Archimedean Mechanical Knowledge in 17th Century China

ZHANG Baichun
(Partner Group of Max Planck Institute for the History of Science)


1. The Origin and Backdrop of Transmission of Western Mechanical Knowledge into China

    Portuguese merchantmen appeared in Chinese sea area in the early 16th century. St. Fran?ois Xavier (1506-1552), a Spanish, arrived at an island nearby Guangzhou in 1552, but he was refused to visit the mainland of China. Almost 30 years later, Italian Jesuit missionaries Michel Ruggieri (1543-1607) and Matteo Ricci (1552-1610) were permitted to inhabit in Macao and successfully acquired opportunities to visit Zhaoqing and other cities in Canton.

     In order to convert the Chinese to Catholicism, Ricci practiced a special policy, namely European missionaries following Chinese customs and citing Confucian words to interpret papistic tenets. He introduced such scholar-bureaucrats as Xu Guangqi (1562-1633) and Li Zhizao (1565-1630) Western knowledge, especially scientific knowledge and technology, and also tried to affiliate with dignitaries to shoot for their help. Missionaries found that Western scientific knowledge, technology and arts could arouse Chinese people's interest of European religion and civilization. Ricci and Xu translated Euclidis Elementorum Libri XV (1574&1591), which had been annotated by Christoph Clavius (1537-1612), into Chinese, named it Jihe Yuanben (JHYB) . Li proposed that an institution should be set up to translate books from European languages into Chinese. He and Ricci translated Clavius' Epitome Arithmeticae Practicae into Chinese and consulted Cheng Dawei's Suanfa Tongzong. Finally, they compiled a book, Tongwen Suanzhi, which was printed in 1613.

     China paid more attention to agriculture and water conservancy. Xu Guangqi became a successful candidate in the imperial examinations at the provincial level in Ming-China in 1597. Seven years later, he became a successful candidate in the highest imperial examinations and joined the Imperial Academy. He was very interested in Western irrigation works Ricci had mentioned. In the light of Ricci's suggestion, Xu consulted Jesuit missionary Sabbathinus de Ursis (1575-1620) about Western water conservancy. Therewithal, they translated Western text into Chinese and compiled a book Taixi Shuifa (TXSF), which was printed in 1612. It depicted such water-lifting devices as long wei che, yu heng che and heng sheng che. Long wei che is water-screw. Yu heng che and heng sheng che are similar to pump invented by Hero of Alexandria (See: Zhang).

     Chinese had a little understanding of geography and culture in Europe, in Africa and in America in 17th century. On the basis of Ricci's map of the world and Didace de Pantoja's (1571-1618) and de Ursis' explications of it , a Italian missionary Giulio Aleni (1582-1649), assisted by Chinese scholar Yang Tingjun, compiled Zhifang Wai Ji (ZFWJ, Record of the places outside the jurisdiction of office of geography) in 1623, which introduced geography, climate, situation of the people, celebrities, products and dextrous devices in the world, including Archimedes and his inventions (See: Aleni, pp.76, 87).

     Every emperor in China attached great importance to the calendar took an particular place in Chinese tradition . Ricci used to suggest that the Jesuits should send missionaries, who are well versed in calendar, into China. A Belgian Nicolas Trigault (1577-1628) arrived in Macao in 1610, and got into other cities next year. He returned to Europe as ordered in 1613. He collected many books and instruments for Jesuit mission in China. A German Johann Terrenz (1576-1630) gave him help . Bringing about 7000 books and instruments, Trigault, Johann Adam Schall von Bell (1592-1666) and other missionaries arrived in China in 1619.

     Under the influence of Confucianism, a Chinese scholar Wang Zheng (1571-1644) had a sense of responsibility for progress of society. When he was young, he often turned ancient China's ingenious machines over and over in his mind, so that his studies of Confucian works were interfered. Round about the winter of 1615 or the Spring of 1616, he got acquainted with a missionary de Pantoja, and joined the Jesuits afterwards (See: Song). He read Aleni's ZFWJ so that he was very interested in remarkable people and wonderful things, such as Toledo's water-lifting devices and Archimedes' inventions. Round about December, 1626 or January, 1627, Wang Zheng came to Beijing and affiliated with Nicclo Longobardi (1559-1654), Terrenz and Adam Schall von Bell. He consulted to them to have a good understanding of machines depicted in ZFWJ. They recommended many European books on machines to him. Wang did not know European languages, but those books amused him very much, and then he asked for Terrenz to help him translate some of the books. According to Wang's record, Terrenz indicated connection between machines and such theoretical knowledge as mathematics:

    "It is not difficult to translate them. This kind of learning is part of such trifling skills as li yi (craft of force), but (we) must study mathematics and surveying before translation. Ingenuity of a machine rests with linear measure and number. Surveying comes into being because of linear measure; calculation comes into being because of number; proportion comes into being because of calculation. On the basis of proportion, man may make a through inquiry into principles of a thing. After that, a method is formed. If man does not understand surveying and calculation, he certainly cannot know proportion so that he cannot have a understanding of diagrams and explanations of the machine. There are some books on surveying. A book on calculation is called TWSZ. JHYB discusses proportion"(See: Terrenz & Wang, p.603)

    Helped by Terrenz, Wang roughly mastered necessary surveying and mathematics after he had spent a few days in studying them. Therewith, They selected many kinds of books on mechanical knowledge and translated some of them. Wang preferred to translate knowledge about "the most important, simplest and most ingenious" machines to serve Chinese people. In February or March, 1627, they finally compiled a 3-volumed book, Yuanxi Qiqi Tushuo Luzui (YXQQTSLZ, for short QQTS, Diagrams and Explanations of the Wonderful Machines of the Far West), which was first printed in Yangzhou in the summer of 1627.

