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Napier also observes that logarithms of a geometric progression differ by a constant value at each stage, namely the logarithm of the multiplier. So if one knows the logarithm of the initial value of a geometric progression and of the multiplier, one can compute the logarithm of each member of the progression by repeated addition of the ...
The English mathematician Henry Briggs visited Napier in 1615, and proposed a re-scaling of Napier's logarithms to form what is now known as the common or base-10 logarithms. Napier delegated to Briggs the computation of a revised table, and they later published, in 1617, Logarithmorum Chilias Prima ("The First Thousand Logarithms"), which gave ...
The 19 degree pages from Napier's 1614 table of logarithms of trigonometric functions Mirifici Logarithmorum Canonis Descriptio. The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him.
Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of Napier's bones and Promptuary (another early calculating device). [11] His invention of logarithms was quickly taken up at Gresham College, and prominent English mathematician Henry Briggs visited Napier in ...
Napier's formulation was awkward to work with, but the book fired Briggs' imagination – in his lectures at Gresham College he proposed the idea of base 10 logarithms in which the logarithm of 10 would be 1; and soon afterwards he wrote to the inventor on the subject. Briggs was active in many areas, and his advice in astronomy, surveying ...
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...
Binary logarithms are also used in computer science, where the binary system is ubiquitous; in music theory, where a pitch ratio of two (the octave) is ubiquitous and the number of cents between any two pitches is a scaled version of the binary logarithm, or log 2 times 1200, of the pitch ratio (that is, 100 cents per semitone in conventional ...
Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication , and also called rabdology , a word invented by Napier.