## Plane and Spherical Trigonometry and Mensuration |

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### Common terms and phrases

a. c. log altitude angle is equal arc increases base characteristic circular co-sine co-tangent complement corresponding cos b cos cosec decimal decreases denote diagonal diameter difference divided entire surface escribed circles Examples Find the angle find the area formulas fourth quadrant function Geometry Given gives greater Hence included angle increases increases from 90 increases numerically inscribed Introducing less logarithm measured minus natural negative one-half the sum opposite angle opposite side passes perpendicular plane polar polygon positive principles Problem proportion Proposition Prove pyramid radius reducing regular remaining required the area respectively right angle secant side adjacent sides sin b sin sine solution species sphere spherical triangle square Substituting supplement Tang tangent third triangle becomes values volume

### 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.