     QQTS was the first monograph to introduce Western mechanical knowledge in Chinese. In the guide to its use, authors said that man must study such disciplines as zhongxue (study of weight), gewu qiongli zhi xue (a study to investigate things to attain knowledge, especially natural philosophy), surveying, mathematics and perspective before he studies the machine . They also wrote an introduction of zhongxue, namely li yi zhi xue (study of the craft of force), including Biao Xing Yan and Biao De Yan. Biao Xing Yan discussed the nature of mechanics, while Biao De Yan explained usage of mechanics.

     Following the introduction, there are three volumes that selectively expounded Western mechanical knowledge and machines from Archimedean time to the early 17th century). The first volume, which consists of 61 sections, was named Zhong Jie (explanations of weight). It discussed weight, center of gravity, geometrical center, specific gravity, buoyancy and other knowledge. The second volume including 92 sections was named Qi Jie (explanations of implements), which discussed the principles and calculations of simple machines, such as balance, steelyard, lever, pulley, wheel, screw and so on. The third volume consists of diagrams and explanations of 54 kinds of machines. Some of the above-mentioned knowledge was new for Chinese people.

     The Chinese government thought the most of calendrical knowledge introduced by Jesuits instead of mechanics. Chinese people originally were good at calendar-making, but calendar-making crisis occurred in the 17th century. The first vice minister of the Ministry of Rites, Xu Guangqi, began to take charge of making a new calendar in September, 1629. He invited Terrenz to help him make a calendar afterwards. After Terrenz died, Adam Schall von Bell and Jacques Rho (1590-1638) were retained by Xu. They had to work hard at the Bureau of Calendar to insure their foothold in China.

     A Belgian Jesuit Ferdinand Verbiest (1623-1688) was appointed the leader of calendar-making at the Astronomical Bureau in 1669. Having made six astronomical instruments, he finished a 16-volumed book Xinzhi Lingtai Yixiang Zhi (XZLTYXZ, A Record of the New-built Astronomical Instruments of Observatory) in 1674. The author mainly expounded his instruments and calendar-making as well as related mathematics and mechanical knowledge , including Galilean mechanics. He applied his mechanical knowledge to making pulleys and other devices to convey heavy weights. On an emperor's order, he made many ingenious tools and devices (See: Golvers, pp.112-114, 117-123).

     On the 16th October, 1683, Verbiest respectfully presented Emperor Kangxi with his new book Qiong Li Xue (mainly on natural philosophy), the great part of which was derived from translated books, mainly from QQTS (See: Wang Bing, pp. 88-101). Verbiest added only his translation of some texts to it.

     Although imperial government often restricted and even forbade any missionaries to missionize in the whole country, some Jesuits still served imperial court in the domains of such astronomy, clock-making and so on in the 18th century. However, there was a little improvement in the introduction of mechanical knowledge.

2. The Introduction of Archimedes

     While missionaries transmitted Western knowledge, they also introduced Ptolemy, Tycho Brahe, Archimedes and other celebrities sometimes.

     The authors of JHYB, TXSF and TWSZ did not mention Archimedes. In the early 1620s, Aleni described Archimedes (287-212 B.C.) as an astronomer in the section Sicily (Sicilia) in Yidaliya (Italia, Italy) of volume 2 of ZFWJ:

    "There was a famous astronomer Yaerjimode1. He had three unique skills. A few hundred ships of an enemy state once reached his island. His compatriots could do nothing about it. He made a large bronze mirror. When he focused sunlight on the enemy ships, they were emblazed. All ships were soon burned. Withal, the king ordered him to build a very large seagoing vessel. After it had been built, it should be launched. However, the vessel could not be moved although the country exerted itself to the utmost, namely applied tens of thousands of cattle, horses and camels to tow it. Jimode invented an ingenious skill so that the vessel was launched just as a hill was moved on the order of the king. In addition, he made an automatic armillary sphere with 12 overlapping rings that correspond the sun, the moon and 5 planets. It could accurately demonstrate the movement of the sun, the moon, five planets and constellations. This transparent instrument was made of glass. Indeed, it was a rare treasure." (See: Aleni, p.87)

    Here, Yaerjimode1 and jimode must be a transliterate of Archimedes.
Archimedes used to pursued his studies in Alexandria. Aleni described Archimedes as an inventor in the section Eruduo (Aigyptos, Egypt) of volume 3 of ZFWJ:

