Well known in Napier's time, and it is quite probable that Napier's line of thought started with this formula, since otherwise it is difficult to account for his initial restriction of logarithms to those of the sines of angles. Napier labored at least twenty years upon his theory, and, whatever the genesis of his idea, his final definition of a logarithm is as follows. Consider a line segment AB and an infinite ray DE, as shown in Figure 54. Let points C and F start moving simultaneously from A and D, respectively, along these