Authors: Michela Fontana
He continued as follows:
My country in the Far West, although small as far as its area is concerned, by far surpasses its neighbours by the strict analytical method by which the vari
ous schools study the phenomena of nature. . . . Savants only accept what has been proved by reason. . . . From the very first moment I set foot on Chinese soil, I noticed that those who study mathematics put all trust in their manuals, and that there is no discussion on fundamental issues. Without solid roots and firm fundaments it is difficult to build something up.
Ricci presented Euclid as the greatest mathematician of all time, the sage who had brought his discipline “to great perfection,” and the author of a book that had become “the daily food for the mathematician.” Nor did he fail to mention Clavius, the great commentator and translator of Euclid, referring to his former professor as Master Ding, the Chinese word for nail and hence equivalent in meaning to Clavius. Ricci asserted that the German Jesuit’s version of Euclid’s work was so soundly commented that it could be used as “a ford in the river . . . a bridge, a shelter in case of danger.”
In the preface to his Latin version of the text, Clavius had sung the praises of mathematics with great emphasis in order to persuade the Jesuit authorities of the need to include the discipline in the syllabuses of their colleges. Ricci did the same, omitting the philosophical arguments that were unsuitable for the Chinese public and instead lingering over an impassioned presentation of the innumerable applications of arithmetic and geometry. Clavius compared mathematics to a fountain from which the other branches of science gush; Ricci compared it to a ladder leading up to the peaks of knowledge. Mathematics, he wrote, makes it possible to penetrate the mysteries of the cosmos, to measure the breadth of the celestial spheres, to draw maps, to predict the course of the seasons, and to create the calendar. It all should be used by all, including men of state. How indeed is it possible to implement an effective foreign policy if you cannot calculate the distances between countries and cities, if you cannot draw the frontiers? Physicians too, he continued, need mathematics if they are to understand the influence of the heavenly bodies on human life. It is hardly surprising that Ricci referred to astrology, since the belief in the influence of the stars on life and health was as widespread in China as in the West.
The Jesuit’s stress on the importance of mathematics in improving military techniques may well have been suggested by his friend Xu Guangqi, who attached great importance to this aspect. Ricci wrote that courage alone was not enough to win a war. It was also essential to calculate precisely the amount of food needed for the soldiers, the distance of the armies from the enemy, the formation to be adopted in battle, and the strategy of attack. He continued in this vein, overlooking no field in which the use of mathematics was of assistance.
Ricci followed this exercise in propaganda by illustrating the hypothetical-deductive method of the
Elements
to his readers. He explained how the Greek mathematician took definitions and axioms as his starting point to derive five hundred theorems and constructions, each of which consisted in a proposition followed by the proof: “The . . . propositions . . . unroll themselves in a straight line from beginning to end. Nowhere can the order be reversed; it is one unbroken chain.”
Aware of the difficulty of the work, Ricci assured readers that the “undoubtable principles at the beginning are extremely simple and clear.” When they encountered “hidden and subtle arguments,” they should be patient because their meaning would become manifest step by step. With a very Chinese touch of poetry, he compared the unveiling of a solution to a mathematical problem to “tense eyebrows that relax into a smile.” Immediately afterward, in more concrete terms, he stated that anyone ambitious and intelligent could understand the
Elements
.
On drawing close to the conclusion, Ricci dedicated the book to his Chinese friends out of gratitude for their confidence in him. Describing himself as a “humble traveler,” he made no attempt to conceal the hard work involved and recalled being forced to pause repeatedly by the difficulties encountered along the way despite the aid of willing helpers: “All beginning is difficult.”
The work of translation would have been impossible without the help of Xu Guangqi, just as the active support of this authoritative scholar was essential to its circulation among Chinese intellectuals. Paul Xu wrote a second preface in praise of Western geometry and published a short essay entitled
Reflections on Euclid
. In accordance with the Confucian approach of seeking confirmation for present-day knowledge in the past, he endeavored to draw arguments in support of the Greek work from the most ancient Chinese traditions, pointing out that mathematics was considered a crucial tool for the management of the state and social life in China during the reigns of the first dynasties in the first and second millennium
bc
, and that there was a rock-solid tradition of mathematical knowledge handed down from master to pupil. This transmission of knowledge was, however, interrupted in 213
bc
, when Ying Zheng, the founder of the Qin dynasty and the first to unify the Chinese empire—known to history as Shi Huangdi, the First Emperor—ordered the burning of all ancient writings so that nobody might invoke tradition to challenge his authority.
13
According to Xu Guangqi, that drastic act severed the continuity of knowledge. Since then, mathematicians had been left with no guidance, groping blindly like someone desperately trying to examine an elephant in the dark with just one candle and managing only a small piece at a time, seeing the head but losing sight of the tail. The remedy in order to salvage the lost tradition was precisely the study of mathematics, a form of “lucid,” “solid,” “well-grounded” knowledge that sharpened the intellect. Moreover, the great strength of Euclid’s work lay in its exposition of the method used to arrive at the results presented. In order to convince his scholarly friends, the
guan
also used the ethical arguments cherished by Confucianism, asserting that the study of mathematics made self-improvement possible and that “hasty people, coarse people, those satisfied with themselves, jealous people, and the arrogant” would be unable to understand it. If the text seemed “obscure,” it was necessary to have trust and persevere. Understanding would come:
It is like when walking through thick mountains you look in all four directions and you don’t see a passage; but then you reach a spot and suddenly the passage opens itself.
The prefaces of Li Madou and Xu Guangqi said everything there was to say in support of the work, and once the book came out in Beijing and was circulated among their friends and the friends of friends in the other provinces, they could only hope for a favorable response on the part of the public.