    "A king once sought a measure to combat a waterlogging. He found Yaerjimode2, a clever and deft man, who invented a water-lifting device. It provided people with incomparable facilities. It is named longweiche (water-screw) now. The people in this country were very tactful. Many of them studied gewu qiongli zhi xue, and were also accomplished in astronomy." (See: Aleni, p.110)

    Yaerjimode1 and yaerjimode2 respectively denotes two Chinese words, any of which was made from five Chinese characters. As two transliterations of Archimedes, these two words have the same pronunciation although their er and mo correspond different Chinese characters. It was possible that Aleni or his coagent regarded Archimedes as two persons.
The authors of QQTS retailed the story about Archimedes' building seagoing vessel and armillary sphere in ZFWJ. Volume one of QQTS mentioned another inventor:

    "There was a great personage who was named Yaximode. He invented water-screw, small screw and other devices. He was able to depict the principles of all kinds of machines." (See: Terrenz & Wang, p.611)

     Yaximode must be Archimedes.

     Volume one of QQTS also mentioned the crown problem, named Archimedes Yaximode:

    "No one is not delighted when he found an ingenious implement by chance. Yaximode once discriminated the reason why silver was mixed into gold, but he could not do it. While he had a bath, he suddenly thought out the reason. He was so delirious with delight that he ran to visit his king nakedly. This is an example." (See: Terrenz & Wang, pp.614-615)
    "There was an example of occasional understanding: A king ordered a craftsman to use pure gold to make an implement. The craftsman mixed silver into gold by stealth. The king want to get a clear understanding of it, but he failed. Yaximode occasionally cleared it up because of a bathe. (He) said that gold and silver are two kinds of things. They have different bulks. Gold is heavy but small, silver is heavy but large. Sink the implements into water, compare how much water has been remained. Thereupon, gold or silver implements were distinguished so that (the king) understood what had been wrong and the craftsman pleaded guilty." (See: Terrenz & Wang, p.612)

    In the 17th century, the last volume of Ouluoba Xijing Lu (XJL, Records of the European Written Calculation) repeated this question, but crown was changed to a cooking vessel (ding). The author named Archimedes Yaerribaila (See: Anonym, 17th century, p.302) . It is interesting that the fifth volume of Celiang Quanyi (CLQY, On Astronomical Surveying) named Archimedes "ajimide, a great personage in antiquity" or "mode, a personage in antiquity", its sixth volume named yaqimode . Afterward, Ajimide became a popular Chinese translation of "Archimedes".

     Consulting the works of such writers as Ricci and Aleni, Verbiest wrote Kunyu Tushuo (KYTS, Maps and Explanations of the World) in order to explain his Kunyu Quan (KYQT, map of the world). KYTS was printed in 1674. This book repeated the stories of Archimedes in ZFWJ (See: Verbiest, pp.6260, 6261, 6263).

3. The Introduction of Archimedean Mechanical Knowledge

(1) Water-screw

    Archimedes is associated with the invention of water-screw (Oleson, pp.291-301). In the first volume of TXSF, de Ursis introduced the water-screw into Chinese. His co-worker, Xu Guangqi, vividly named it long wei che :

    "So-called long wei che is shui xiang (water-restricting tool). It steers water ascend meanderingly. Long wei is made from six parts: the first part is named shaft. The shaft is the main rotational part. Water ascends from below along it. The second part is named wall. It channels water to ascend along it. The third is named wei (tube). Wei is a outer object. It surrounds or enclasps something (the wall). The fourth is named pivot, which is a rotational center. The fifth is named wheel, which is driven. The sixth is named underprop. It bears the pivot, on which wheel turns. No other than these six parts can constitute a machine. A deft man applies manpower or waterpower or wind power or animal power." (See: de Ursis & Xu, vol.1)

    Right along, de Ursis and Xu expounds the kinds of shaft, wall, wei, pivot, wheel and underprop, as well as their materials, manufacturing and usage. They presented the explanations of water-screw with five iconographs (figure 1).

    Terrenz and Wang not only explained the structure and usage of water-screw in the third volume of QQTS, but also analyzed its geometrical principle in the second volume. They used such Chinese words as tengxian (voluble rattan or vine), tengxian qi (implement like a voluble ratan) luosi (volution) and longwei to denote helix, screw or spiral. In the second volume, section 82 indicates the relation between a helix and a inclined plane: "an inclined plane wraps a cylinder, as a result, a helix or a screw comes into being" ; sections 83-85 indicate relation between lead angle of helix and transmission effect of force (See: Terrenz & Wang, pp.649-650). Sections 89-92 give a few example to illustrate how force or lead angle is calculated. Section 74 emphasizes that tengxian qi has many advantages and uses, thereby yaximode (Archimedes) often used this kind of wonderful implement. Man can easily make all kinds of machines if he understand the why and wherefores of this implement (See: Terrenz & Wang, p.648).

(2) Mechanical Propositions

     QQTS introduced western mechanical knowledge about floating and equilibrium and related calculations, including Archimedean propositions.

     Section 36 of the first volume: "Water floats along with surface of the earth that is a large round. Water adheres to the earth, so water's surface is round too."(See: Terrenz & Wang, p.625) This is similar to the Archimedean proposition 2 in On Floating Bodies (See: Archimedes, p.254).

