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Of the Measurement and Calculation of Lines and Angles,

39

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ELEMENTS OF SURVEYING.

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INTRODUCTION,

CHAPTER I.

OF LOGARITHMS.

1. LOGARITIIMS of numbers are the indices that denote the different powers to which a given number must be raised to produce those numbers.

2. If a be the given number, whose indices and powers are to be considered, then a being put equal to n, a, the given number, or root, is called the base of the system of logarithms, n the number whose logarithm is considered, and ±r, the logarithm of that number.

3. Any number, except 1, may be taken for the base of a system of logarithms. In the system in general use, the base is 10; and this system affords the greatest facilities in calculations, because 10 is the base of the common numeration, both in whole numbers and decimal fractions.

4. Taking a±*=n, we have, x=log. n; and putting a±v= m, gives, y=log. m. If the equations a2=n, and a"=m, be multiplied together, member by member, we have, aa × ao= nxm, or a2+y=nXm. In this expression, x+y is the logarithm of n xm (2); from which we conclude, that the sum of the logarithms of any two numbers, is equal to the logarithm of their product.

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