Logarithmic and Trigonometric Tables

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D. C. Heath & Company, 1895 - Logarithms - 87 pages

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Page iii - The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For the investigations of these rules the student is referred to the " Treatise on Trigonometry,
Page iii - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page iii - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page iv - ... the decimal point. The characteristic of the logarithm of a number less than unity is negative, and one more than the number of ciphers immediately after the decimal point.
Page iv - ... of .03333 = .0035 nearly, and this added to .3000 gives .3035, a result a little too large. By shorter methods of higher mathematics, the logarithm of 2 is known to be 0.3010300, true to the seventh place.
Page iii - 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.
Page vii - ... 8916.31. The following rule is derived from the above : Find from the table the next less mantissa, the four figures corresponding, and the tabular difference. (See Note III.) Subtract the next less mantissa from the given mantissa, and divide the remainder by the tabular difference. (See Note VI.) ^Annex the quotient to the first four figures of the number, and point off the result. (See Note V.) Note V. The rules for pointing off are the reverse of the rules for characteristic ; they may be...
Page iv - ... characteristic) followed by a decimal fraction (mantissa), which has the property of being incapable of being fully written out, since it goes on ad infinitum. Fortunately it is only in rare cases, that more than seven decimal places of this fraction are required : in general indeed four or five suffice, and it is only for the most accurate computations that six or seven are used.
Page viii - For angles between 0 and 45, the required functions are printed at the top of the columns, the number of degrees at the top of the page, and the number of minutes in the lefthand column.
Page vi - Hence, assuming that the increase of the logarithm is proportional to the increase of the number...

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