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)

In this article, I address the epistemological role that geometry plays in Kepler’s Harmonices Mundi Libri V and argue that the framework he develops there is meant to address concerns regarding the confirmation of astronomical hypotheses, which are supported by comments in earlier works regarding empirical underdetermination. The geometrical epistemology that he constructs to combat these concerns in the Harmonices Mundi is introduced in Book I and then is extended to his theory of harmonic proportion in Book III, finally providing (...) the foundation for his derivation of the planetary motions in Book V. To argue for these claims, I begin by discussing Kepler’s concern with underdetermination in earlier works. Then I turn to the Harmonices Mundi and argue that Kepler seeks to provide a geometrical system that directly links the theorist with the world. Finally, I show how he applies this system to his astronomy via his harmonic theory. This account not only helps us to understand Kepler’s scientific methodology better but also sheds light on Kepler’s enthusiasm for the results of the Harmonices Mundi by showing how they provide an example of the successful application of his geometrical epistemology. (shrink)

The formal study of both astronomy and astrology in later medieval Europe was firmly based in the universities. Instruction in astrology is attested by the presence of an educational board game, known as the ludus astronomorum, in several university-related miscellanies of fifteenth-century English provenance. William Fulke also published an edition of the game a century later , which is attested in a number of Elizabethan libraries. The game serves to rehearse for its players the celestial motions and astrological principles described (...) by Ptolemy. It also employs principles of stellar rays described by al-Kindi in his De radiis stellarum. (shrink)