tag="{http://www.w3.org/1999/xhtml}a">182
The final object of Geometry 184
- Nature of Geometrical Measurement 185
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- 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
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- 1. To find the most suitable Property 195
- 2. To pass from the Concrete to the Abstract 197
- Illustrations:
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- Orbits of the Planets 198
- Figure of the Earth 199
The two general Methods of Geometry 202
- Their fundamental Difference 203
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- 1â°. Different Questions with respect to the same Figure 204
- 2â°. 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
CHAPTER II.
- ANCIENT OR SYNTHETIC GEOMETRY 212
- Its proper Extent 212
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- Lines; Polygons; Polyhedrons 212
- Not to be farther restricted 213
- Improper Application of Analysis 214
- Attempted Demonstrations of Axioms 216
- Geometry of the right Line 217
- Graphical Solutions 218
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