Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página vii
... regular prism . . 166 Area of a regular pyramid . • . 167 Area of a frustum of a regular pyramid . . 168 Area of a cylinder . . 168 Area of a cone . • . 169 Area of a frustum of a cone . . 169 Area of a sphere . . 170 Area of a zone ...
... regular prism . . 166 Area of a regular pyramid . • . 167 Area of a frustum of a regular pyramid . . 168 Area of a cylinder . . 168 Area of a cone . • . 169 Area of a frustum of a cone . . 169 Area of a sphere . . 170 Area of a zone ...
Página viii
... regular polyhedron . Volume of a regular polyhedron . . 182 . 183 TABLES . . 185 INTRODUCTION . LOGARITHMS . 1. Definition . A logarithm of CONTENTS .
... regular polyhedron . Volume of a regular polyhedron . . 182 . 183 TABLES . . 185 INTRODUCTION . LOGARITHMS . 1. Definition . A logarithm of CONTENTS .
Página 80
... regular inscribed hex- agon , which is equal to the radius or 1. But the sine of 30 ° is equal to one - half the chord of 60 ° . . * . ( 1 ) sin 30 ° = 1 , - ( 2 ) cos 30 ° = V1 } = { √3 . Dividing ( 1 ) by ( 2 ) , then ( 2 ) by ( 1 ) ...
... regular inscribed hex- agon , which is equal to the radius or 1. But the sine of 30 ° is equal to one - half the chord of 60 ° . . * . ( 1 ) sin 30 ° = 1 , - ( 2 ) cos 30 ° = V1 } = { √3 . Dividing ( 1 ) by ( 2 ) , then ( 2 ) by ( 1 ) ...
Página 162
... regular poly- gons each of whose sides is 1 , as given in the table subjoined . 167. Table . Triangle = 0.4330127 . Octagon = 4.8284271 . Square = 1.0000000 . Enneagon = 6.1818242 . Pentagon 1.7204774 . Decagon = 7.6942088 . Hexagon ...
... regular poly- gons each of whose sides is 1 , as given in the table subjoined . 167. Table . Triangle = 0.4330127 . Octagon = 4.8284271 . Square = 1.0000000 . Enneagon = 6.1818242 . Pentagon 1.7204774 . Decagon = 7.6942088 . Hexagon ...
Página 163
... regular dodecagon each of whose sides is 100 ? Ans . 111961.524 . 5. What is the area of a regular enneagon each of whose sides is 30 ? Ans . 5563.64178 . 170. Formulas for the Circle . Let r be the radius , d the diameter , c the ...
... regular dodecagon each of whose sides is 100 ? Ans . 111961.524 . 5. What is the area of a regular enneagon each of whose sides is 30 ? Ans . 5563.64178 . 170. Formulas for the Circle . Let r be the radius , d the diameter , c the ...
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Términos y frases comunes
a. c. log adjacent angles adjacent side altitude angle is equal angle opposite applying logarithms arc increases arc is equal arc OT Article 98 circumscribed circle co-sine co-tangent co-versed-sine complement cos b cos cos² cosec decreases denote diagonal divided entire surface escribed circles Examples Find the angle find the area Find the logarithm fourth quadrant frustum functions given angle greater than 90 Hence hypotenuse included angle increases from 90 increases numerically inscribed log blog M.
M. Cosine M.
M. Sine mantissa minus Napier's principles negative number corresponding one-half the sum opposite angle perpendicular plane polygon positive Problem quadrant from H required the area right angle Right Triangles secant second quadrant side adjacent sin a sin slant height solution species spherical triangle supplement Tang tangent third quadrant triangle becomes Trigonometry versed-sine
Pasajes populares
Página 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.
Página 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 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.
Página 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...
Página 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.
Página 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 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.
Página viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Página 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.
Página 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.