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IX, pag. 261, tom. XIV, pag. 324 et 337. J. D. G. 1 A theorem on continued fractions 47 Its negative value will therefore be yD 1 1 1 C C1 1 2 1 C C1 1 1 2 C C:::::: 1 The two values of x will therefore be x D 3C 1 1 1 C C1 1 2 1 C C1 1 1 2 C C:::: 1 xD3 1 1 1 C C1 1 2 1 C C1 1 1 2 C C::::: 1 of which the latter, in virtue of the known formula p 1 Dp q 1C 1 1 , 1C q 1 becomes x D1C 1 1 1 C C1 1 1 1 C C1 1 1 2 C C1 1 1 1 C C1 2 1 C : : : (*) (*) Several researches on the same subject may be found in the present collection Vol.

In 1830, however, the two words both had two main meanings: on the one hand they were both used to mean ‘pure mathematician’ generically, though the former had overtones of ‘algebraist’; on the other hand they indicated practitioners of the main subdivisions of pure mathematics. They derive of course from the nouns analyse and géométrie. These were parts of mathématiques or sciences mathématiques, a broad area that included both pure and applied mathematics and more besides. Thus, for example, Vol.

I am inclined to doubt it, though. And I doubt very much that it is where he got his concept—there is nothing like his notions of groupe in Poinsot’s preface. Reading what Galois wrote I get a strong impression that, as I have explained above, he began by simply using the word groupe as an ordinary and convenient noun. He could as well have chosen some other collective noun, except that groupe is simple and direct and has the associated verb grouper. It seems extremely unlikely that he owed it to Poinsot.

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