HUMBERT, MARIE-GEORGES.

Sur les courbes algébriques planes rectifiables (+) Sur quelques propriétés des aires sphériques (+) Sur le théorème d'Abel et quelques-unes de ses applications a la geometrie (+) Sur une classe de courbes planes, et sur une surface remarquable du quatrième ordre (+) Sur les surfaces desmiques du quatrième ordre (+) Sur quelques points de la théorie des courbes et des surfaces algébriques

Paris, Gauthier-Villars, 1888-1890 4to. Bound with the front wrappers in contemporary half cloth. In "Journal de Mathématiques pures et appliquées". With two paper labels to spine and with the author's name to top of each wrapper. A stamp to front free end paper and first wrapper. Otherwise fine.

First appearance of this collection of important papers which, amongst others, contains the questions to whether the involutes are algebraic.

"Besides his two pedagogical works, it was through numerous memoirs (approximately 150, which have been collected) that Humbert held a major place in the mathematical discovery and production of his time. His writings were inspired by his interest in the study of algebraic curves and surfaces and were marked by the lucidity with which he related the problems biography in encountered in this area to questions of analysis and number theory.
He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. He also pointed out the resulting consequence: the existence of a group of transformations of certain surfaces into themselves constitutes an essential difference between the geometry of surfaces and that of curves. But, most important, he completed the work of Hermite by pursuing the applications to number theory throughout his life."

The present volume also contain contribution by Caspary and Hilbert.

Order-nr.: 49018