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By Jean-Claude Martzloff

This ebook is made from elements, the 1st dedicated to normal, old and cultural historical past, and the second one to the advance of every subdiscipline that jointly include chinese language arithmetic. The publication is uniquely available, either as a topical reference paintings, and in addition as an summary that may be learn and reread at many degrees of class via either sinologists and mathematicians alike.

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Cf. Li Qun ( l ' ) , 1975, p. 101 ff. In modern notation, Shen Gua's summation formula corresponds to + where a and b are given integers and A = a (n - l ) , B = b + ( n - l ) , respectively. More precisely, Shen Gua was interested in calculating the number of objects composing a solid made of n superposed rectangular layers having ( a k ) ( b k ) objects each (0 5 k 5 n - 1 ) respectively, each dimension being diminished by one unit from each layer to the next. Note that this formula includes as a special case, the formula for the sum of the squares of the first n numbers.

Dehergne, op. , p. 343. 61Cf. Bernard-Maitre (4), 1940, p. 112. 62Collani (l),1985. "See Dehergne ( l ) , 1973, p. 359. 64Cf. Bernard-Maitre (6), 1942. 6%n the mathematics training received in France by these Jesuit fathers, see Delattre ( l ) , 1949-1 957, 111, p. 1186. 66 " L i Madou [Matteo Ricci] suo yi, yin wenfa bu ming, xianhou nan jie, gu ling yi " (Given that Matteo Ricci's translation of (Euclid's Elements) is written in confused language and that it is difficult to understand its organisation, we have produced a new translation).

69. 44"all wtronomy," in other words Tycho Brahe's system. See Sivin ( l ) , 1973; Hashimoto ( 2 ) , 1988. 45The second part concerns astronomy itself. 47As the above quotation explains, this text may be viewed as a work tool for practitioners of astronomy, who could find everything they might require in it. This explains its quite special orientation as far as mathematics is concerned, including the description of calculating instruments, trigonometric formulae and tables, and various mathematical facts about polyhedra, conics and the number n,as the following brief description of the main mathematical works included in the Chongzhen lishu shows: The Chousuan describes the counting-rods invented by Napier (commonly known as Napier's rods) to facilitate multiplication.

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