The Geometry
David Eugene Smith and Marcia L. Latham (1925)
René Descartes's La Géométrie (1637), published as an appendix to his Discourse on Method, founded analytic geometry by uniting algebra with geometry—showing that geometric problems can be recast as algebraic equations and their solutions carried out by construction. Book I lays the groundwork: every problem is reduced to finding the lengths of lines, the operations of arithmetic (including the extraction of roots) are performed geometrically with ruler and compass, an algebraic notation is introduced, and quadratic equations are solved by simple constructions. The translation is David Eugene Smith and Marcia L. Latham's of 1925. (This edition presents Book I through the quadratic constructions; Descartes' concluding treatment of the Pappus problem is not yet included.)
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