This unabridged republication features the definitive English translation of a monumental classic in science, originally published in 1637. It has been hailed as "the greatest single step ever made in the progress of the exact sciences" and as a work that "remade geometry and made modern geometry possible." This volume marks the founding of modern analytical geometry, bridging geometry with algebra and analysis. Descartes systematically classified curves and demonstrated the algebraic solutions of geometric problems, while his geometric interpretation of negative quantities laid the groundwork for later concepts of continuity and the theory of functions. The third book offers significant contributions to the theory of equations. This edition includes the complete Smith-Latham translation of Descartes' three 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. Each page of the translation is interleaved with a facsimile of the original 1637 French text, complete with Descartes' original illustrations. Additionally, 248 footnotes provide clarifications and further bibliographic resources.
