Astronomical Images : Axes, 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. These woodcuts have no models in Peuerbach's original (c. 1474) edition. The woodcut at the top shows that, in Peuerbach's words, the axis of the epicycle of the Moon 'lies perpendicular to the circumference of the eccentric, so that the plane of the circumference of the epicycle, which the centre of the Moon describes by the motion of the epicycle, remains in the plane of the eccentric, never departing from that'. Then Peuerbach explains that the rotation of the epicycle around its centre is irregular but that 'this irregularity is reduced to uniformity' as 'the Moon is uniformly removed from the point of the mean apogee of the epicycle [a puncto augis epicycli mediae â?¦ regulariter elongetur], wherever that is, by receding in every natural day by thirteen degrees and about four minutes'. Thus, the lower woodcut shows how to find the mean apogee of the epicycle (aux epicycli media). The main lines and circles of the Theorica orbium Lunae are delineated. The outermost circle, whose centre is the centre of the World (d), represents either the outermost 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 circle is the eccentric deferent of the epicycle of the Moon (deferens epicyclum Lunae) and the centre of the epicycle of the Moon is attached to it. 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. Point k, which is opposite the centre of the deferent is the 'opposite point' (punctum oppositum). The mean apogee of the epicycle (aux media epicycli) is at M, 'the point of the circumference of the epicycle, which is determined by the line drawn through the centre of the epicycle from the point diametrically opposite the centre of the eccentric in the small circle, that is from k (punctum oppositum). The true apogee of the epicycle (aux vera epicycli) is at A, 'the point of the circumference that is determined by the line drawn through the centre of the epicycle from the centre of the World', that is from d. We may observe that the line that determines this true apogee of the epicycle coincides with the line of the mean motion, or longitude, of the Moon: both are drawn through the centre of the epicycle from the centre of the World. However, the mean motion is a point marked on the zodiac (or an arc of circle measured on the zodiac), whereas the true apogee of the epicycle of the Moon is a point marked on the circumference of the epicycle. In any case, 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'. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).