The Scottish theologian and mathematician John Napier (1550-1617) studied at the University of St Andrews, the oldest university in Scotland, and spent several years in Continental Europe. He invented logarithms, a mathematical device which simplified and speeded up manual calculations and aided the work of scholars for centuries. This inspired the invention of the slide rule during the 1600s, which was excellent for multiplication and division and the calculation of powers and roots. The Apollo lunar program in the United States as late as the 1960s kept slide rules as backups for their electronic calculators. Napier improved and popularized the decimal notation introduced by the Flemish mathematician Simon Stevin.- - - - - - - - -
The Swiss mathematician, clockmaker and astronomer Joost Bürgi (1552-1632) independently invented a system of logarithms which he published in 1620, but Napier has the priority due to his publication in 1614 of his Mirifici Logarithmorum Canonis Descriptio. Napier’s system was extended and improved by his admirer Henry Briggs (1561-1630), an English professor of geometry at Gresham College in London, who visited Napier at Edinburgh in 1615. Briggs is especially known for his publication of tables of logarithms to the base 10, first one in 1617 and later the Arithmetica Logarithmica in 1624.
Adriaan Vlacq (1600-1667), a book publisher born in Gouda in the Netherlands, extended the earlier work of Briggs and in 1628 published the first full table of logs from 1 to 100,000, calculated to ten places. The Slovenian mathematician Jurij Vega (1754-1802) attended school in Ljubljana and became professor of mathematics at the Austrian Imperial Artillery School in Vienna. As an artillery officer he fought against the Turks near Belgrade in 1788, but he is best remembered for his accurate tables of logarithms based on those of Vlacq.
Basel in Switzerland had been a free city and a center of learning for centuries. The sciences flourished there as it did in the Dutch and Flemish cities. The Bernoulli merchant family were originally religious refugees of the Protestant faith fleeing from persecution by the Spanish rulers of the southern Netherlands who had come to Basel from Antwerp via Amsterdam
The Bernoullis were to become the world’s most successful mathematical family. The founding member and arguably also the most gifted representative of this famous scientific family was the brilliant mathematician Jacob Bernoulli (1654-1705), whose father was an important citizen of Basel. Jacob Bernoulli was one of the early students of probability theory, on which subject he wrote the Ars Conjectandi (The Art of Conjecturing), published posthumously by his nephew in 1713. This work contains the theorem of Bernoulli and the Bernoulli numbers, which are among the most interesting number sequences in mathematics, particularly important in number theory.
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