Astronomical Images : Mean and true apogees of the epicycle of the Moon

Peter Apian

Astronomical Images

This Venetian edition of Peuerbach's Theoricae novae was copied from Apian's 1528 edition, printed in Ingolstadt. Subsequently, the work went through several further editions. Apian's edition added new woodcuts as well as notations to some of those from earlier editions. Some errors in the woodcuts in the 1528 edition were repeated in this Venetian edition of 1537. This diagram has no model in Peuerbach's original (c. 1474) edition. It complements the preceding diagram in Apian's edition (fol. 9r), as it too is principally concerned with the distinction between the mean and true apogees of the epicycle of the Moon. The preceding diagram illustrates the definition of these apogees; this one shows that they change continually as the epicycle follows the rotation of the eccentric deferent. The outermost semicircle, whose centre is the centre of the World (d), represents either the most exterior orb of the Moon or the zodiac, despite the fact that the epicycle (normally contained within the boundaries of the eccentric deferent orb) intersects it: obviously, the diagram does not respect proportions. The middle semicircle is the eccentric deferent of the epicycle of Moon (deferens epicyclum Lunae) and the centre of the epicycle of the Moon is attached to it. This epicycle is shown in six successive positions. The small interior circle is the circle described by the centre of the eccentric deferent (c) as it moves around the centre of the World (d). The vertical line is the axis of the deferent orbs of the apogee of the Moon. Point k, which is diametrically opposite to the centre of the deferent, is the 'opposite point' (punctum oppositum). For each position of the epicycle (except when its centre is on the axis of the deferent orbs of the apogee of the Moon), the diagram shows three lines intersecting at the centre of the epicycle. Two of these lines were already drawn in the preceding diagram: the one that is drawn from point k ends up at M, indicating the mean apogee of the epicycle (aux media epicycli); the one drawn from point d, the centre of the World, ends up at V, indicating the true apogee of the epicycle (aux vera epicycli), as in the preceding diagram. Although the diagram does not quite show it clearly, M and V are marked on the circumference of the epicycle. The woodcut shows that when the centre of the epicycle is on the axis of the deferent orbs of the apogee of the Moon, the true and mean apogees of the epicycle coincide. In Peuerbach's words, the 'two apogees coincide when the centre of the epicycle is in the apogee or perigee of the deferent', that is on the axis of the deferent orbs of the apogee (represented by the vertical line); 'everywhere else, however, they diverge'. The third line is drawn from point c, the centre of the eccentric deferent of the epicycle of the Moon. It serves to illustrate the fact that 'no identical point of the cavity in which the epicycle is situated remains continuously over the mean or true apogee of the epicycle' (nullus idem punctum concavitatis, in qua epicyclus situatur, continue super auge epicycli media sive vera maneat). Only when the centre of the epicycle is on the axis of the deferent orbs of the apogee of the Moon does the line drawn from the centre of the eccentric deferent (c) coincide with the lines drawn from d and from k. In every other position of the epicycle, the true apogee 'is always between the mean apogee and the point of the cavity under which the true apogee usually is, when the centre of the epicycle is in the apogee or perigee of the deferent' (aux vera semper â?¦ sit inter augem mediam et punctum concavitatis sub quo aux vera, dum centrum epicycli in auge deferentis vel opposite fuerit, esse solet). Thus, the line drawn from c to the centre of the epicycle always indicates the 'point of the cavity of the epicycle' under which the true and mean apogee of the epicycle are situated when these apogees are on the axis of the deferent orbs of the apogee of the Moon; and, as shown on the diagram, line dV is always (except in the two aforementioned cases) between line kM and the line drawn from c. In other editions of Peuerbach, as in the Wittenberg 1535 edition, the point marked on the circumference of the epicycle by this line drawn from c is labelled punctum cavitatis in the legend of diagrams. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).