Contributions to Ramanujan's Continued Fractions, Class by Chan H.H.

By Chan H.H.

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However, it is a quite fitting stand for someone so concerned as Lacroix with geometrical interpretations of analytical concepts. Naturally this chapter starts with the most classic methods: separation of variables and integrating factors, applied to first-order and first-degree equations. But even in regard to these simpler cases, Lacroix complains about the imperfection of analysis, which does not provide a better algorithm than groping for an integrating factor [Traité, II, 251]. He alludes to general methods proposed by Fontaine and Condorcet,17 but justifies not saying anything about them with their unpracticality; still, their references appear in the table of contents [Lacroix Traité, II, vi].

Apart from the fact that one should read “rational” instead of “integer”, this is misleading because Lacroix shows the recursive relation between the coefficients independently of n being integer or not [Traité, I, 19-22]. My mistake resulted from the physical separation between this and the general proof that the first two terms in the expansion of (1 + x)n are 1 + nx [Traité, I, 49]. 12 “at one stroke” 28 Chapter 2. An overview of Lacroix’s Traité Then, after establishing the iterative relation between the coefficients and thus renaming them to f(x + k) − f(x) = f (x)k + f (x) 2 f (x) 3 k + k + etc.

An interesting issue is that of the languages of the works included. Memoirs are cited only as, say, “Nouv. Mém de Petersbourg, T. XV et XVI. (Lexell)” [Lacroix Traité, I, xxx] – thus not indicating in which language they were written. Therefore, it would be impracticable to give precise quantitative data. 3. Volume I: differential calculus (1797) 25 safe to say that French is the most common language, followed by Latin. Of course, this only reflects the weight of these languages in the scientific community at the time (the memoirs of the Berlin Academy for instance, were usually in French).

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