Chapter I A General View of Geometry 179
The true Nature of Geometry 179 Two fundamental Ideas 181
1. The Idea of Space 181
2. Different kinds of Extension 182
The final object of Geometry 184
Nature of Geometrical Measurement 185
Of Surfaces and Volumes 185
Of curve Lines 187
Of right Lines 189
The infinite extent of its Field 190
Infinity of Lines 190
Infinity of Surfaces 191
Infinity of Volumes 192
Analytical Invention of Curves, &c. 193
Expansion of Original Definition 193
Properties of Lines and Surfaces 195 Necessity of their Study 195
1. To find the most suitable Property 195
2. To pass from the Concrete to the Abstract 197 Illustrations:
Orbits of the Planets 198
Figure of the Earth 199
The two general Methods of Geometry 202
Their fundamental Difference 203
1⁰. Different Questions with respect to the same Figure 204
2⁰. Similar Questions with respect to different Figures 204 Geometry of the Ancients 204 Geometry of the Moderns 206 Superiority of the Modern 207 The Ancient the base of the Modern 209