The base of natural logarithms

The base of natural logarithms - Petropoli edited by P H...

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The base of natural logarithms. This constant, 2.71828. .., was referred to in Edward Wright's English translation of Napier's work on logarithms, published in 1618. The first symbol used for the constant mentioned by Cajori is the letter b used by Leibniz in letters to Huygens in 1690 and 1691. Leonhard Euler (1707-1783) introduced e for this constant in a manuscript, Meditatio in Experimenta explosione tormentorum nuper instituta (Meditation on experiments made recently on the firing of cannon), written at the end of 1727 or the beginning of 1728 (when Euler was just 21 years old). The manuscript was first printed in 1862 in Euler's Opera postuma mathematica et physica,
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Unformatted text preview: Petropoli, edited by P. H. Fuss and N. Fuss (vol ii, pp. 800-804). The manuscript describes seven experiments performed between August 21 and September 2, 1727: For the number whose logarithm is unity, let e be written, which is 2,7182817. .. [sic] whose logarithm according to Vlacq is 0,4342944. .. [translated from Latin by Florian Cajori]. Euler next used e in a letter addressed to Goldbach on November 25, 1731, writing that e "denotes that number whose hyperbolic logarithm is = 1." The earliest appearance of e in a published work was in Euler's Mechanica (1736), in which he laid the foundations of analytical mechanics (Maor, p. 156)....
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This note was uploaded on 02/04/2011 for the course PB HLTH 140 taught by Professor Tarter during the Fall '10 term at Berkeley.

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