The Geometry of René Descartes: with a Facsimile of the First Edition (Dover Books on Mathematics)

This is an unabridged republication of the definitive English translation of one of the very greatest classics of science. Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard). With this volume Descartes founded modern analytical geometry. Reducing geometry to algebra and analysis and, conversely, showing that analysis may be translated into geometry, it opened the way for modern mathematics. Descartes was the first to classify curves systematically and to demonstrate algebraic solution of geometric curves. His geometric interpretation of negative quantities led to later concepts of continuity and the theory of function. The third book contains important contributions to the theory of equations. This edition contains the entire definitive Smith-Latham translation of Descartes' three books: Problems the Construction of which Requires Only Straight Lines and Circles ; On the Nature of Curved Lines ; and On the Construction of Solid and Supersolid Problems . Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography. This is an unabridged republication of the definitive English translation of one of the very greatest classics of science. Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard).This edition contains the entire definitive Smith-Latham translation of Descartes' three books: __Problems the Construction of which Requires Only Straight Lines and Circles__; __On the Nature of Curved Lines__; and __On the Construction of Solid and Supersolid Problems__. Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography. The great work that founded analytical geometry. Included here is the original French text, Descartes' own diagrams, together with the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill. Cover Title Page Copyright Preface CONTENTS Book First Book Second Book Third Index