Mathematical Tables: Containing the Logarithms of Numbers; Logarithmic Sines, Tangents, and Secants, to Seven Decimal Places, and a Traverse Table. To which are Prefixed, Logarithmical Arithmetic, and Plane Trigonometry ...

P. Hill, 1789 - 40 pages

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Page 4 - And also, when 1 is borrowed, in the left-hand place of the decimal part of the logarithm, add it to the index of the divisor when...
Page 7 - Divide the logarithm of the power or given number, by its index, and the quotient will be the logarithm of the root required. Note, When the index of the logarithm is negative, and the divifor is not exactly contained in it without a remainder, increafe...
Page 5 - ... by the foregoing rules ; the remainder will be the logarithm of the 4th term required. Or in any compound proportion whatever, add together the logarithms of all the terms that are to be multiplied, and from that fum take the fum of the others ; the remainder will be the logarithm of the term fought. But infteadof fubtrafting any logarithm, we may add its complement, and the refult will be the fame.
Page 12 - The three angles of every plane triangle are, together, equal to two right angles, or 180 degrees.
Page 6 - Rule. Multiply the Logarithm of the given number by the Index of the proposed power, and the product will be the Logarithm, whose natural number is the power required.
Page 2 - To find the number indicated by a given logarithm. Look for the decimal part of the given logarithm in the different columns, and if it cannot be found exactly, take the next less. Then under N in the left-hand column, and in a line with the logarithm found, are three figures of the number required, and on the top of the column in which the found logarithm stands is one figure more ; place the decimal point...
Page 1 - ... index of -0032549 is — 3, because the first significant figure is the third decimal, &c. of any other sum. If the given sum for which the logarithm is required contains or consists of both integers and decimals, the index is determined by the integer part, without having any regard to the other. 1. To find the logarithm of any whole number under 100. Look for the number under N in the first page of any Logarithmic Table ; then immediately on the right of it is the logarithm required, with its...
Page 25 - Having the three ßdes ; to find any Angle. Add the three fides together, and take half the fum, and the differences betwixt the half fum and each fide : Then add the complements of the Logarithms of the half-fum, and of the difference between the half fum and the fide oppofite to the angle fought, to the Logarithms of the differences of the half-fum and the other fides ; half their...
Page 2 - The decimal of ^ = -4375 ; and the logarithm of this decimal is = -1.640978 or, subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm, which, being that of a decimal fraction, must always have a negative index.
Page 26 - ... to the difference of the fegments of the bafe, made by a perpendicular upon it from the oppofite angle.

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