Mathematical Tables for Practical Men: Comprising Several New and Useful Tables Adapted to the Wants of Surveyors, Engineers, and Navigators

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C. Wells, 1845 - Mathematics - 59 pages

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Page viii - Arithmetic, write them orderly under one another, with the signs of proportion ; then add the logarithms of the second and third terms together, and from their sum subtract the logarithm of the first term, and the remainder will be the logarithm of the fourth term, or answer.
Page vi - D, the number on the same horizontal line with the logarithm, and multiply this number by the numbers that have been considered as ciphers : then, cut off from the right hand as many places for decimals as there are figures in the multiplier, and add the product, so obtained, to the first logarithm, for the logarithm sought.
Page vii - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Page ix - Divide the logarithm of the given number by the index of the root ; and the quotient will be the logarithm of the required root (Art.
Page viii - PROBLEM III. — To perform Multiplication by Logarithms. RULE. — Add the logarithms of the factors, and the sum is the logarithm of the product. If there are...
Page xii - USE OF THE ABOVE TABLE To find the area of a segment of a circle. Rule. — Divide the height, or versed sine, by the diameter of the circle, and find the quotient in the column of versed sines.
Page ix - ... searching for the next less (or greater) logarithm, attention must be paid to the fact that the functions are found in different columns according as the angle is below or above 450. If, for example, the next less logarithmic sine is found in the column with
Page viii - ... affirmative index, makes 3, from this take 3, the sum of the negative indices, the remainder is 0, which is the index of the sum of the logarithms. 5. Required the product of 23.14 and 50.62, by logarithms. Ans. 117.1347 6l Required the product of 3.12567, .02868, and .12379, by logarithms.
Page ix - 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 xiii - To find the length of an arc of a circle, or the curve of a right semi-ellipse. RULE. — Divide the height by the base, and the quotient will be the height of an arc of which the base is unity. Seek, in the Table of Circular or of Semi-elliptical arcs, as the case may be, for a number corresponding to this quotient, and take the length of the arc from the next right-hand column. Multiply the number thus taken out by the...

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