is probably not true, but it is, perhaps, worth repeating, as it was credited at the time and casts a light on the age. During his short life Regiomontanus accomplished much, and gave promise of more. In particular he greatly improved the doctrine of trigonometry. Purbach and himself were the very first Europeans to utilize the discoveries of the Arabs in this science. As every astronomical calculation depends upon the solution of spherical triangles, the tables of sines and tangents computed by Regiomontanus were of fundamental importance, since they gave numerical values of these trigonometric functions calculated once for all, and saved the computer endless special reckonings.
It is difficult for us to conceive the state of science in those days. The school-boy problem: given a, b, c, in a spherical triangle, to find A, B, C, was considered operose by Regiomontanus and his friends, although the solution had been reached long before, by Albategnius. Blanchini, a contemporary of note, sends him the following equations for solution:
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A star rises at Venice at 3h 25m, and transits at 7h 38m, after midnight; required its longitude and latitude: is a problem addressed to Blanchini, in return. The Arabs five centuries earlier would have found these questions easy. Regiomontanus was, nevertheless, the most accomplished man of science in Europe. The ancients determined the longitude of a planet somewhat as follows: The difference of longitude between the planet and the moon was measured (A.) and next the difference of longitude between the moon and the sun (B). The longitude of the sun was calculated from the solar tables (C). The sum of A, B and C gave the planet's longitude. In Walther's observatory the angular distances of the planet from known stars were measured and the required longitude and latitude of the planet were calculated, by the formulae of spherical trigonometry, from the known longitudes and latitudes of the stars. The gain in precision was considerable, and the observations could be made on any clear night, whether the moon was or was not above the horizon.
Walther survived his friend for many years and carried on the observations which they had begun together. It was in their observatory that clocks (not pendulum-clocks) were first employed to measure short intervals of time and that observations were first corrected for terrestrial refraction. A star seen through the atmosphere appears higher above the horizon than if the atmosphere were absent. Its apparent position must then be corrected for refraction in order to obtain its true place. At an altitude greater than 45° the correction is less than 1′, which was inappreciable before the day of the telescope; but near the horizon the correction is large (the line of sight passing
