longer than that of kv. Its length is still at last three chi. The longer, the farther it extends out. However, the spigot must be a bit smaller than the body of the tube for the sake of the power of spraying water. At the place where the long right-angled tube and the short one are linked together, a groove and nails must be used, too, as in the method mentioned above. Then, one person can turn this tube with his hands either upward or downward or in the center or obliquely, and in all directions, it can spray water to the place on fire. This machine has two types, which can either be settled at one place as in the first diagram, or can be used with a boat or vehicle without wheels, as in the second diagram. The methods are all the same. There is another type. The machine is the same. However, it is on a vehicle with wheels, and there is no crossbeam used, but stick-shaped balances are used as the third diagram (shows). Man takes the circumstances into consideration and makes it at his discretion. As to the method to transport water, line many people. Every one can receive and pass the water in leather bags into the tank where the cylinders are, going on repeatedly without an end. Leather bags must be used to carry water. Compared with other containers, they are convenient and can’t be damaged.
This water cannon can put out a fire, keep out a fire and can prevent a fire. It is a new machine. Its capability is the most convenient, largest and the most wonderful. It is difficult for other machines to rival in terms of its functions. At the critical moment, when the fire is scorching, people can’t get close. But with this machine, then, five or six people can be used to take the place of several hundred people, and no drop of water will be wasted. However high and far, (water) can reach at once. It seems that heavy rain is pouring down in the sky, and no place is not soaked. Not only can it (be used to) put out the burning fire but also can prevent fire from starting to burn. Moreover, there are diagrams and explanation so that it is not difficult to make. It needs not very much labour and money. In every workshop, village, town and city should be set this machine two or three absolutely. It is the most beneficial to protect from calamities and keep out disasters. A model has been made and tested, and it proves to be good. The one, who desires to perform kindly acts to people, wishes to recommend and make it widely. |
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