I interpret John Napier's definition of a logarithm to show in modern terms how closely his arithmetic methods foreshadowed elements of differential and integral calculus, and I include a related iteration used by Henry Briggs to compute his first base-10 logarithms; the algebraic structure of the iteration yields an algorithm for computing natural logarithms using Bernoulli numbers. This text complements a slide and video presentation for the 11th International Leibniz Conference in Hannover, Germany, July 31 - August 4, 2023. It includes software that can be copied and executed in Casio's free online Keisan Calculator while reading the text. The slides and video will be made publicly available in early August, 2023. This Introduction ...