Mathematical Tables: Containing the Common, Hyperbolic, and Logistic Logarithms, Also Sines, Tangents, Secants, and Versed Sines Both Natural and Logarithmic. Together with Several Other Tables Useful in Mathematical Calculations. Also the Complete Description and Use of the Tables |
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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 xix - ... which must be subtracted from 10. But when the index is negative, add it to 9, and subtract the rest as before.
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 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 ix - N is =r ; so that the radix, r, is always that number, whose logarithm is 1, in every system. When the radix r =2.718281828459, &c., the indices n are the hyperbolic or Napier's logarithm of numbers N; so that n is always the hyperbolic logarithm of the number N, or (2.71628 182*3459)".
Page xlvii - Having two sides and the angle between them. ; 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....
Page xxxviii - The product of radius and the cosine of the sum of two arcs, is equal to the product of the cosines of the arcs — the product of their sines.
Page xviii - I is borrowed in the left-hand place of the decimal part of the logarithm, add it to the index of the divisor...