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The first book on group theory, giving a then-comprehensive study of permutation groups and Galois theory. The first comprehensive work on transformation groups, serving as the foundation for the modern theory of Lie groups.
In this book, Jordan introduced the notion of a simple group and epimorphism (which he called l'isomorphisme mériédrique), Publication data: 3 volumes, B. Teubner, Verlagsgesellschaft, mb H, Leipzig, 1888–1893. Description: Gave a complete proof of the solvability of finite groups of odd order, establishing the long-standing Burnside conjecture that all finite non-abelian simple groups are of even order.
Contained rules for manipulating both negative and positive numbers, rules for dealing the number zero, a method for computing square roots, and general methods of solving linear and some quadratic equations, solution to Pell's equation.Included are Galois' papers Mémoire sur les conditions de résolubilité des équations par radicaux and Des équations primitives qui sont solubles par radicaux.Online version: Online version Traité des substitutions et des équations algébriques (Treatise on Substitutions and Algebraic Equations).(NB While analytic geometry as use of Cartesian coordinates is also in a sense included in the scope of algebraic geometry, that is not the topic being discussed in this article.) The major paper consolidating the theory was Géometrie Algébrique et Géométrie Analytique by Serre, now usually referred to as GAGA.A GAGA-style result would now mean any theorem of comparison, allowing passage between a category of objects from algebraic geometry, and their morphisms, and a well-defined subcategory of analytic geometry objects and holomorphic mappings.
The text contains 33 verses covering mensuration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chh Ay A), simple, quadratic, simultaneous, and indeterminate equations.