Astronomical Images : Motion of Mercury, figure 5

Johannes Regiomontanus

Astronomical Images

In his Disputationes contra Cremonensia deliramenta, the last book printed before his untimely death in 1476, Regiomontanus offered a critique of the Theorica planetarum communis, a thirteenth-century textbook attributed to Gerard of Cremona, in comparison to the relative advantages offered by Georg Peuerbach's Theoricae novae planetarum. Adopting the form of a dialogue between 'Viennensis' (representing Regiomontanus) and 'Cracoviensis' (representing Martin Bylica of Ilkusch), the work utilises geometrical proofs, often supplemented by diagrams, to refute specific claims in the earlier Theorica. The is one of several diagrams used to criticise errors in the Theorica planetarum communis regarding the basic geometry of Ptolemy's Mercury model ' one of his most complex. Consistent with most of Ptolemy's planetary models, Mercury was said to revolve on the circumference of an epicycle, the centre of which was carried by an eccentric deferent. In order to fit the observational data, this deferent too had to be carried on a small eccentric deferent circle. Often referred to as a 'crank mechanism', this small circle carried on its circumference the centre of the large deferent, thereby cyclically moving it closer to and farther away from the Earth (represented at n). This diagram represents the innermost geometry of the model, the circle centred on f representing the crank mechanism. The circle of the eccentric deferent is not delineated; its only pictorial remnant is its centre, here represented at h (bottom left). This image, along with several others presented by Regiomontanus, concerns the problematic claims of the Theorica planetarum communis regarding the two perigees of the epicycle centre in the Mercury model. Having first noted that the perigees of the deferent centre occur at the two points 120 degrees from the apogee (rather than at 180 degrees, as for most other planets), Regiomontanus utilises this diagram to attack one of the Theorica's comments on the properties of the epicycle centre when it is in the 120 degree arc between its two perigees. In this configuration, according to the Theorica, the epicycle centre will always be opposite the aux of the deferent. Regiomontanus shows this to be false, since it violates the fundamental requirement of the model that the epicycle centre move around the equant point at the same rate as the eccentric deferent moves around the centre of the small circle.