Astronomical Images : Motion of the epicycle of the Moon

Erasmus Reinhold

Astronomical Images

This Parisian edition was copied from the first edition of the commentary of Peuerbach by Erasmus Reinhold, printed in Wittenberg by Hans Lufft in 1542. Subsequently, in 1556, Charles Perier published a new edition, copied from the revised edition printed by Lufft in 1553, which contained additions to the theory of the Sun ([Theoricae] auctae novis scholiis in theoria Solis ab ipso autore). This diagram was first used in the 1542 edition of Reinhold's commentary. It has no equivalent in the original (c. 1474) edition of the Theoricae novae, but the commentary of Capuanus (Venice, 1495), the editions procured by Oronce Fine (Paris, 1525) and Peter Apian (Ingolstadt, 1528), and the edition printed in Wittenberg in 1535 contain similar figures (though less legible and accurate). In the 1551 Wittenberg edition of the Theoricae novae, this Reinhold diagram has been introduced. This woodcut shows the position of the axis of the epicycle of the Moon, and the true and mean apogees of this epicycle. According to Peuerbach, 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'. The rotation of the epicycle around its centre is irregular, but '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'. The main lines and circles of the Theorica orbium Lunae are delineated. The outermost circle, whose centre is the centre of the World (T), represents the ecliptic. The middle circle (HEK) is the eccentric deferent of the epicycle of Moon (deferens epicyclum Lunae) and the centre (E) of the epicycle of the Moon (BAFD) is attached to it. The legend specifies that in the 'superior part' of this epicycle (DCBA) the Moon moves westward (contra seriem Signorum), whereas in the 'inferior part' (AGFD) it moves eastward (secundum series Signorum). Line DEA is the axis of the epicycle, perpendicular to the radius of the eccentric (SE), which, 'by its movement, defines the plane of the eccentric [ad cuius semidiametri motum superficies plana eccentrici describitur], so that the axis of the epicycle falls orthogonally on that plane [huic itaque superficiei orthogonaliter incumbent dictus axis epicycli]'. Reinhold then refers to the chapter on the latitudes of the planets (in the second part of the Theoricae novae), that will clearly show that the plane of the epicycle of the Moon must be part of the plane of the eccentric (planum epicycli Lunae esse partem plani eccentrici). The small interior circle is the circle described by the centre of the eccentric deferent (S) as it moves around the centre of the World (T). The vertical line is the axis of the deferent orbs of the apogee. Point V, diagrammatically opposite to the centre of the eccentric deferent (S), is the 'opposite point' (punctum oppositum). The mean apogee of the epicycle (aux media epicycli) is at B, the point of the circumference of the epicycle, which is determined by the line drawn through the centre of the epicycle from the 'opposite point' (V). The true apogee of the epicycle (aux vera epicycli) is at C, the point of the circumference that is determined by the line drawn through the centre of the epicycle from the centre of the World (T). 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. The mean and true 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 (line HSTVK). Translated quotations of Peuerbach's Theoricae are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.