# Elements of Geometry and Trigonometry: With Applications in Mensuration

A.S. Barnes & Burr, 1864 - Geometry - 324 pages
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### Contents

 BOOK I 9 Axioms 16 BOOK II 38 Problems relating to the First and Second Books 5368 53 BOOK III 69 BOOK IV 82 Measurement of Areas and Proportions of Figures 8210 109
 BOOK V 116 BOOK VI 126 Appendix 163164 163 OF LOGARITHMS 165176 165 APPLICATIONS OF GEOMETRY 211 MENSURATION OF SOLIDS 239

### Popular passages

Page 58 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 80 - 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 will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 125 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.
Page 123 - If a pyramid with a polygon for its base be cut by a plane parallel to the base, the section will be a polygon similar to the base.
Page 32 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.
Page 205 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Page 122 - ... or cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a...
Page 11 - A circle (Fig. 38) is a figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within, called the center.
Page 81 - A are verti' cal, produce the sides GE, CD till they meet in H. The two rectangles ABCD, AEHD, having the same altitude, AD, are to each other as their bases, AB, AE.
Page 12 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.