     Section 40 of the first volume: "There is an object. If its benzhong (specific gravity) is equal to water's, it will not sink neither will it float, its top is at the same level as water's surface."(See: Terrenz & Wang, p.626) It almost repeats the Archimedean proposition 3 in On Floating Bodies (See: Archimedes, p.255).

     Section 41 of the first volume: "There is an object. If its specific gravity is lighter than water's, it will not totally sink; one part of it will be on water, another part will be in water." "Because water is heavier than the object, water may lift it up."(See: Terrenz & Wang, p.626) This is equal to the Archimedean proposition 4 in On Floating Bodies (See: Archimedes, p.256).

     Section 43 of the first volume: "There is an object. If its specific gravity is lighter than water's, the weight of total object will be equal to the weight of water, the volume of which is the same as the volume of the part of object that sinks in water."(See: Terrenz & Wang, p.626) It is close to the Archimedean proposition 5 in On Floating Bodies (See: Archimedes, p.257).

     Section 42 of the first volume: "There is an object. If its specific gravity is heavier than water's, object will not stop until it sinks to the bottom."(See: Terrenz & Wang, p.626) Section 46 of the first volume: "Solid in water is lighter than it in air. The weight difference is weight of the water, volume of which is occupied by the solid."(See: Terrenz & Wang, p.627) It is almost equal to the Archimedean proposition 7 in On Floating Bodies (See: Archimedes, p.258).

     Sections 44-61 of the first volume explain how to calculate weight and volume of an object in water, and discuss pressure of water. These calculations were scarce in ancient China.

     Section 19 of the second volume (explanations of the steelyard): "There are two weights that are in a state of balance. The proportion between the large weight and the small weight is equal to the proportion between the length of the long section and the length of the short section of the beam that is in level position. Likewise, the proportion between the large weight and the short section's length is equal to the proportion between the long section's length and the small weight." "This is the most cardinal principle of 'study of weight' (mechanics). All calculations are based on it."(figure 2) ( See: Terrenz & Wang, p.636)

     Section 36 of the second volume (explanations of the lever) almost repeats that principle: "A lever is horizontally supported by a fulcrum. There is a weight at its head. A force (li) acts on its handle. The proportion between the weight and the force is equal to the proportion of length between two sections of lever." (figure 3) (See: Terrenz & Wang, p.639) Here and in other sections, the authors used such concepts as li (force) or nengli (capacity) many times, both of them are interchangeable (See: Terrenz & Wang, pp.641-651). After section 36, this principle is applied to analyses and calculations of the pulley and wheel as well as other devices.

     The principle narrated in section 19 and section 36 actually is lever principle, namely Archimedean proposition 6 and proposition 7 in On the Equilibrium of Planes (See: Archimedes, p.192).

     Section 16 of the first volume: "There is a rectangle, center of gravity of which is at the midpoint of any radial line of two midpoints of subtenses."(See: Terrenz & Wang, p.621) This may be regarded as a special example of Archimedean proposition 9 in On the Equilibrium of Planes (See: Archimedes, p.194).

     Section 12 of the first volume: "There is a triangle. Draw a line from an angle to the midpoint of its subtense, well then the center of gravity of the triangle must be at the line. " Section 13: "There is a triangle. Its center of gravity is the same point as its geometrical center."(See: Terrenz & Wang, p.620) These sentences should be equal to Archimedean proposition 13 in On the Equilibrium of Planes (See: Archimedes, p.198).

     Section 14 of the first volume: "The method to find the center of gravity of a triangle is as following: drawing a line from the midpoint of any side to its corresponding angle. The center of gravity is at the point of intersection of two lines."(See: Terrenz & Wang, p.621) This is Archimedean proposition 14 in On the Equilibrium of Planes (See: Archimedes, p.201).

     Section 18 of the first volume: "The geometrical center of circle or ellipse is the same as it's center of gravity."(See: Terrenz & Wang, p.621) This is identical with Archimedean proposition 6 in The Method (See: Archimedes, supplement, p.27).

     Section 20 of the first volume: "The center of gravity of any regular prism is at its axis."(See: Terrenz & Wang, p.622) This is similar to Archimedean proposition 7 in The Method (See: Archimedes, supplement, p.30).

     The phraseologies in QQTS are different from the original dictions Archimedes used in his works mainly because Terrenz and Wang consulted some books printed in Europe in the 16-17th centuries instead of Archimedes' works. In addition, they did not translate European texts literally.

     According to H. Verhaeren's textual research, most of books upon which QQTS had been based were collected in the Beitang Library . The authors of some of the book gave them Terrenz as presents (See: Verhaeren). He identified that the first volume and the second volume of QQTS are derived mainly from Simon Steven's Hypomnemata Mathematica…Mauritius, Princeps Auraicus, Comes Nassoviac…, (1608) . The first part of the book, which discusses surveying, calculations, proportion and other geometrical knowledge, is identical with what Wang studied before the translation.

