Astronomical Images : Orbs and axes of the motion of Mercury

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 shows the orbs and axes of Mercury, at the beginning of the chapter devoted to this planet. It is an enlarged copy of the diagram conceived by Oronce Fine for his edition of the commentary on Peuerbach by Sylvester de Prierio (Paris, 1515), and re-used in his own edition of Peuerbach (Paris, 1525). The Fine diagram itself imitated a figure in the Margarita philosophica, the first to combine two figures of the original edition of the Theoricae novae (c. 1474): one of the orbs of Mercury (Theorica orbium Mercurii), and one of its axes (Theorica axium et polorum). Like the Fine diagram, this one is labelled with letters, but there is no legend, and the letters are not referred to in the text. Mercury has five orbs and one epicycle. The outermost orb (y) is said to be 'deformed' or 'relatively eccentric' (eccentricus secundum quid), as its convex surface is concentric to the World, while its concave surface is eccentric. This orb is contiguous to another orb (x), whose two surfaces have different centres, both distinct from the centre of the World; these orbs are printed black, and are separated by a white circle. The two innermost orbs constitute a similar system, except that the innermost surface is concentric to the World, while the outermost surface is eccentric. The eccentric white orb sandwiched between the two pairs of black orbs is the deferent orb of the epicycle (whose centre, at t in the diagram, is attached to the circle in the middle). Peuerbach calls it 'the fifth orb' (orbis quintus). We could, then, number the interior deformed orbs 1 and 2, and the exterior ones 3 and 4. Like the superior planets and Venus, Mercury has an eccentric equant (a circle in relation to whose centre the centre of the epicycle moves regularly). Consequently, Mercury's theorica has four primary centres (what concerns the epicycle being omitted): first the centre of the World (marked 'd [centrum] mundi'), second the centre of the eccentric equant (c equant[is]), third the centre of the eccentric deferent (e [centrum] defe[rentis]), and fourth the centre of the concave surface of the outermost orb (orb 4) and of the convex surface of the innermost orb (orb 1), and also of the contiguous surfaces of orbs 3 and 2. This fourth centre (h [centrum] parvi cir[culi]) is 'as distant from the centre of the equant as the centre of the equant is from the centre of the World' (tantum a centro aequantis, quantum centrum aequantis a centro distat). It is itself 'the centre of the small circle, which the centre of the deferent describes, as will be seen' (et ipsum est centrum parvi circuli, quem centrum deferentis, ut videbitur, describit). The vertical line passes through the apogees of the eccentric deferent and of the eccentric equant, the centre of the World, the centre of the equant, and the centre of the 'small circle'. The centre of the deferent is also on this line, at the two points where the small circle crosses it, at the apogee or at the perigee (where it coincides with the centre of the equant): on the diagram, it is at the apogee. The four centres are thus aligned on the line of the apogee, from the centre of the World to the centre of the deferent, each at equal distance to the next one. The outermost orb (orb 4) and the innermost orb (orb 1), which have the same centres, 'are called the deferent orbs of the apogee of the equant, and they move with the motion of the eighth sphere on the axis of the zodiac' (vocantur autem deferentes augem aequantis, et moventur ad motum octavae sphaerae super axe zodiaci). Orbs 3 and 2, whose centres coincide, respectively, with the centre of the eccentric deferent of the epicycle and with the fourth centre (that is, as noted above, the centre of the concavity of the fourth orb, and centre of the small circle), are called 'the deferent orbs of the apogee of the eccentric; they move uniformly on the centre of the small circle westward with such speed that exactly in the time that the line of mean motion of the Sun makes one revolution, the orbs likewise complete one in the opposite direction' (augem eccentrici deferentes vocantur, et moventur regulariter super centro parvi circuli contra successionem Signorum tali velocitate, ut praecise in tempore, quo linea medii motus Solis unam facit revolutionem, et orbes isti in partem oppositam similiter unam perficiant). The fifth orb, that is the deferent orb of the epicycle, moves eastward uniformly about the centre of the equant with 'such speed that the centre of the epicycle revolves once in the same time that the line of mean longitude of the Sun completes one revolution' (hanc tamen habet velocitatem, ut centrum epicycli in eo tempore semel revolvatur, in quo linea medii motus Solis unam complet revolutionem). In other words, Mercury has the same mean motion as the Sun and Venus. Therefore, the fifth orb and the deferent orbs of the apogee of the eccentric move at the same speed, but in opposite directions. Line lm, passing through the centre of the World, is the axis of the ecliptic (also the axis of the deferent orbs of the apogee of the equant). Line ihk, passing through the centre of the small circle, is the axis of the deferent orbs of the apogee of the eccentric. Line rg, passing through the centre of the deferent, is the axis of the eccentric deferent orb of the epicycle. All these axes are parallel, and perpendicular to the line of the apogee. The spatial relations of the orbs of Mercury and their movements are more clearly shown in the three-dimensional diagram provided in Erasmus Oswald Schreckenfuchs' Commentaria in novas theoricas planetarum Georgii Purbachii (Basel: Henricus Petri, 1556), plate after p. 204. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).