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
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
"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 &
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
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,
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
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,
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,
3. The Introduction of Archimedean Mechanical Knowledge
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,
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
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,
(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
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:
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:
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,
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,
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
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
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
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
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
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:
"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)
"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
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 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
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
"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
(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 phonetic letters/names of missionaries and Chinese characters)
Aleni, Guilio 艾儒略
Beitang Library 北堂图书馆
von Bell, Johann Adam Schall 汤若望
Cao Chong 曹冲
Cheng Dawei 程大位
Chengwu Zhonglu Shu 称物重率术
Clavius, Christoph 丁先生
gang gan 杠杆
gewu qiongli zhi xue 格物穷理之学
Gujin Tushu Jicheng 古今图书集成
heng sheng che 恒升车
Jihe Yuanben 几何原本
Jiuzhang Lice 九章蠡测
Kunyu Wanguo Quan Tu 坤舆万国全图
li yi zhi xue 力艺之学
Li Zhizao 李之藻
Lin Zexu 林则徐
long wei 龙尾
long wei che 龙尾车
Longobardi, Nicclo 龙华民
Mao Zongdan 毛宗旦
Nalan Chengde 纳兰成德
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 Baocong 钱宝琮
Qian Yong 钱泳
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
Taixi Shuifa 泰西水法
Terrenz (Schreck), Johann 邓玉函
Tongwen Suanzhi 同文算指
Trigault, Nicolas 金尼阁
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
Yan Dunjie 严敦杰
Yang Tingjun 杨廷筠
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 Jie 重解
zhong xue 重学
Zhu Geng 祖暅
International Congress of History of Science, Mexico City, July,