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Sines, Versines and Haversines in Nautical Astronomy

Of immense importance to nautical astronomers are tables of trigonometrical functions. The history of these begins with the table of chords first suggested by Hipparchus two centuries before the beginning of the Christian Era. The earliest table of chords extant is that computed by Ptolemy (fl. c. 150 a.d.) whose table, true to the sexagesimal tradition, is based on the division of the radius of a circle into sixty parts. The first table of half-chords, or sines, is supposed to be of Indian origin and to date from the sixth century; but credit for being first to use a table of half-chords for solving spherical triangles belongs to the Arab mathematician Albategnius who flourished during the tenth century. The first printed table of sines, according to De Morgan, is a small work giving sines to each minute of arc from 0° to 90°, undated and unsigned but evidently published before 1500.