The Messenger of Mathematics Volume 20 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1891 Excerpt: ...tres-remurguable, and Lacroix promises to return to the subject in the third volume of his Treatise: but I have not been able to find that he did so. (iv) F RANQAIS, J. F; Du calcul des derivations ramene & ses verz'ta6lcs principes, ou t/zeorie du developpement desfonctions, et clu retour des suites. Gergo-nne, Ann. Math. VI. pp. 61-111 (1815). (No. 17, in R. S. Catalogue). Francais was professeur a l'ecole royale de l'artillerie et du genie, and his paper bears the date "Metz, le 5 de mai, 1815." Lacroix alludes to him (Ualc. (t. i, p. XXX) as "geometre distingue, qui s'est rendu famflier ce calcul des derivations, it la izaissance duquel fl a pour ainsi dire assiste." And adds il " en a tire un tres-grand' parti clans un Mernoire 'inecZz't sur le mouvement des priyectiles soumis it la resistancc dc l'a2'r." In the present memoir Francais shows his appreciation of Arbogast's truly remarkable results, but points out grave defects in the discoverer's account--chiefly a lack of precision and a certain expansiveness, "dc sorte gue ce qui pouvait etre presente dams guelques feuillea d'z'm, pressi0n est. aievenu un gros in-4." Francais defends a special notation against Lacroix (and Paoli) on the grounds of simplicity, and on the principle that as the development is really a question of the coefficients, it is inappropriate to arrive at the result by changes in the variable. The memoir consists of three parts. In the first and second are discussed the development of functions and the reversion of series; while, to avoid interrupting the exposition, the longer proofs are given in...