# Plane and Spherical Trigonometry and Mensuration

American Book Company, 1875 - Measurement - 251 pages
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### Contents

 INTRODUCTION 9 To find the number corresponding to a logarithm 16 Evolution by logarithms 22 The sine of an 29 The cotangent of an 35 Natural functions 41 Logarithmic functions 43 Case I 51
 Mauduits principles 112 Remarks 119 32 122 Proposition II 125 Proposition VII 129 viii 130 33 138 Values of P as B increases from 0 to 360 140

 Case II 58 Case III 64 Problems 70 Each function in terms of the others 76 Sine and cosine of the sum of two angles 83 Consequences of a b c 90 23 91 27 104 Applications 106
 Case III 147 Area of a quadrilateral 154 Area of a regular polygon 161 Area of a regular prism 167 Area of a regular polyhedron 173 MENSURATION OF VOLUMES 174 Volume of a wedge 180 43 1 Copyright

### Popular passages

Page 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Page 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 122 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 141 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 17 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 120 - The sines of the sides of a spherical triangle are proportional to the sines of their opposite angles. Let ABC be a spherical triangle.
Page viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Page 63 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page viii - In general, if the number is not an exact power of 10, its logarithm, in the common system, will consist of two parts — an entire part and a decimal part. The entire part is called the characteristic and the decimal part is called the mantissa.