Here's an even better one, which explains not only how Euler calculated logarithms with the bisection method, but also how he used some smart Taylor series tric

Here's an even better one, which explains not only how Euler calculated logarithms with the bisection method, but also how he used some smart Taylor series tricks too to get the (natural) logarithms of the integers from 1 to 10, with 25 decimals. http://eulerarchive.maa.org/hedi/HEDI-2005-07.pdf http://eulerarchive.maa.org/hedi/HEDI-2005-07.pdf How good was Euler at that? I checked his results with a multiple precision library (mpmath) and Euler got all the correct digits for 7 out of 10, he rounded off the last decimal in the wrong direction in 2 cases. Just for log(7) he got 21 correct decimals and the last 4 were wrong. Here's the link to Euler's book [1], where these logarithms are on page 118. His values are l1 = 0,00000 00000 00000 00000 00000 l2 = 0,69314 71805 59945 30941 72321 l3 = 1,09861 22886 68109 69139 52452 l4 = 1,38629 43611 19890 61883 44642 l5 = 1,60943 79124 34100 37460 07593 l6 = 1,79175 94692 28055 00081 24773 l7 = 1,94591 01490 55313 30510 54639 l8 = 2.07944 15416 79835 92825 16964 l9 = 2,19722 45773 36219 38279 04905 l10 = 2,30258 50929 94045 68401 79914 The correct values are l1 = 0,00000 00000 00000 00000 00000 l2 = 0,69314 71805 59945 30941 72321 l3 = 1,09861 22886 68109 69139 52452 l4 = 1,38629 43611 19890 61883 44642 l5 = 1,60943 79124 34100 37460 07593 l6 = 1,79175 94692 28055 00081 24774 l7 = 1,94591 01490 55313 30510 53527 l8 = 2.07944 15416 79835 92825 16964 l9 = 2,19722 45773 36219 38279 04905 l10 = 2,30258 50929 94045 68401 79915 [1]https://scholarlycommons.pacific.edu/cgi/viewcontent.cgi?article=1100&context=euler-works https://scholarlycommons.pacific.edu/cgi/viewcontent.cgi?art...