Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 Seiten |
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Seite iii
... application of Logarithms to the processes of Mul- tiplication and Division , Involution and Evolution , the order of treatment is , first , the proposition and its demonstration ; next , the rule , then the solution of examples , thus ...
... application of Logarithms to the processes of Mul- tiplication and Division , Involution and Evolution , the order of treatment is , first , the proposition and its demonstration ; next , the rule , then the solution of examples , thus ...
Seite 50
... Applying logarithms to these formulas , we have ( 1 ) { log p 10 . logh log sin P - log blog hlog sin B — 10 . } ( 2 ) { log sin P10 + log p log h . log sin B10 + log b log h . ( 3 ) { log p - logh log cos log b - log hlog cos B - 10 ...
... Applying logarithms to these formulas , we have ( 1 ) { log p 10 . logh log sin P - log blog hlog sin B — 10 . } ( 2 ) { log sin P10 + log p log h . log sin B10 + log b log h . ( 3 ) { log p - logh log cos log b - log hlog cos B - 10 ...
Seite 52
Aaron Schuyler. h sin P Introducing radius , we have , p == R Applying logarithms , we have , log plog h + log sin P - 10 . log h ( 365 ) = 2.56229 log sin P ( 33 ° 12 ' ) = 9.73843 log p = 2.30072 ... = p 199.85 .. In like manner , from ...
Aaron Schuyler. h sin P Introducing radius , we have , p == R Applying logarithms , we have , log plog h + log sin P - 10 . log h ( 365 ) = 2.56229 log sin P ( 33 ° 12 ' ) = 9.73843 log p = 2.30072 ... = p 199.85 .. In like manner , from ...
Seite 53
Aaron Schuyler. Applying logarithms , we have , log sin P = 10 + log p ― log h . log p ( 97 ) 1.98677 - log h ( 112 ) log sin P - 2.04922 = 9.93755 P60 ° 00 ' 17 " . B 90 ° P - 90 ° -60 ° 00 ′ 17 ′′ -29 ° 59 ′ 43 ′′ . = - bh sin B , or ...
Aaron Schuyler. Applying logarithms , we have , log sin P = 10 + log p ― log h . log p ( 97 ) 1.98677 - log h ( 112 ) log sin P - 2.04922 = 9.93755 P60 ° 00 ' 17 " . B 90 ° P - 90 ° -60 ° 00 ′ 17 ′′ -29 ° 59 ′ 43 ′′ . = - bh sin B , or ...
Seite 54
... applying logarithms , as in the preceding cases , we find p = 183.95 . = Either side adjacent to the right angle is equal to the co - sine of the adjacent acute angle multiplied by the hypotenuse . b = ... b h cos P ; .. h = COS P ...
... applying logarithms , as in the preceding cases , we find p = 183.95 . = Either side adjacent to the right angle is equal to the co - sine of the adjacent acute angle multiplied by the hypotenuse . b = ... b h cos P ; .. h = COS P ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Seite 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.
Seite 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...
Seite 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.
Seite 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 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.
Seite viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Seite 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.
Seite 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.