Astronomical Images : Motion of Mercury, figure 2

Johannes Regiomontanus

Astronomical Images

<p style='text-align: justify;'>In his <i>Disputationes contra Cremonensia deliramenta</i>, the last book printed before his untimely death in 1476, Regiomontanus offered a critique of the <i>Theorica planetarum communis</i>, a thirteenth-century textbook attributed to Gerard of Cremona, in comparison to the relative advantages offered by Georg Peuerbach's <i>Theoricae novae planetarum</i>. 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 <i>Theorica</i>. This is one of several diagrams used to criticise errors in the <i>Theorica planetarum communis</i> 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. This image, along with several others presented by Regiomontanus, concerns the problematic claims of the <i>Theorica planetarum communis</i> 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 refute the claim of the <i>Theorica</i> that when the line from Earth n to the centre of the deferent h is on the tangent to the small circle, the epicycle centre k is on the tangent line as well. However, due to the relative motions of the deferent and crank mechanism (in which the centre of the epicycle and the centre of the deferent are moved uniformly but in opposite directions), angles afh and agk should be equal; Regiomontanus' diagram clearly demonstrates that according to the claims of the <i>Theorica</i> they are not, and thus the assertion that the epicycle centre will lie on the tangent line is proved erroneous.</p>


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