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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Longman & Company, 1855 - Logarithms - 368 pages
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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 xix - ... which must be subtracted from 10. But when the index is negative, add it to 9, and subtract the rest as before.
Page lxii - ... the distance consists of two significant 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 design of this table is for the ready and exact working of traverses ; but it may also be applied to the solution of the several cases of plain sailing, and to some other uses PROP. I. — Having the course and distance, to▀nd the difference of latitude and departure.
Page xix - Multiply the logarithm of the number giren by the proposed index of the power, and the product will be the logarithm of the power sought.
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 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 x - ... of powers, to the multiplying the logarithm of the root by the index of the power ; and the extracting of roots, to the dividing the logarithm of the given number by the index of the root required to be extracted. So, iising L.
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)".

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