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قراءة كتاب An Elementary Course in Synthetic Projective Geometry

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‏اللغة: English
An Elementary Course in Synthetic Projective Geometry

An Elementary Course in Synthetic Projective Geometry

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دار النشر: Project Gutenberg
الصفحة رقم: 6

class="pginternal" tag="{http://www.w3.org/1999/xhtml}a">133. Double rays

  • 134. Conic through a fixed point touching four lines
  • 135. Double correspondence
  • 136. Pencils of rays of the second order in involution
  • 137. Theorem concerning pencils of the second order in involution
  • 138. Involution of rays determined by a conic
  • 139. Statement of theorem
  • 140. Dual of the theorem
  • 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
  • 166. Extension of the theory of poles and polars to space
  • 167. Desargues's method of describing a conic

    • Pages