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procedures of nine categories) compiled no later than the fi rst century ce
contained the Pascal triangle (referred to by Biot as ‘binomial expansions
up to the sixth degree’,^8 which could hardly be seen as ‘elementary’, and
yet argued for the inferiority of the Chinese mathematical treatises. Th e
following phrase of Biot seemingly explains his reasons: ‘[Th e treatises]
are collections of problems, the most part of them elementary, with the
solutions given without demonstrations’. 9 Th e word ‘demonstrations’ might
make one think that Biot meant a comparison with the European textbooks
of his time written in ‘Euclidean’ style, as lists of theorems accompanied
by proofs. Th is conjecture, however, lacks any supporting evidence; on
the contrary, an anti-Euclidean trend was rather powerful among French
educators at the moment when Biot was writing his lines, as the following
quotation shows:
Whoever wishing from now on to put geometry within the reach of mind and to
teach it in a rational way should, I think, present it as we just have seen it [above]
and remove all that is no more than just a vague expression and pure hassle. Th is
bothering equipment of defi nitions, principles, axioms, theorems, lemmas, scholia,
corollaries, should be completely eliminated, as well as all other futile particularities
[of the same kind], the only eff ect of which is that they put too heavy a burden on
the [human] spirit and make it tired in its progress. 10
Moreover, a cursory analysis of the contemporaneous French arith-
metical textbooks suggests that by ‘demonstrations’ Biot most likely meant
step-by-step explanations of numerical solutions found in a large number
of French textbooks published by the mid nineteenth century, and notway he approached the documents transpires from his remark on the Zhou bi suan jing : ‘Th e
Zhou bi , which has in China an immense reputation, presents several exact notions concerning
the movement of the sun and the moon surrounded by strange absurdities’
(Le Tcheou-pei , qui a une réputation immense en Chine, présente, au milieu d’étranges
absurdités, quelques notions exactes sur les mouvements du soleil et de la lune) (p. 262).
Moreover, Biot did not have access to the Jiu zhang suan shu (Computational
procedures of nine categories), the cornerstone of the mathematical curriculum, and made his
judgement solely on the basis of the Suan fa tong zong (Summarized fundamentals
of computational methods, 1592) by Cheng Dawei the contents of which he believed to
be identical with that of the Jiu zhang suan shu ( ibid .).
8 Biot 1847 : 262.
9 ‘[Les ouvrages] sont des collections de questions qui sont, pour la plupart, élémentaires,
et dont la solution est donnée sans démonstration’ (Biot 1847 : 262).
10 ‘Quiconque voudra désormais mettre la géométrie à la portée des intelligences et l’enseigner
d’une manière rationnelle, devra, je crois, la présenter telle que nous venons de la voir et en
écarter tout ce qui n’est que vague expression et pure enfl ure. Cet attirail embarrassant de
défi nitions, de principes, d’axiomes, de théorèmes, de lemmes, de scolies, de corollaires, doit
être mis complètement de côté, ainsi que les autres distinctions futiles qui n’ont d’autre eff et que
de surcharger l’esprit et de le fatiguer dans sa marche’ (Bailly 1857 : 11–12).