appeared in print in 1614, and so Napier usually is credited with the invention.

The basic idea that lies behind logarithms is the correspondence between geometric progressions r1, r2, r3,... and the arithmetic progressions formed by the exponents:

Multiplying two numbers in the geometric series together is equivalent to adding the corresponding exponents. The closer r is taken to 1 the closer adjacent terms in the geometric progression are to each other, and the geometric progression can be made to include as many numbers as one requires within a given interval.

From this basic idea, Napier developed a geometrical definition of logarithms, illustrated in Figure 7.6. The upper line AB is of fixed finite length, and

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