PROBLEMS
CHAPTER IX - METRICAL PROPERTIES OF INVOLUTIONS
141. Introduction of infinite point; center of involution
142. Fundamental metrical theorem
143. Existence of double points
144. Existence of double rays
145. Construction of an involution by means of circles
146. Circular points
147. Pairs in an involution of rays which are at right angles. Circular
involution
148. Axes of conics
149. Points at which the involution determined by a conic is circular
150. Properties of such a point
151. Position of such a point
152. Discovery of the foci of the conic
153. The circle and the parabola
154. Focal properties of conics
155. Case of the parabola
156. Parabolic reflector
157. Directrix. Principal axis. Vertex
158. Another definition of a conic
159. Eccentricity
160. Sum or difference of focal distances
PROBLEMS
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