Astronomical Images : Orbs, centres and axes of Mercury

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 is a re-use or a close copy of a woodcut in the Wittenberg edition of Peuerbach (1535). The Wittenberg editor had followed two models: a figure devised by Oronce Fine for his edition of the commentary of Sylvester de Prierio (Paris, 1515) and re-used in his edition of Peuerbach (Paris, 1525), and a similar figure in the Apian edition of Peuerbach (Ingolstadt 1528, reproduced in our 1537 edition, fol. 19v). The lettering of the Wittenberg diagram (re-used in the commentary of Reinhold) is, for the most part, taken from Fine's figure, but a few letters come from the Apian diagram. Like the diagram of the 1525 Fine edition, the Wittenberg diagram has a legend. In Reinhold's commentary, the legend has grown into scholia. Mercury has five orbs and one epicycle. The outermost orb (B) 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 (marked 'H', barely legible), whose two surfaces have different centres, both distinct from the centre of the World: in the diagram these orbs are printed black, and separated by a white circle. The two innermost orbs (I and G) 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 is attached, at T, 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). The eccentric equant is labelled RNO and the eccentric deferent RTSO, according to the legend. Consequently, Mercury's theorica has four primary centres (what concerns the epicycle being omitted): first the centre of the World (C), second the centre of the eccentric equant (D), third the centre of the eccentric deferent (F), 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 (E) 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 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. On the diagram, the four centres (C, D, E, F) are thus aligned on the line of the apogee, from the centre of the World to the centre of the deferent, at equal intervals. Reinhold notes that, according to Ptolemy, the distance between the centre of the equant and the centre of the World is 3/60 parts of the radius of the eccentric (centrum aequantis D distat a centro mundi C juxta Ptolemaeum 3 partibus qualium semidiameter eccentrici 60). Therefore, when the centre of the eccentric deferent of the epicycle (F) is at the apogee of the small circle, its distance from the centre of the World is 9/60 parts, whereas the distance is only 3/60 parts when it is at the perigee of the small circle (and coincides with the centre of the equant). Reinhold also notes that the line of the apogee of the equant and the line of the apogee of the eccentric do not always coincide, as the diagram shows, for they do not follow the same movements. 'The line of the apogee CDEA, that is the two centres of the equant and of the small circle, does not move, except under the effect of the very slow movement of the eighth sphere. The line of the apogee of the eccentric is not fixed like that of the equant, but it has a sort of swaying and see-saw motion, in keeping with the periodical motion of the eccentric' (linea apogii aequantis CDEA, id est duo centra, nempe aequantis, et parvi circuli non progrediuntur, nisi tardissimo octavae sphaerae motu. Linea apogii eccentrici non itidem est fixa, ut aequantis, sed habet suam quondam nutationem ac reciprocationem, convenienter tamen cum motu periodico eccentrici). 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 [as mentioned above] 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; and 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 LCM, passing through the centre of the World (C), is the axis of the ecliptic (also the axis of the deferent orbs of the apogee of the equant). Line QEP, passing through the centre of the small circle, is the axis of the deferent orbs of the apogee of the eccentric. Line OFR, passing through the centre of the deferent (F), 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). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.