# John Napier

John Napier was born in Merchiston Tower in Scotland, 1550. He was known as the Marvelous Merchiston, a title received for his genius and imaginative vision in a number of fields. Napier studied briefly at St. Andrews University beginning at the age of 13. On his marriage in 1572, he was provided with an estate by his father, Sir Archibald Napier of Mechiston. He passed the remainder of his life as a land proprietor, devoting his free time to mathematics, invention, and theology. Napier died at Merchiston castle on April 14, 1617. Beginning in about 1594, Napier worked for 20 years in developing deas on logarithms and tables of logarithms.

During this period he elaborated his systems whereby products, quotients, and roots could quickly be determined from his tables, which showed powers of 10 with a fixed number used as a base. Napiers system relied on the fact that all numbers can be expressed in exponential form. For instance, in a base 2 system, 4 can be written as 2 and 8 can be written as 2 , while 5, 6, and 7 can be written using some fractional exponent between 2 and 3. Once numbers were written in this exponential form, multiplication could be done basically by adding the exponents, and division ould be done by subtracting the exponents.

This considerably simplified computations such as trigonometric calculations used in astronomy. Napier finally published his tables of logarithms in 1614 in his Mirifici Logarithmorum Canonis Descriptio (A description of the marvelous rule of logarithms) which also told the steps which had led to their invention. In 1615 the English mathematician Henry Briggs talked with Napier, and together they developed the rules of Common logarithms, using 10 as a base. Briggs published his tables of Common logarithms in 1617.

Napiers second published work on logarithms, the Mirifici Logarithmorum Canonis Construction (The construction of the marvelous rule of logarithms), published in 1619 fully described the methods he used in creating his tables of Napierian Logarithms, today relating directly to Natural Logarithms. Without Napiers works on logarithms, other mathematicians and inventors might not have made their own great advancements in the fields of astronomy, dynamics, and physics, and Charles Richter would not have been able to successfully create his table for measuring intensities of earthquakes.

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