closer than the nearest table value. See lookup table for more details. Reverse identities The product formulas can also be manipulated to obtain formulas that express addition in terms of multiplication. Although less useful for computing products, these are still useful for deriving trigonometric results: See also Slide rule References External links Prosthaphaeresis formulas Daniel E. Otero Henry Briggs. Introduction: the need for speed in calculation. Mathworld: Prosthaphaeresis formulas Adam Mosley. Tycho Brahe and Mathematical Techniques. University of Cambridge. IEEE Computer Society. History of computing: John Napier and the invention of logarithms. Math Words: Prosthaphaeresis Beatrice Lumpkin. African and African-American Contributions to Mathematics. Discusses Ibn Yunis's contribution to prosthaphaeresis. Prosthaphaeresis and beat phenomenon in the theory of vibrations, by Nicholas J. Rose Trigonometry Arithmetic