Astronomical Images : The 'small circle' of Mercury compared to that of the Moon

Erasmus Reinhold

Astronomical Images

<p style='text-align: justify;'>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 (<i>[Theoricae] auctae novis scholiis in theoria Solis ab ipso autore</i>). This diagram is a new version of a figure devised by Peter Apian for his edition of the <i>Theoricae novae</i> (1528; see fol. 20v in our 1537 edition) and imitated in the Wittenberg edition of Peuerbach (1535). It has a remote model in the commentary of Franciscus Capuanus (Venice, 1495; Paris, 1515). In the new edition of the <i>Theoricae novae</i>, printed in Wittenberg in 1551, the Reinhold diagram replaces the previous one. Peuerbach examines the similarities and the differences between Mercury and the Moon, notably in relation to the circulation of the centre of the eccentric deferent on the 'small circle'. The centre of the eccentric of the Moon also circulates on a 'small circle', but this lunar small circle is centred on the centre of the World, whereas the small circle of Mercury is not. As a consequence, the apogee of the eccentric deferent of Mercury does not move circularly, as that of the Moon, but 'proceeds at one time eastward, and at another time westward â?¦ it continuously rolls forward and rolls back, ascending and descending under the arc of the zodiac formed by two lines drawn tangent to the small circle from the centre of the World to the zodiac' (<i>nunc secundum successionem Signorum, nunc contra procedit â?¦ continue sub arcu zodiaci a duabus lineis circulum parvum contingentibus a centro mundi ad zodiacum ductis comprehenso ascendendo et descendendo volvitur atque revolvitur</i>). The diagram pertains to a note of Reinhold. It shows the difference between the small circle that describes the centre of the eccentric of the Moon, due to the movement of the deferent orbs of the apogee westward, and the small circle of Mercury. The lunar small circle is centred on the centre of the World, which is exterior to that of Mercury. If FODP represents the small circle of the Moon, E will be the centre of the World. But if FODP is the small circle of Mercury, the centre of the World is at C. We must remember that the apogee of the eccentric is marked by the line drawn from the centre of the World and passing through the centre of the deferent of the epicycle. If we imagine that this centre is P, moving on FODP against the order of the numbers (we understand that the order of the numbers is the order of the Signs), line CP, tangent to FODP, will show the apogee of the eccentric. This line CP will meet the circumference of the small circle at any point of it during its periodical (that is annual) revolution. But as the motion of P is not around the centre of the World, the apogee of the eccentric will not have complete rotations, but will travel during the whole period between the two tangents CP and CO; the same will happen to the perigee. The letters FODP divide the circle into four parts. The first and last, FP and OF, are four Signs long, the second and third, PD and DO, two Signs long. The demonstration is carried further in the next diagram (plate after fol. 68) that replaces the small circle in a more complete representation of the motions of Mercury. Translated quotations of Peuerbach's <i>Theoricae</i> are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>