Chapter I: Page

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
1°. Different Questions with respect to
the same Figure 204
2°. 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