# Elements of Geometry and Trigonometry (Google eBook)

A. S. Barnes and Company, 1838 - Geometry - 359 pages

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### Contents

 The principles 9 The Circle and the Measurement of Angles 41 Problems relating to the First and Third Books 57 The Proportions of Figures and the Measurement of Areas 68 Problems relating to the Fourth Book 98 BOOK VI 126 Polyedrons 142 BOOK VIII 166
 Quadrantal Triangles 263 Mensuration of Surfaces 274 Mensuration of Solids 285 Prop 15 Book I 31 Seh of 4 54 9 65 of 19 145

 BOOK IX 186 APPENDIX 205 Division of the Circumference 201 General Ideas relating to the Trigonometrical Lines 208 Theorems and Formulas relating to the Sines Cosines Tan 222 Description of Table of Logarithmic Sines 228 Solution of Rectilineal Triangles by Logarithms 235 SPHERICAL TRIGONOMETRY 252
 Cor 2 174 31 233 35 250 5 257 15 265 Cor 1 of 41 293 Cor of 15 15

### Popular passages

Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.