CHAPTER II.

ANCIENT OR SYNTHETIC GEOMETRY

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ITS PROPER EXTENT 212 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 _Descriptive Geometry_ 220

ALGEBRAICAL SOLUTIONS 224 _Trigonometry_ 225 Two Methods of introducing Angles 226 1. By Arcs 226 2. By trigonometrical Lines 226 Advantages of the latter 226 Its Division of trigonometrical Questions 227 1. Relations between Angles and trigonometrical Lines 228 2. Relations between trigonometrical Lines and Sides 228 Increase of trigonometrical Lines 228 Study of the Relations between them 230