The Geometry of René Descartes

The Geometry of René Descartes, translated by David Eugene Smith and Marcia L. Lantham (New York: Dover Publications, 1954).


If a mathematician were asked to name the great epoch-making works in his science, he might well hesitate in his decision concerning the product of the nineteenth century ; he might even hesitate with respect to the eighteenth century ; but as to the product of the sixteenth and seventeenth centuries, and particularly as to the works of the Greeks in classical times, he would probably have very definite views. He would certainly include the works of Euclid, Archimedes, and Apollonius among the products of the Greek civilization, while among those which contributed to the great renaissance of mathematics in the seventeenth century he would as certainly include La Geometrie of Descartes and the Principia of Newton.


But it is one of the curious facts in the study of historical material that although we have long had the works of Euclid, Archimedes, Apollonius, and Newton in English, the epoch-making treatise of Descartes has never been printed in our language, or, if so, only in some obscure and long-since-forgotten edition. Written originally in French, it was soon after translated into Latin by Van Schooten, and this was long held to be sufficient for any scholars who might care to follow the work of Descartes in the first printed treatise that ever appeared on analytic geometry. At present it is doubtful if many mathematicians read the work in Latin ; indeed, it is doubtful if many except the French scholars consult it very often in the original’ language in which it appeared. But certainly a work of this kind ought to be easily accessible to American and British students of the history of mathematics, and in a language with which they are entirely familiar.