# The Elements of Geometry

H. Holt, 1897 - Geometry - 227 pages

### Contents

 PRELIMINARY 1 Triangles Intersecting Lines 13 Parallels and Parallelograms 37 Miscellaneous Propositions 44 The Circle 53 BOOK II 77 Limits 87 Regular Polygons 109
 Supplementary Propositions 141 BOOK IV 163 Polyhedral Angles 173 The Cylinder and the Cone 190 BOOK VI 197 Spherical Surface Geometry 203 Figures of Revolution 211 NOTES ON MODELS FOR SOLID GEOMETRY 218

 Symmetry 115 Measurement of Surfaces 130

### Popular passages

Page 29 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 148 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 9 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 193 - A sphere is a solid bounded by a surface, all the points of which are equally distant from a point within called the center.
Page 150 - Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Page 80 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Let...
Page 10 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Page 90 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 181 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.