Mathematical Tables: Containing the Common, Hyperbolic, and Logistic Logarithms, Also Sines, Tangents, Secants, and Versed Sines, Both Natural and Logarithmic...

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Longman, Rees, Orme, 1834 - Logarithms - 368 pages
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Page xxxvii - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page lvii - Ixi following. But when the perpendicular falls out of the triangle, the difference of the two angles will be the angle required. PROP. XXII. — Having two sides, and the angle be/ween them ; tond either of the other angles.
Page xix - ... which must be subtracted from 10. But when the index is negative, add it to 9, and subtract the rest as before.
Page xii - Then, because the sum of the logarithms of numbers, gives the logarithm of their product ; and the difference of the logarithms, gives the logarithm of the quotient of the numbers : from the tw...
Page lxii - ... figures, the difference of latitude, and the departure, is each to be taken out at twice ; and if of three figures, at thrice. The chief...
Page xii - And thus, computing, by this general rule, the logarithms to the other prime numbers, 7, 11, 13, 17, 19, 23, &c, and then using composition and division, we may easily find as many logarithms as we please, or may speedily examine any logarithm in the table...
Page xviii - DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor ; the remainder will be the logarithm of the quotient EXAMPLE I.
Page xlvi - Add the logarithm of the given side to the sine of the angle opposite to the side required, and from the sum subtract the sine of the angle opposed to the given side ; the remainder will be the logarithm of the side required. SYSTEM. There is much propriety in the remark, that "system is the handmaid of science," and the term may be considered as used in contradistinction to disorder, irregularity, or random.
Page liii - PZ 38 30' ; to find the angle ZPS. PROP. XVIII. — Having the three angles ; to find any of the sides. Let the angles be changed into sides, taking the supplement of one of them ; then the operation will be the same as in the former proposition. PROP. XIX. — Having two angles, and a side opposite to one of them ; to find the side opposed to the other angle.
Page xlvii - Having two sides and the angle between thent ; to find the other two angles, and the third side. If the angle included be a right angle, add the radius to the logarithm of the less side, and from the sum subtract the logarithm of the greater side, or add its arith. сотр. : the remainder or sum will be the tangent of the angle opposed to the less side. Example. In the triangle BCD, having the side BE 197'3, and CD 251 -9; to find the angles BCD, CBD, and the side св. 7-5987728 ar. com. log....

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