Plane and Spherical Trigonometry |
From inside the book
Results 1-5 of 7
Page 151
... COLUMN B 1 . .1 .01 .001 .0001 .00001 .000001 .0000001 .00000001 .000000001 || COLUMN A COLUMN B COLUMN A 101 10 100 102 100 10-1 103 1000 10-2 104 [ ] 10000 10-3 105 100000 10-4 106 1000000 10-5 107 10000000 10-6 108 100000000 10-7 109 ...
... COLUMN B 1 . .1 .01 .001 .0001 .00001 .000001 .0000001 .00000001 .000000001 || COLUMN A COLUMN B COLUMN A 101 10 100 102 100 10-1 103 1000 10-2 104 [ ] 10000 10-3 105 100000 10-4 106 1000000 10-5 107 10000000 10-6 108 100000000 10-7 109 ...
Page 151
... column A is called the common logarithm of the number opposite in column B ; thus log 10 = 1 , log 100 = 2 , log 1000 = 3 , etc .; log 1 = 0 , log .1 log .01 = 2 , log .001 - 1 ; 3 , etc. In general , if 102 = n , 7 is called the common ...
... column A is called the common logarithm of the number opposite in column B ; thus log 10 = 1 , log 100 = 2 , log 1000 = 3 , etc .; log 1 = 0 , log .1 log .01 = 2 , log .001 - 1 ; 3 , etc. In general , if 102 = n , 7 is called the common ...
Page 151
... column marked N for the first three digits and select the column headed by the fourth digit : the mantissa will be found at the intersection of this row and this column . Thus to find the logarithm of 72050 , observe first ( Rule I ) ...
... column marked N for the first three digits and select the column headed by the fourth digit : the mantissa will be found at the intersection of this row and this column . Thus to find the logarithm of 72050 , observe first ( Rule I ) ...
Page 151
... column and to the right and below for 737 , which we find in column 8 opposite 168. The number is therefore 1688. Since the characteristic is +1 , we begin at the left , count 2 places , and place the point ; hence ∞ = 16.88 . Example ...
... column and to the right and below for 737 , which we find in column 8 opposite 168. The number is therefore 1688. Since the characteristic is +1 , we begin at the left , count 2 places , and place the point ; hence ∞ = 16.88 . Example ...
Page 151
... column in this table gives multiples of M , or ( preferably ) by Table VIII , page 115. Adding the five logarithms just mentioned , we find log π = .49714 98727 4 , which is surely correct to within 1 in the tenth place . The correct ...
... column in this table gives multiples of M , or ( preferably ) by Table VIII , page 115. Adding the five logarithms just mentioned , we find log π = .49714 98727 4 , which is surely correct to within 1 in the tenth place . The correct ...
Other editions - View all
Common terms and phrases
13 co-function 15 read 9 Prop abscissa angle of elevation angle XOP antilogarithms axis base bottom c d L Ctn characteristic colog cologarithm column COMMON LOGARITHMS computation cos² cotangent Ctn c d decimal places decimal point distance equations Example exponent feet Find the value formulæ hence L Cos d L Sin d law of cosines law of sines log cot log csc log sin Log10 Value Log10 loga loge Logo Value mantissa miles multiple negative OA OA opposite ordinate perpendicular polar triangle positive quadrant radians radius read as printed read co-function result right triangles sec² significant figures sin b sin sin² SOLUTION OF RIGHT spherical triangle tabular difference tan-¹ tan² tangent terminal side theorem tion trigonometric functions Va² Value Log10 Value Value Logo Whence write zero
Popular passages
Page 71 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 151 - I. The logarithm of a product is equal to the sum of the logarithms of the factors : log ab = log a + log b. This follows from the fact that if 10¡ = a and lO1- = 6, 101+£ = a • b.
Page 98 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 151 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 34 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 129 - The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times as the polygon has sides, less two.
Page xx - The proportional parts are stated in full for every tenth at the right-hand side The logarithm of any number of four significant figures can be read directly by addN...
Page 35 - The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root.
Page 97 - But a' = 180° - a, c' = 180° - c, and CAB' = 180° - A Hence cos (180° — a) =cos b cos (180° - c) + sin b sin (180° - c) cos (180a- A)9 or, cos a = cos b cos с -f- sin b sin с cos A, which- proves the law of cosines for all cases.
Page 32 - ... consists of two parts, an integral part and a decimal part. The integral part is called the characteristic of the logarithm, and may be either positive or negative.