Chapter X - on the History of Synthetic Projective Geometry

161. Ancient results 162. Unifying principles 163. Desargues 164. Poles and polars 165. Desargues’s theorem concerning conics through four points 166. Extension of the theory of poles and polars to space 167. Desargues’s method of describing a conic 168. Reception of Desargues’s work 169. Conservatism in Desargues’s time 170. Desargues’s style of writing 171. Lack of appreciation of Desargues 172. Pascal and his theorem 173. Pascal’s essay 174. Pascal’s originality 175. De la Hire and his work 176. Descartes and his influence 177. Newton and Maclaurin 178. Maclaurin’s construction 179. Descriptive geometry and the second revival 180. Duality, homology, continuity, contingent relations 181. Poncelet and Cauchy 182. The work of Poncelet 183. The debt which analytic geometry owes to synthetic geometry 184. Steiner and his work 185. Von Staudt and his work 186. Recent developments INDEX