     However, Yan Dunjie thought that much of the second volume of QQTS is considerably identical with Galileo's Le Mecaniche (1600), and discourses on floating bodies is identical with Galileo's Discuso…intorno alle cose che stanno in su l'acqua (1612)(See: Yan. 1964). It is possible that Terrenz consulted Galileo's works in view of the relationship between them.

     Verhaeren additionally identified that some of the third volume of QQTS derived from Agostino Ramelli's Le Diverse e Artificiose Machine del Capitano (See: Verhaeren). Joseph Needham further investigated sources of the third volume (See: Needham, pp.211-225).

(3) The Crown Problem

    Chinese scholars regarded Archimedean crown problem as an arithmetic problem. The first Chinese book that introduced the crown problem was TWSZ, but it changed crown into lu :

    "Question: one hundred jin of gold is used to make a golden lu . When it has been finished, man doubted that a craftsman stole gold and mixed silver into gold. He would damage it to test it, but feared economic losses. How to find how much silver has been mixed into gold?

     The solution: A container is full of water. The water's weight is known. When the 'golden' lu of 100 jin is put in the water, water of 65 jin overflows the container. Do not put water in the container until it is full of water again. When pure gold of 100 jin is put in the water, water of 60 jin overflows the container. Do not add water to the container until it is full of water again. Put silver of 100 jin into the water, as a result, water of 90 jin overflows the container. Now, suppose silver of 40 jin is what the craftsman mixed into gold, arrange this number at the upper left corner (figure 4). Remaining gold in the lu is 60 jin, the number is arranged at the left line and is close to the upper left corner. The lu makes water of 65 jin overflow out of the container. According to the fact that pure golden (lu) makes only water of 60 jin overflow out of the container, gold of 60 jin in the lu should make water of 36 jin overflow out of the container. Additionally, according to the fact that pure silvern (lu) makes water of 90 jin overflow out of the container, the silver of 40 jin, which was mixed into gold, should make water of 36 jin overflow out of the container. So, water of 72 jin in all should overflow out of the container. Comparing 72 jin with original number 65 jin, man may get a surplus of 7 jin, and then arrange 7 lower at the left line. Withal, suppose silver of 30 jin is what the craftsman mixed into gold, and arrange the number at the upper right corner. Remaining gold in the lu is 70 jin, this number is arranged at the right line and is close to the upper right corner. According to the fact that pure golden (lu) makes only water of 60 jin overflow out of the container, gold of 70 jin in the lu should make water of 42 jin overflow out of the container. In addition, according to the fact that pure silvern (lu) makes water of 90 jin overflow out of the container, the silver of 30 jin, which was mixed into gold, should make water of 27 jin overflow out of the container. So, water of 69 jin in all should overflow out of the container. Comparing 69 jin with original number 65 jin, we have a surplus of 4 jin, and then arrange the number 4 lower at the right line. One surplus minus another surplus is a divisor (3). The upper right number times the lower left number is 210, and the upper left number times the lower right number is 160. The former minus the later is a dividend (50). The dividend divided by the divisor is sixteen and two-thirds jin, which is the weight of silver which the craftsman mixed into gold. In fact, there is only pure gold of eighty-three and one-third jin. A rate tells us, gold of eighty-three and one-third jin will make water of 50 jin overflow out of the container if gold of 100 jin makes water of 60 overflow out of it; silver of sixteen and two-thirds jin will make water of 15 jin overflow out of the container if silver of 100 jin makes water of 90 overflow out of it. 50 plus 15 makes 65, which is identical with the original question."(See: Ricci & Li, p.177)


    It is worth emphasizing that the above-mentioned calculation is identical with the yingbuzu method in Chinese mathematical tradition. The book XJL related the similar problem to Archimedes:

    "A monarch ordered a craftsman to use pure gold of 100 (jin) to make a cooking vessel (ding). The craftsman stole some of gold and mixed silver into gold. After the vessel had been finished, it was presented to the monarch. He noticed the gold's colour was light, whereupon he order an astronomer Yaerribaila (Archimedes) to calculate how much gold was stolen. The answer: gold of sixteen and two-thirds jin was stolen, gold of eighty-three and one-third jin remains.

     The solution: Yaerribaila received the order, but he could not think up a solution temporarily. He hesitatingly looked around. While taking a bath, he noticed that water overflowed and suddenly thought up a solution. He ran so delighted that he forgot he was still naked." (See: Anonym, 17th century, p.302)

     The calculating method in XJL is the same as in TWSZ. The only difference between the two is as follows:
    "60 times 4 is 240. 70 times 7 is 490. 490 minus 240 is 250. 250 is divided by 3 is eighty-three and one-thirds (jin), namely weight of the remaining gold. So, gold of sixteen and two-thirds is stolen."(See: Anonym, 17the century, p.302)

    Section 29 and section 30 of the first volume of QQTS introduced knowledge related to the crown problem: "There are two objects. Becaues they have the same weight and the same volume, they must be the same kind of weight." "The same kind of weights have the same specific gravity."(See: Terrenz & Wang, p.624)

4. The Differences of Mechanical Knowledge between Archimedes and the Chinese Tradition

     Comparing Archimedean mechanical knowledge with related knowledge in ancient China, we can find out that there are resemblance and differences between the two.

