Prosthaphaeresis

Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximating products 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 prosthesi and afairo, meaning addition and subtraction, two steps in the process.

The identities

The trigonometric identities exploited by prosthaphaeresis relate products of trigonometric functions to sums. They include the following:

Related Topics:
Trigonometric identities - Trigonometric function

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• sin a sin b = ½
• cos a cos b = ½
• sin a cos b = ½
• cos a sin b = ½

The first two of these are believed to have been derived by Bürgi, who related them to Brahe; the others follow easily from these two. If both sides are multiplied by 2, these formulas are also called the Werner formulas.

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