The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. What has not always been clear, however, is that the circle continued to serve Kepler as a central element in his astronomy after the discovery of the elliptical orbit of Mars. Moreover, the circle also functioned for Kepler in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology (...) to select the basic aspects. His basic set of polygons consisted of those figures that could be constructed using only a compass and a rule; the set of fundamental harmonies consisted of the consonances of the just intonation; and the traditional set of astrological aspects were enlarged by Kepler to include three new aspects in order to make the astrological set consistent with geometry and music. And as the circle served to unify these three areas, so also did it serve to supply the fundamental answers to astronomical problems well after the discovery of his new astronomy—a topic to be discussed in Part II of this paper. (shrink)

The change from ancient and medieval to modern natural science, called Wende , must be associated with the work of Johannes Kepler and not that of Nicolaus Copernicus. Copernicus merely showed the way, introducing heliocentricity as the order of the planets. This Wende resulted from the synthesis of several disciplines formerly isolated from each other, namely mathematical astronomy, new physics, mathematical harmony, astrology, new physical optics, and natural theology. Whereas Copernicus united mathematical astronomy and peripatetic physics, Kepler was first to (...) see the necessity for providing a physical explanation and an ontological foundation to the heliocentric system. He was the first to consider and measure the movement of the planets in depth. The elements for his new physics Kepler obtained not from newly observed data, but from a harmonic archetypus of the regular polyhedra fitted in between excentric planetary spheres. On the basis of this archetypus he accepted the new heliocentric planetary system as a physical reality. That is why astronomy, by way of taking into account stereometric quantities, is, in Kepler's eyes, a kind of divine worship. Later, the best empirical data had also to be taken into consideration as a means of proving this a priori archetypus .The result was, on the one hand, a universal natural science able to explain natural processes in grater abundance than ever before or since in the history of science. Although accepted only in parts, it resulted in founding a new natural science with adherent mathematical and empirical methods. It also led Kepler to establish, step by step, the elliptical path of the planets, thereby overcoming, for the first time, the two axioms of ancient astronomy, requiring uniform and circular planetary motion.It has been shown that this Keplerian Wende was possible only within the Historischen Erfahrungsraum of Renaissance Humanism , which came about itself as the result of reactivating the scientific and philosophical thinking of the ancient Greeks and was accomplished by three steps relating to the revival of original ancient writings, the ancient knowledge of natural facts and data, and the ancient scientific and philosophical ideas and mentalities. (shrink)

By a simple revision of Newton's diagram for Proposition 6 of the third edition of the Principia, one can see directly how the mathematics of uniform circular motion have been employed to solve the Kepler problem of elliptical planetary motion in Proposition 11. Newton strove initially to build his dynamics on the linear kinematics of Galileo; and, in this utilization of uniformly accelerated linear motion to solve more complicated problems, he can be seen as revolutionary. But he could not escape (...) completely from the coils of celestial circularity, and in his utilization of uniform circular motion to solve problems of elliptical motion, he can be seen as reactionary. The key to understanding Newton's mature dynamics resides in the discussion of the alternate dynamics ratio, as presented here in section six. (shrink)