- ?Lv 71 decade agoFavorite Answer
The method of logarithms was first publicly propounded in 1614, in a book entitled Mirifici Logarithmorum Canonis Descriptio, by John Napier, Baron of Merchiston, in Scotland. (Joost Brgi independently discovered logarithms; however, he did not publish his discovery until four years after Napier.) Early resistance to the use of logarithms was muted by Kepler's enthusiastic support and his publication of a clear and impeccable explanation of how they worked. Their use contributed to the advance of science, and especially of astronomy, by making some difficult calculations possible. Prior to the advent of calculators and computers, they were used constantly in surveying, navigation, and other branches of practical mathematics. It supplanted the more involved method of prosthaphaeresis, which relied on trigonometric identities as a quick method of computing products. Besides the utility of the logarithm concept in computation, the natural logarithm presented a solution to the problem of quadrature of a hyperbolic sector at the hand of Gregoire de Saint-Vincent in 1647. At first, Napier called logarithms "artificial numbers" and antilogarithms "natural numbers". Later, Napier formed the word logarithm to mean a number that indicates a ratio: λόγος (logos) meaning proportion, and ἀριθμός (arithmos) meaning number. Napier chose that because the difference of two logarithms determines the ratio of the numbers they represent, so that an arithmetic series of logarithms corresponds to a geometric series of numbers. The term antilogarithm was introduced in the late 17th century and, while never used extensively in mathematics, persisted in collections of tables until they fell into disuse.