Geometry of Rene Descartes

First published in English in 1925, The Geometry of Rene Descartes brings to audiences one of the most revolutionary works in mathematics since Euclid. Descartes changed the field of mathematics with his invention of analytic geometry. He loved Euclid, because Euclidean geometry offered truth and certainty, and all of its conclusions were drawn from irrefutable axioms.

Descartes wanted to have this kind of certainty in all areas of life, and so he sought to answer questions about the real world using algebra combined with geometry. This produced the Cartesian plane, which suddenly allowed equations to be graphed. It was a revolution.

In this book, mathematicians can follow a true genius as he explains his mathematical principles and truths.

New York lawyer and mathematician DAVID EUGENE SMITH (1860-1944) authored a number of books while a professor of mathematics at Columbia University, including The Teaching of Elementary Mathematics (1900), A History of Japanese Mathematics (1914), and History of Modern Mathematics (1896).

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.
Translated by David E. Smith and Marcia L. Latham.