"The biggest improvement in arithmetic during the sixteenth and seventeenth centuries was the invention of logarithms. The basic idea was noted by Stifel. In Arithmetica Integra [1544] he observed that the terms of the geometric progression 1, r, r2, r3, ... correspond to the terms in the arithmetic progression 0, 1, 2, 3, ... . Multiplication of two terms in the geometric progression yields a term whose exponent is the sum of the corresponding terms in the arithmetic progression. Division of two terms in the geometric progression yields a term whose exponent is the difference of the corresponding terms in the arithmetic progression. This observation had also been made by Chuquet in Le Triparty en la science des nombres (1484). Stifel extended this connection between the two progressions to negative and fractional exponents. Thus the division of r2 by r3 yields r-1, which corresponds to the term -1 in the arithmetic progression. Stifel, however, did not make use of this connection between the two progressions to introduce logarithms. John Napier, the Scotsman who did develop logarithms about 1594, was guided by this correspondence between the terms of a geometric progression and those of the corresponding arithmetic progression. Napier was interested in facilitating calculations in spherical trigonometry that were being made on behalf of astronomical problems."