Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful Tables

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Harper & Bros., 1848 - Logarithms - 150 pages

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Page v - In a system of logarithms all numbers are considered as the powers of some one number, arbitrarily chosen, which is called the base of the system, and the exponent of that power of the base which is equal to any given number, is called the logarithm of that number. Thus, if a be the base of a system of logarithms, N any number, and x such that N = a* then x is called the logarithm of N in the system whose base is a.
Page vi - The integral part is called the characteristic, and may be known from the following RULE. The characteristic of the logarithm of a number greater than unity, is one less than the number of integral figures in the given number.
Page vi - The accompanying table contains the logarithms of all numbers from 1 to 10,000 carried to 6 decimal places. To find the Logarithm of any Number between 1 and 100. Look on the first page of the table, along the column of numbers under N, for the given number, and against it, in the next column, will be found the logarithm, with its characteristic. Thus, opposite 13 is 1.113943, which is the logarithm of 13 ; " 65 is 1.812913, " " 65. To find tht Logarithm of any Number consisting of three Figures.
Page xvi - The given middle latitude is to be found either in the first or last vertical column, opposite to which, and under the given difference of latitude, is inserted the proper correction in minutes, to be added to the middle latitude to obtain the latitude in which the meridian distance is accu rately equal to the departure.
Page xii - Required the logarithmic tangent of 73 35' 43". The logarithmic tangent of 73 35' 40" is 10.531031. Proportional part for 3" is 23. Logarithmic tangent of 73 35' 43" 10.531054. When a cosine is required, the degrees and seconds must be sought at the bottom of the page, and the minutes on the right, and the correction for the odd seconds must be subtracted from the number in the table. Required the logarithmic cosine of 59 33
Page x - The logarithmic cosine of 59 33' 40" is 9.704682 Proportional part for 7" is 25 Logarithmic cosine of 59 33' 47
Page v - The logarithm of every number between 10 and 100 is some number between 1 and 2, ie, is 1 plus a fraction. The logarithm of every number between 100 and 1000 is some number between 2 and 3, ie, is 2 plus a fraction, and so on.

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