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 "Rudolphine Tables". Also at the court in Prague was the mathematician Nicolaus Reimers (Ursus), with whom Tycho had previously corresponded, and who, like Tycho, had developed a geo-heliocentric planetary model, which Tycho considered to have been plagiarized from his own. Kepler had previously spoken highly of Ursus, but now found himself in the problematic position of being employed by Tycho and having to defend his employer against Ursus' accusations, even though he disagreed with both of their planetary models. In 1600, he finished the tract "Apologia pro Tychone contra Ursum" (defense of Tycho against Ursus). Kepler had great respect for