THE VICARIOUS HYPOTHESIS AND ITS FAILURE
Having finished the necessary preliminaries, i.e., having set the correct point of reference, determined the nature and value of the inclination of the orbits to the ecliptic, and established the need for the equant for the orbit, Kepler was ready to develop his theory of Mars. Accordingly, he selected twelve observations at oppositions -- ten from Tycho's and two from his own. Kepler also verified some of these observations by comparing them with data obtained by Fabricius in East Friesland.
Kepler wanted to determine the orbit of Mars. These elements -- the position of the line of apsides (longitude at aphelion), the eccentricity, the period, the epoch, and the size of the orbit -- would determine the orbit, since at this stage, like all other astronomers of the day, he believed in the inviolability of the principle of circularity. However, unlike most of his colleagues, he refused to subscribe to Ptolemy's bisection of the eccentricity according to which the center of the orbit of Mars exactly bisected the distance between the centers of the equant and the sun (earth). Kepler considered such a bisection totally unwarranted and a source of errors and imperfections in the