n Brianchon's theorem
86. Construction of the penvil by Brianchon's theorem
87. Point of contact of a tangent to a conic
88. Circumscribed quadrilateral
89. Circumscribed triangle
90. Use of Brianchon's theorem
91. Harmonic tangents
92. Projectivity and perspectivity
93. Degenerate case
94. Law of duality
PROBLEMS
CHAPTER VI - POLES AND POLARS
95. Inscribed and circumscribed quadrilaterals
96. Definition of the polar line of a point
97. Further defining properties
98. Definition of the pole of a line
99. Fundamental theorem of poles and polars
100. Conjugate points and lines
101. Construction of the polar line of a given point
102. Self-polar triangle
103. Pole and polar projectively related
104. Duality
105. Self-dual theorems
106. Other correspondences
PROBLEMS
CHAPTER VII - METRICAL PROPERTIES OF THE CONIC SECTIONS
107. Diameters. Center
108. Various theorems
109. Conjugate diameters
110. Classification of conics
111. Asymptotes
112. Various theorems
113. Theorems concerning asymptotes
114. Asymptotes and conjugate diameters
115. Segments cut off on a chord by hyperbola and its asymptotes
116. Application of the theorem
117. Triangle formed by the two asymptotes and a tangent
118. Equation of hyperbola referred to the asymptotes
119. Equation of parabola
120. Equation of central conics referred to conjugate diameters
PROBLEMS
CHAPTER VIII - INVOLUTION
121. Fundamental theorem
122. Linear construction
123. Definition of involution of points on a line
124. Double-points in an involution
125. Desargues's theorem concerning conics through four points
126. Degenerate conics of the system
127. Conics through four points touching a given line
128. Double correspondence
129. Steiner's construction
130. Application of Steiner's construction to double correspondence
131. Involution of points on a point-row of the second order.
132. Involution of rays
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. Int