Translator’s Preface In the late 1890s Gaston Darboux was named as the editor of a set of text- books, resources for the teaching of mathematics (Cours Complet Pour la Classe de Math´ ematiques ´ ementaires ). Darboux commissioned several mathematicians to write these materials. Jacques Hadamard, having taught on the high school (lyc´ ee) level,1 was asked to prepare the materials for geometry. Two volumes resulted: one on plane geometry in 1898 and a volume on solid geometry in 1901. Hadamard clearly saw this work as important, as he revised it twelve times during his long life, the last edition appearing in 1947. (Hadamard died in 1963 at the age of 97.) The present book is a translation of the thirteenth edition of the first volume, first printed by Librarie Armand Colin, Paris, in 1947 and reprinted by Editions´ Jacques Gabay, Sceaux, in 1988. It includes all the materials that this reprint contains. The volume on solid geometry has not been included here. A companion volume to this translation, not based on the work of Hadamard, includes solutions to the problems as well as ideas for classroom use. Hadamard’s vision of geometry is remarkably fresh, even after the passage of 100 years. The classical approach is delicately balanced with modern extensions. The various geometric transformations arise simply and naturally from more static considerations of geometric objects. The book includes a disk for use with the Texas Instruments TI-NSpireTMsoft- ware∗. This disk is not meant to exhaust the possibilities of applying technology to these materials. Rather, it is meant to whet the appetite of the user for exploration of this area. The same can be said about all the materials in the companion volume: Hada- mard’s book is a rich source of mathematical and pedagogical ideas, too rich to be exhausted in one supplementary volume. The supplementary materials are intended to invite the reader to consider further the ideas brought up by Hadamard. A word is in order about the process of translation. Hadamard was a master of mathematics, and of mathematical exposition, but not particularly of the language itself. Some of his sentences are stiffly formal, others clumsy, even ambiguous (al- though the ambiguity is easily resolved by the logic of the discussion). In some cases (the appendix on Malfatti’s problem is a good example) footnotes or depen- dent clauses seem to have been piled on as afterthoughts, to clarify a phrase or logical point. This circumstance presents an awkward dilemma for the translator. 1 The best account of Hadamard’s life, including those episodes alluded to in this preface, can be found in the excellent book by Vladimir Maz’ya and Tatyana Shaposhnikova, Jacques Hadamard, A Universal Mathematician, American Mathematical Society, Providence, Rhode Island, 1998. ∗ TI-Nspire is a registered trademark of Texas Instruments. ix

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