Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página 99
... escribed circles . The escribed circles are the three circles external to the triangle , each tangent to one side and to the pro- longation of the other sides . The centers of the escribed circles are the points of CIRCULAR FUNCTIONS . 99.
... escribed circles . The escribed circles are the three circles external to the triangle , each tangent to one side and to the pro- longation of the other sides . The centers of the escribed circles are the points of CIRCULAR FUNCTIONS . 99.
Página 100
... escribed circles . Ans . 3.854 , 6.745 , 13.49 . 2. Given p = 100 , A = 55 ° , B = 60 ° , C = 65 ° , required the radii of the three escribed circles . [ See ( 2 ) , Art . 111. ] Ans . 26.028 , 28.867 , 31.854 . 113. Theorem . The ...
... escribed circles . Ans . 3.854 , 6.745 , 13.49 . 2. Given p = 100 , A = 55 ° , B = 60 ° , C = 65 ° , required the radii of the three escribed circles . [ See ( 2 ) , Art . 111. ] Ans . 26.028 , 28.867 , 31.854 . 113. Theorem . The ...
Página 101
... inscribed circle , the sum of the reciprocals of the radii of the escribed circles , and the sum of the reciprocals of the perpendiculars let fall from the vertices of the three angles on the opposite sides of a triangle are equal to ...
... inscribed circle , the sum of the reciprocals of the radii of the escribed circles , and the sum of the reciprocals of the perpendiculars let fall from the vertices of the three angles on the opposite sides of a triangle are equal to ...
Página 103
... inscribed circles . Ans . 8.353 . 117. Problem . To find the distance between the centers of the circumscribed and escribed circles . Let r ' , r " , r ' " be the radii of the escribed circles , and D ' , D ' , D " " , be the distances ...
... inscribed circles . Ans . 8.353 . 117. Problem . To find the distance between the centers of the circumscribed and escribed circles . Let r ' , r " , r ' " be the radii of the escribed circles , and D ' , D ' , D " " , be the distances ...
Página 104
... escribed circles . Ans . 25.19 , 26.64 , 29.73 . 2. The angles of a triangle are 56 ' , 60 ' , 64 ° , the greatest side is 25 ; required the distances from the center of the circumscribed circle to the centers of the three escribed ...
... escribed circles . Ans . 25.19 , 26.64 , 29.73 . 2. The angles of a triangle are 56 ' , 60 ' , 64 ° , the greatest side is 25 ; required the distances from the center of the circumscribed circle to the centers of the three escribed ...
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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.