     So far, we have not found any trace of screw in ancient Chinese sources and archaeological materials. There was the square-pallet chain-pump instead of the water-screw. According to San Guo Zhi (History of the Three Kingdoms), Cao Chong (196-208 A.D.) used a boat to weigh up an elephant. He drove the elephant onto the boat, and made a notch on the side of the boat to show a waterline. Afterwards, he replaced the elephant with weights. Having weighing up the weights, he knew weight of the elephant (See: Chen, p.580). However, we have found no theoretical generalization that is similar to Archimedes' proposition 5 in On Floating Bodies.

     A theoretical analysis of lever problem was found in Mojing (Mohist) which came into being in the 3-4th century B.C.:

    The beam (heng)…. Explained by: gaining.

    The side of it on which you lay a weight will necessarily decline, because the two sides are equal in weight (zhong) and positional advantage (quan). If you level them up (xiang heng), the tip will be longer than the butt; and when you lay equal weights on both sides the tip will necessarily fall, because the tip has gained in positional advantage (quan) (See Graham, p.388).

    People of later time had different understandings and explanations for this exposition, it's controversial that if heng is unequal-armed steelyard. For example, Qian Baocong believed that the sentences are talking about steelyard, and a character bu, which means 'not', should be put in front of xiang heng (See: Qian). In Graham's opinion, the first sentence is referring to equal-armed balance, the second indicates moving of fulcrum brings 'the tip will be longer than the butt'. In any case, Mojing did not indicate any quantitative relation between weight and distance.

     A mathematician Zu Geng, who was active around 6th century, compiled Quanheng Jing (Book on the Balance) and Chengwu Zhonglu Shu (Methods of Weighing Objects), in which calculation of balance and steelyard was probably be mentioned. But these two books were missing, its content in detail is not known.

     In mathematical books formed at the end of Ming Dynasty, we finally find some exercises about balance of steelyard (namely lever). In 1592, Cheng Dawei (1533-1606) a 17-volume book Zhizhi Suanfa Tongzong (SFTZ, General Collection of Algorithms), into which a lot of calculations in business were collected. There were two exercises concerning steelyards on page 48 in volume 4 of this book:

Exercise 1
    "Now there is a pig. Because there is not a big steelyard, a steelyard of small size has to be used to weigh the pig, but the weight of pig exceeds weighing capacity of small steelyard. The weight of the original moving weight (of small steelyard) weighs one jin and ten liang. When weighing the pig, besides the original moving weight, put on another moving weight that weighs one jin and four liang and eight qian, then result indicated on beam of the small steelyard is 67 jin. How heavy is the pig actually?

Answer: The pig weighs 120 jin and 9 liang and 6 qian.

Algorithm: weight of original moving weight is 26 liang, weight of the second moving weight put on later is 20 liang and 8 qian, sum of them is 46 liang and 8 qian. The sum is multiplied by the number received, 67 jin, result is 3135.6 jin. This number then is divided by weight of the original moving weight, 26 liang, it turns to be 120.6 jin. 0.6 jin may be conversed into 9 liang and 6 qian."(See: Cheng, p.1288)

Exercise 2
"Weight of an object weighed on a steelyard is 8 jin and 2 liang. As original moving weight of the steelyard is lost, now intend to buy a new moving weight to fit the steelyard, but do not know how heavy the new moving weight. Well, weigh the object mentioned above with a moving weight of 2 jin and 5 liang. Then outcome received is 6 jin. What is the weight of the original moving weight?

Answer: the original moving weight weighs 1 jin and 11 liang and 3 qian.

Algorithm: when the new moving weight is used, the object weighs 6 jin. 6 jin may be conversed into 96 liang, multiply it by 37 liang conversed from 2 jin and 5 liang, the product received is then divided by 130 liang, conversed from 8 jin and 2 liang, result is 27 liang and 3 qian. This is the answer."(See: Cheng, p.1288)

    Cheng Dawei didn't explain how he deduced his formula. We can't be sure either he derived the answer to the exercise from ready formulas, or he summed it up from practices of steelyard-making and application. He didn't mention relations among dead weight of steelyard, center of gravity, null point and fulcrum . Although a weight indicated by scale on beam of the steelyard, namely a number of scale marks, is analogous to distances from a fulcrum to a spot where moving weight is hung, the numerical value of scale in Cheng's calculation was not of an exact concept of distance. Thereby what he focused on was algorithms, not mechanical meaning of the problems.

     Terrenz and Wang discussed much about mechanical concepts, propositions and calculating exercises, but they did not introduce the related proofs and other Archimedean propositions.

