Regiomontanus' Astronomical Tables
A page from Regiomontanus's 
One scholar has remarked that Regiomontanus was a "lightning calculator, and a very accurate one too." Certainly, he was a prolific compiler of tables and ephemerides. He produced tables of sines at intervals of sixths of a degree in which the value of sin 90° was set at 6 000 000 and 10 000 000; these were printed by Johann Schöner in 1541. His Tabulae primi mobilis, completed in Hungary and dedicated to King Matthias, were first published in 1514. They gave values of a, an unknown side of a right-spherical triangle, in accordance with the relationship a = sin-1 (sin a sin c) for values of a and c from 1 to 90° at one degree intervals. Never widely used, they were rendered obsolete by the advent of logarithmic calculating techniques. The Tabulae directionum, produced with the assistance of Martin Bylica, were primarily for astrological use and seem to have been correspondingly more popular: they were first printed in 1490, and went through eleven editions up to 1626. In addition to tables for calculating horoscopes, the collection included a table of the declination of the sun for every degree of longitude in the ecliptic, and introduced, probably for the first time in the Latin West, a table of tangents. Tan 45° was set to 100 000, in accordance with Regiomontanus' developing and influential preference for a decimal system over a sexagesimal one for performing such calculations.
With respect to astronomical tables proper, Regiomontanus expressed misgivings about both the Alfonsine and the Toledan Tables. He did not live to produce tables of his own, but did issue almanacs and calendars from his press in Nuremberg. The calendars included the times of new and full moons and eclipses for the years 1475-1531; the almanacs gave mean planetary positions, true positions for the sun and moon, and eclipse times for 1475-1506. Both were extremely popular, and an edition of the almanacs was used by Christopher Columbus.