Approximate multiplication and division using formulas from trigonometry
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Prosthaphaeresis (from the Greek προσθαφαίρεσις) was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek prosthen (πρόσθεν) meaning before and aphaeresis (ἀφαίρεσις), meaning taking away or subtraction.[1][2][3]
In ancient times the term was used to mean a reduction to bring the apparent place of a moving point or planet to the mean place (see Equation of the center).
Nicholas Copernicus mentions "prosthaphaeresis" several times in his 1543 work De Revolutionibus Orbium Coelestium, to mean the "great parallax" caused by the displacement of the observer due to the Earth's annual motion.
^prosthaphæresis in The Century Dictionary, The Century Co., New York, 1911.
^Pierce, R. C. Jr. (January 1977). "A Brief History of Logarithms". The Two-Year College Mathematics Journal. 8 (1). Mathematical Association of America: 22–26. doi:10.2307/3026878. JSTOR 3026878.
Prosthaphaeresis (from the Greek προσθαφαίρεσις) was an algorithm used in the late 16th century and early 17th century for approximate multiplication and...
invention, there had been other techniques of similar scopes, such as the prosthaphaeresis or the use of tables of progressions, extensively developed by Jost...
formula and the binomial theorem. The product-to-sum identities or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the...
t sin b t {\displaystyle \sin at\sin bt} term and utilizing the prosthaphaeresis (product to sum) identity, sin a sin b = cos ( a − b ) − cos...
of several mathematicians sometimes credited with the invention of prosthaphaeresis, which simplifies tedious computations by the use of trigonometric...
logarithms. In the 16th and early 17th centuries an algorithm called prosthaphaeresis was used to approximate multiplication and division. This used the...
corresponds to the top graph (labelled "50% Modulation") in figure 4. Using prosthaphaeresis identities, y(t) can be shown to be the sum of three sine waves: y...
astronomical data, Tycho relied heavily on the then-new technique of prosthaphaeresis, an algorithm for approximating products based on trigonometric identities...
For the 25 years preceding the invention of the logarithm in 1614, prosthaphaeresis was the only known generally applicable way of approximating products...
and statistics. Methods of numerical approximation existed, called prosthaphaeresis, that offered shortcuts around time-consuming operations such as multiplication...
potential of the recent developments in mathematics, particularly those of prosthaphaeresis, decimal fractions, and symbolic index arithmetic, to tackle the issue...
Sher and Dean C. Nataro conceived a new type of slide rule based on prosthaphaeresis, an algorithm for rapidly computing products that predates logarithms...
one of Werner's formulas, it was essential for the development of prosthaphaeresis and logarithms decades later. Ibn Yunus described 40 planetary conjunctions...
in reference to surpluses and deficits in business problems 1490: Prosthaphaeresis, invented by Johannes Werner 1525: The "√" symbol, first published...
the world, as well as the publication of the mathematical model of prosthaphaeresis. History has sided with Ursus on the later issue, and he had stated...
Greeks, in particular Hipparchus, knew the equation of the center as prosthaphaeresis, although their understanding of the geometry of the planets' motion...
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