## Plane and Spherical Trigonometry and Mensuration |

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### Common terms and phrases

a. c. log altitude angle is equal arc increases Arithmetic base becomes cents characteristic circular co-sine complement cosec Cotang decimal decreases denote diagonal diameter difference divided edge entire surface escribed circles estimated Examples find the area find the volume formulas fourth quadrant functions Geometry given gives greater Hence included angle increases from 90 increases numerically inscribed Introducing length less logarithm M.
M. Cosine M.
M. Sine mantissa measured minus natural negative opposite opposite angle opposite side origin passes perpendicular plane polygon positive principles Problem proportion Prove pyramid radius reducing regular remaining required the area respectively right angle secant segment side sin b sin solution species sphere spherical triangle square Substituting supplement Tang tangent third triangle values vers volume

### 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.