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
Armillary sphere the crown escapement which has been developed from 14th century, and is applied to gear system which had been improved until the middle of 17th century in Western-style clockwork. In particular, timing device of Song I-yŏng's Armillary Clock adopts the early 17th century pendulum clock system which could remarkably improve the accuracy of a clock. Further advances in the instrument were made by Danish astronomer Tycho Brahe (1546–1601), whose elaborate armillary spheres passing into astrolabes are figured in his "Astronomiae Instauratae Mechanica". Armillary spheres were among the first complex mechanical devices. Their development led to many improvements in techniques and