G.B. Riccioli's geo-heliocentric use of Epicepicycles, ellipses and spirals

According to Giovanni Battista Riccioli (1598–1671), planets describe orbits in a fluid heaven in a helio-geocentric model of cosmos. In his Almagestum Novum (1651) he stresses the need for a novel and rigorous geometrical explanation for the motion of heavenly bodies, which considers a separate Primum Mobile as an unnecessary hypothesis. Riccioli rejects the standard eccentric-epicycle theory as unsatisfactory and argues for what he calls “Eccentrepicyclos” or “Epicepicycles.” He takes the Keplerian elliptical theory into account and includes a variable oscillation of both the mobile eccentric center and the variation of the epicycle’s diameter. As a result, planets move along spiral orbits that have variable sizes. The inequalities, which astronomers had always tried to explain, are now justified: the spiral trajectory, obtained by means of the oscillation of the eccentric center, warrants the first inequality, about the variation of the planets’ velocity. The variable amplitude of the spirals, obtained by the variation of the epicycle’s diameter, explains the second inequality, namely the apparent retrograde or progressive planetary motion. In the later work Astronomia Reformata (1665), Riccioli uses explicitly the term “ellipse.” Riccioli’s innovations are of great interest and help to understand the complexity of the astronomical debates about the best world-system.