     Chinese sciential tradition seemed to lack such representations as conceptualization of knowledge about nature and constructing and proving propositions. Chinese people had abundant experiential knowledge about machines and engineering, but the knowledge was still not systemic in 17th century. However, European mechanical knowledge was systematizing into a learning step by step at that time. What Terrenz and Wang introduced just was the European zhongxue (study of weight). Biao Xing Yan of QQTS explained a few basic concepts: "li yi (the craft of force) means zhongxue"; "li (force) means strength or power"; "yi (craft) means a skill and an ingenious implements of exerting force"; "the unique function of zhongxue is to move weights"(See: Terrenz & Wang, p.610) Biao Xing Yan and Biao De Yan of QQTS gave emphasis to the relation between the craft o force and both mathematics and surveying:
    "Study of the craft of force is based on surveying and mathematics. All knowledge of the study follows some principles and rules, so only such study is exact."(See: Terrenz & Wang, p.614)

     Europeans tried to use their mathematics and created mechanical concepts to analyze simple machines and further to understand complicated machines. Such li yi zhi xue was a new system of ideas in 17th century China.

5. The Influence of Archimedean Mechanical Knowledge on China

     Reprints of such books as ZFWJ and QQTS reflected Chinese attention to western knowledge and its influence on China to a certain extent. KYTS and QQTS were included in Gujin Tushu Jicheng (GJTSJC, Collection of Ancient Chinese Books ) that was first printed in 1726. ZFWJ, KYTS and QQTS were included in Si Ku Quan Shu (SKQS, Complete Collection in Four Treasuries), which was compiled during the reign of Emperor Qianlong (1736-1795A.D.). QQTS was reprinted a few times in 19th century. Chouren Zhuan, which was completed at the end of 18th century, included a biography of yaqimode (Archimedes) that was a copy of Archimedean mathematical knowledge in CLQY (See: Ruan, p.507).

     GJTSJC and SKQS are all large-scale series of books that the imperial government organized to compile. Compilers' select and books' abstracts that were written by the compilers approximately reflect the attitude of mainstream of Chinese society to knowledge. The first volume and second volume of QQTS were deleted by the compilers of GJTSJC. Obviously, they paid much attention to practical technology instead of theoretical knowledge. The author of abstract of QQTS in SKQS said:
    "Both Biao Xing Yan and Biao De Yan exaggerated marvellousness of those methods. (In fact,) most of them are absurd and unrestrained, and were not worth cross-examining. But then machine building in the book is actually the most ingenious in history."(See: Anonym. 18th century)

     There was a similar evaluation of ZFWJ in its abstract in SKQS. Differences of knowledge structure between China and the Western are probably one of the main reasons why some of Chinese people misunderstood and did not recognize western mechanical knowledge .

     Before the end of 19th century, European mechanical knowledge did not become a part of elementary knowledge of Chinese society for it was neither included in educational system nor turned it into contents of the imperial examination. In fact, missionaries were protagonists of introduction and study of European mechanical knowledge. While western mechanics was introduced into China after 1840, many Chinese mechanical terms such as zhongxue, zhongxin (center of gravity), ganggan (lever), liuti (liquid) and luoxuan (screw, helix) were accepted by translators and researchers. The Chinese word lixue was probably an abbreviation of li yi zhi xue (study of the craft of force).

     Practical technology was much humbler than Confucianism, but practicers and some scholar-bureaucrats, who intended to deal with matters relating to agriculture and engineering, paid attention to it. Wang Zheng said in preface of QQTS:
    "Knowledge always is expected to do good to society, no matter how perfect or how rough is it. Man always is expected to go against the will of God, no matter where he comes from, China or the West. What are recorded here are trifling skills, they are beneficial to the peoples' livelihood and the nation's prosperity."(See: Terrenz & Wang, p.603)

     Wang became a successful candidate in the highest imperial examinations in 1622. Afterwards, he worked as an official at Guangping. He ordered craftsmen to make the water-screw and other machines.

     In 1630s, Xu Guangqi and his disciples finished a book Nongzheng Quanshu (NZQS, Complete Treatise on Agriculture), in which the depiction of a water-screw and pumps were copied from TXSF. He compared the water-screw with Chinese square-pallet chain-pump, and laid emphasis on advantage of the former (See: Xu, pp.577-594). After that, such scholars as Nalan Chengde (1654-1685) praised good function of the water-screw (See: Group, pp.89, 205-206).

     There were some accounts of manufacturing and use of the water-screw in 18th and 19th centuries. Xu Chaojun, a descendants of the 5th generation of Xu Guangqi, had a good grasp of astronomy and clock-making. A book, which printed before 1911, told us that he constructed a water-screw that could be driven by a child to irrigate crop in 1809. A procurator ordered some people to print drawing of the water-screw to popularize it in a few counties (See: Group, p.213).

     Qi Yanhuai (1774-1841) first held office as a county magistrate in Jinkui and afterwards as a prefect in Suzhou. According to his works, he constructed a water-screw and a pump on the basis of what TXSF had depicted. He believed that one water-screw is analogous to five square-pallet chain-pump (See: Group, pp.205-206). Lin Zexu (1785-1850), a dignitary in Jiangsu province , commended Qi for his construction. Lin suggested that this kind of machine should be spread in the countryside, but he failed.