It was not easy, however, to judge the impact of such an innovative text in a short period. Full appraisal would entail waiting for the new ideas to take root in Chinese culture and to undergo gradual development at the hands of specialists. The honest judgment that Ricci gives in his history of the mission is that the work was “admired more than understood.” In actual fact, far from being unnoticed, the book was discussed and commented on all through the seventeenth century and into the eighteenth and stimulated scholars to compare it with Chinese texts, thus fostering the progress of autochthonous mathematical research. The translation by Ricci and Xu Guangqi is still remembered today in Chinese history books, where it is referred to as a work translated by the latter with the help of Li Madou.
Prompted by a certain desire for revenge on the literati who were hostile to him, Ricci did detect one immediate effect of the book’s circulation even before objective assessment of the publication was possible. In his view, the treatise on geometry was the first book written in Chinese that the
shidafu
found difficult to understand:
[The publication of the
Elements
] served very well to humble Chinese pride, as it forced their greatest scholars to confess that they had seen a book in their writing and studied it with great attention but had failed to understand it, something that had never happened to them before.
14
The Fruits of the School of Mathematics:
Works of Trigonometry and Astronomy
Ricci maintained that Euclidean geometry was the foundation of every other sector of mathematics and science. Xu Guangqi was aware that it offered a method of analysis and investigation of nature that would serve in a variety of spheres. In developing the studies commenced with Ricci in greater depth, Paul Xu ascertained that the ideal geometric figures and theorems of Euclid’s geometry, though abstract and apparently far removed from the real world, were extraordinarily effective tools serving to address and solve the practical problems that interested him so much. The first proof of this came when he studied and translated with Ricci part of Clavius’s
Practical Geometry
, published in 1604, and saw how geometry could be applied to the study of the position of bodies in the sky and to the techniques of topographical surveying used to describe the configuration and dimensions of the earth’s surface on paper. The result was
Celiang fayi
(“Explanations of the Methods of Measurement”), published in 1607, which explained how to construct a geometric quadrant and use it to measure heights and distances. In accordance with the typical approach of Chinese mathematical works, Xu Guangqi presented a list of fifteen concrete problems, such as calculating the depth of a well, the height of a hill, or the altitude of the sun over the horizon at a given hour of the day, and showed how they could be solved with the methods of Western geometry.
In contemporary terms, the calculations involved were above all a matter of trigonometry, the branch of mathematics that studies the relations between the sides and angles of a triangle. Derived from the Greek for measuring triangles, the term “trigonometry” was very recent in Ricci’s day, having been introduced in a work published in Heidelberg at the end of the sixteenth century by the German mathematician Bartholomaeus Pitiscus. The origin of the discipline was, however, ancient. Hipparchus, the greatest astronomer of the Greek world, used rudimentary trigonometric techniques to measure the diameter of the earth and the distance of the moon and the sun from our planet as early as the second century
bc
. While the discipline had developed over the centuries and had experienced further growth in the sixteenth century in Europe, it remained at a somewhat primitive stage in China. According to the historian of Chinese science Joseph Needham, the work by Ricci and Xu Guangqi was the first modern work of trigonometry to appear in the Chinese language.
15
In presenting the book to readers with the customary preface, Xu Guangqi wrote that, even though the Western techniques were similar to the Chinese, they were to be preferred because they made it possible to solve more complex problems and also provided an explanation of how they worked.
While working with Paul Xu in Beijing, Ricci kept in contact by letter with Li Zhizao, who had not been back to the capital for nearly four years. In 1606, the year before, the Jesuits’ friend unexpectedly lost his position as superintendent of the Imperial Canal and was demoted as a disciplinary measure, the reasons for which are not known. Deeply embittered, he chose to withdraw to the Zhejiang province, his homeland, rather than return to Beijing. He continued to study during this voluntary exile, however, and published a book about astronomy based on the works by Clavius that he had read with Ricci in Beijing. Entitled
Huangai tongxian tushuo
(“Diagrams and Explanations Regarding the Sphere and the Astrolabe”), it presented the Ptolemaic theory of the universe and described techniques for the construction of astrolabes and other equipment of astronomical observation, which Li Zhizao had himself learned to make.
16
Ricci was very pleased with his friends’ work and realized that his dream of teaching European science systematically to the Chinese was finally coming true with their aid. Unfortunately, however, the fruitful collaboration with Paul Xu was also interrupted by the unexpected death of his father at the end of 1607, which obliged him to leave the Hanlin Academy and return to Shanghai for the customary three-year period of mourning. Even though he could no longer work side by side with Ricci, Xu Guangqi continued his studies and kept in constant contact with the Jesuit by letter. He was determined to develop his grasp of Western knowledge, not in order to repudiate his own culture but to rediscover its peculiar characteristics and revitalize them with the aid of the new skills and the new method he had learned from Ricci.
17
To this end, he devoted himself to the study of ancient Chinese works of mathematics and in 1608 published
Celiang yitong
(“Similarities and Differences in Measurement”), in which he compared the Western and Chinese methods of surveying and planimetry with respect to six problems. Written together with his pupil Sun Yuanhua in 1609,
Gougu yi
(“Principles of the Right Triangle”) applied the Pythagorean theorem to fifteen problems in accordance with the classical Chinese methods and then put forward a new solution based on the methods taught by Ricci.
Xu Guangqi and Li Zhizao also worked together in later years, and in 1613, after Ricci’s death, they published
Tongwen suanzhi
(“Rules of Arithmetics Common to Cultures”), in which the Jesuit’s methods of arithmetic and algebra were once again compared to those presented in the classical texts. Their work in rediscovering Chinese mathematics and comparing it with its Western counterpart in search of an original synthesis, which was continued by other Chinese scholars after their death, is regarded by historians as part of the essential heritage of Chinese science.