# Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

A.S. Barnes & Company, 1857 - Geometry - 448 pages

### Contents

 INTRODUCTION 9 Propositions 21 BOOK II 47 BOOK III 57 Problems relating to the First and Third Books 76 BOOK IV 87 Problems relating to the Fourth Book 122 BOOK V 135
 Problems 267 Table of Natural Sines 273 Solution of Triangles 281 Solution of RightAngled Triangles 287 ANALYTICAL PLANE TRIGONOMETRY 297 of Formulas 306 Homogeneity of Terms 313 SPHERICAL TRIGONOMETRY 321

 BOOK VI 156 BOOK VII 174 BOOK VIII 202 BOOK IX 227 PAGE 245 PLANE TRIGONOMETRY 255 Multiplication by Logarithms 261
 Napiers Analogies 329 Of Quadrantal Triangles 335 MENSURATION OF SURFACES 347 Area of a Regular Polygon 353 Mensuration of Solids divided into Two Parts 358 Convex Surface of a Cone 364

### Popular passages

Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Page 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 30 - B : hence the 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 : hence, the two triangles are equal (Th.
Page 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.