'The Geometry of René Descartes: with a Facsimile of the First Edition'
By Rene Descartes (Author), David Eugene Smith (Translator), Marcia L. Latham (Translator)
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'
More than Bacon, Rene Descartes must be considered as the founder of modern philosophy. A French Catholic philosopher well versed in medieval thought, Descartes also studied mathematics. However, he gradually turned away from the classical formulations of medieval philosophy in order to seek a new foundation for certitude upon the wake of his famous method of Cartesian doubt which led him to the assertion 'I think therefore I am' (cogito ergo sum). This most famous dictum is, in a sense, the foundation of modem philosophy in that it posits the cogni- tive act of the individual ego and human reason independent of revela- tion as the ultimate criterion of the truth and even the foundation of exis- tence. This is why many consider him as the father of modem rationalism. Descartes' famous works Discourse on the Method and Meditations on Prime Philosophy, as well as the Principles of Philosophy, which contain his cosmology, are models of French prose and have had immense influence upon modern thought.
Descartes asserted the famous dualism according to which reality consists of two dimensions or two substances, one being the world of extension or matter and the other the world of consciousness or thought. Henceforth, European philosophy has always had difficulty in understanding the relation between the two. Later philosophers have continu- ously asked how can one substance which is the mind know the other which is the world of matter. It is from this radical dualism that has issued the later division of much of modem philosophy into the camp of the materialists and that of the idealists, or those who consider the mater- ial substance to be real and the other unreal or on the contrary, those who believe the world of the mind or "idea" to be real and the second unreal. In any case, the role of Descartes in the foundation of modem philoso- phy is immense. Moreover, his mathematicization of space and the discovery of many important mathematical ideas, especially descriptive geometry, were also very influential in the rise of modern science although his physics was totally rejected by Newtonian physics which became accepted as the norm a generation after Descartes.