Tycho Brahe produce much of his astronomical data, Tycho relied heavily on the then new technique of "prosthaphaeresis", an algorithm for approximating products based on trigonometric identities that predated logarithms. Although Tycho admired Copernicus and was the first to teach his theory in Denmark, he was unable to reconcile Copernican theory with the basic laws of Aristotelian physics, that he considered to be foundational. He was also critical of the observational data that Copernicus built his theory on, which he correctly considered to have a high margin of error. Instead, Tycho proposed a "geo-heliocentric" system in which the Sun and Moon orbited
Tycho Brahe excruciating pain. The night before he died, he suffered from a delirium during which he was frequently heard to exclaim that he hoped he would not seem to have lived in vain. Before dying, he urged Kepler to finish the "Rudolphine Tables" and expressed the hope that he would do so by adopting Tycho's own planetary system, rather than that of Copernicus. It was reported that Brahe had written his own epitaph, "He lived like a sage and died like a fool." A contemporary physician attributed his death to a kidney stone, but no kidney stones were found during an