Excerpt from Elements of Plane and Spherical Trigonometry, 1868: With Their Applications to Mensuration, Surveying, and Navigation

Article 1.

Logarithms are numbers designed to diminish the labor of Multiplication and Division, by substituting in their stead Addition and Subtraction. All numbers are regarded as powers of some one number, which is called the base of the system, and the exponent of that power of the base which is equal to a given number, is called the logarithm of that number. The base of the common system of logarithms (called, from their inventor, Briggs logarithms) is the number 10. Hence all numbers are to be regarded as powers of 10. Thus, since l l, 0 is the logarithm of 1 in Briggs system, 10==10, 1 10 10==100, 2 100 10=1000, 3 1000 10=10000, 4 10, 000 . c., c., o., whence it appears that, in Briggs system, the logarithm of every number between 1 and 10 is some number between 0 and 1, i. e., is a proper fraction. The logarithm of every number between 10 and 100 is some number between 1 and 2, i, e, , is 1 plus a fraction. The logarithm of every number between 100 and 1000 is some number between 2 and 3, i.e., is 2 plus a fraction, and so on.(2.) The preceding principles may be extended to fractions by means of negative exponents. Thus, since 10 =0.1, 1 is the logarithm of 0.1 in Briggs system o.

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