# Plane and Spherical Trigonometry and Mensuration

American Book Company, 1875 - Measurement - 251 pages

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### Contents

 INTRODUCTION 9 Evolution by logarithms 22 The cotangent of an arc 35 Logarithmic functions 43 Case I 51 Case III 64 Problems 70 Each function in terms of the others 76
 Remarks 119 Proposition II 125 Proposition VII 129 Principles 144 MENSURATION 150 Area of an irregular polygon 159 Area of a segment of a circle 165 Area of a zone 171

### Popular passages

Page 30 - 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 104 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 120 - 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 139 - 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 15 - 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 18 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 118 - 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 vi - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Page 61 - 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 vi - 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.