     Makers and users found that the water-screw has also some disadvantages. Qian Yong told us a short story. A water-screw was made in Suzhou in 18th century. It may irrigate cropland of thirty or forty mu (a traditional unit of area) every day. However, It cost more than one hundred jin. The moment it was damaged, it could not be used. A majority of farmers was so poor that they were not able to make it (See: Group, p.209). Zheng Guangzu recorded that a water-screw was made in an area nearby the Great Canal in Jiangsu province in 1836. It was so large that it needed one hundred people to carry it. Many people drove it to irrigate cropland rapidly, but cost three thousand jin. It was not only expensive but also delicate (See: Group, pp.209-210). Craftsmen and farmers could skillfully manufacture, operate and repair traditional Chinese water-lifting devices that were actually not inferior to the water-screw in function. A ripe technical tradition seems to exclude new technology from other traditions to a certain extent.

     On all accounts, part of Archimedean mechanical knowledge exerted a limited influence on China in 17th century. It had partly been recognized by Chinese by the mid-19th century.

6. Conclusion

(1) As a walking stick of the European religion, scientific knowledge and technology including mechanical knowledge was introduced into China in 17th century.

(2) European missionaries and their Chinese co-workers selected and translated the water-screw, part of Archimedean mechanical propositions and relating calculations from western language into Chinese, but they did not introduced the other Archimedean propositions and the related mathematical proofs.

(3) Structure and representation of Archimedean mechanics was different from the Chinese tradition. Chinese paid much attention to depictions of phenomena and skills, calculations instead of mechanical propositions and their proofs. Theoretical analyses of the machine had hardly been recognized by most of Chinese scholars by the mid-19th century.

(4) Chinese people attached importance to such European inventions as clock. Craftsmen were concerned about skills, namely how to do. The water-screw and other European-styled machines had hardly been popularized by the second half of 19th century.

(5) Mechanical knowledge introduced by missionaries, especially theoretical analyses, had not been part of essential knowledge of Chinese society.


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Chinese Glossary
(Chinese phonetic letters/names of missionaries and Chinese characters)

Ajimide 阿基米德
Aleni, Guilio 艾儒略
Anhui 安徽
Beitang Library 北堂图书馆
von Bell, Johann Adam Schall 汤若望
benzhong 本重
bu 不
Cao Chong 曹冲
Cheng Dawei 程大位
Chengwu Zhonglu Shu 称物重率术
Clavius, Christoph 丁先生
ding 鼎
gang gan 杠杆
gewu qiongli zhi xue 格物穷理之学
Gujin Tushu Jicheng 古今图书集成
Guangping 广平府
heng 衡
heng sheng che 恒升车
Jihe Yuanben 几何原本
Jiangxi 江西
jin 斤
Jinkui 金匮
Jiuzhang Lice 九章蠡测
Kunyu Wanguo Quan Tu 坤舆万国全图
li 力
li yi zhi xue 力艺之学
Li Zhizao 李之藻
liang 两
Lin Zexu 林则徐
liuti 流体
lixue 力学
long wei 龙尾
long wei che 龙尾车
Longobardi, Nicclo 龙华民
luosi 螺丝
luoxuan 螺旋
Mao Zongdan 毛宗旦
mode 默德
Mojing 墨经
mu 亩
Nalan Chengde 纳兰成德
Nanchang 南昌
nengli 能力
Nongzheng Quanshu 农政全书
Ouluoba Xijing Lu 欧罗巴西镜录
de Pantoja, Didace 庞迪我
Qi Jie 器解
Qi Yanhuai 齐彦槐
qian 钱
Qian Baocong 钱宝琮
Qian Yong 钱泳
Qianlong 乾隆
quan 权
Quanheng Jing 权衡经
Rho, Jacques 罗雅谷
Ricci, Matteo 利玛窦
Ruggieri, Michel 罗明坚
San Guo Zhi 三国志
Shanhai Yudi Quantu 山海舆地全图
Si Ku Quan Shu 四库全书
Suzhou 苏州
Taixi Shuifa 泰西水法
tengxian 藤线
tengxianqi 藤线器
Terrenz (Schreck), Johann 邓玉函
Tongwen Suanzhi 同文算指
Trigault, Nicolas 金尼阁
Tunxi 屯溪
de Ursis, Sabbathinus 熊三拔
Verbiest, Ferdinand 南怀仁
Wang Zheng 王徵
Xavier, St. Fran?ois 沙勿略
xiang heng 相衡
Xinzhi Lingtai Yixiang Zhi 新制灵台仪象志
Xu Chaojun 徐朝俊
Xu Guangqi 徐光启
Yaerjimode1 亚而几默德
Yaerjimode2 亚尔几墨得
Yaerribaila 亚尔日白腊
Yan Dunjie 严敦杰
Yang Tingjun 杨廷筠
Yaqimode 亚奇默德
Yaximode 亚希默德
yidaliya 意大里亚
yingbuzu method 盈不足术
yu heng che 玉衡车
Yuanxi Qiqi Tushuo Luzui 远西奇器图说录最
Zheng Guangzu 郑光祖
Zhifang Wai Ji 职方外纪
Zhizhi Suanfa Tongzong 直指算法统宗
zhong 重
Zhong Jie 重解
zhong xue 重学
zhongxin 重心
Zhu Geng 祖暅


International Congress of History of Science, Mexico City, July, 2001