Astronomical Images : Orbs and axes of Mercury's motion

Gregor Reisch

Astronomical Images

The Margarita philosophica was a compendium, or 'Epitome' of university learning in the sixteenth century. It was written by the prior of the house of Carthusians at Freiburg, Gregor Reisch (d. 1525), and was first published in 1503 in Freiburg by Johannes Schott, a printer from Strasbourg. The work was illustrated amply with somewhat crude woodcuts, and was divided into twelve books, with one book each dealing with the trivium (grammar, dialectic and rhetoric) and quadrivium (arithmetic, music, geometry, astronomy), four books devoted to natural philosophy, and one book on moral philosophy. It was a popular work, reprinted numerous times during the sixteenth century, including the unauthorized, augmented editions by another printer at Strasbourg, Johann Grueninger. Oronce Fine edited and added to the Latin text of the 1535 edition. In book 7, the Margarita includes a summary of Peuerbach's Theoricae novae planetarum and reproduces some of its original diagrams. This one combines 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). The outermost circle represents the ecliptic. Inside it, we see the five orbs of Mercury. The exterior orb (marked 'deferens augem equantis') 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 (printed black in the diagram), whose two surfaces have different centres, both distinct from the centre of the World. The two innermost orbs constitute a similar system, except that the innermost surface is concentric to the World, while the outermost is eccentric. The innermost orb is printed black; in the contiguous orb, we read 'deferens augem equantis', but we must understand that this label pertains to the interior black orb. The eccentric orb sandwiched between the two pairs of deformed orbs is the deferent orb of the epicycle, with the middle circle where the centre of the epicycle is attached (the epicycle itself is not drawn). Peuerbach calls this eccentric deferent 'the fifth orb' (orbis quintus). We could, then, number the interior deformed orbs 1 and 2, and the exterior ones 3 and 4. The two intersecting circles are the eccentric deferent circle of the epicycle (deferens) and the eccentric equant (equans). As a consequence, Mercury's theorica has four primary centres (what concerns the epicycle being omitted): first the centre of the World (c[entrum] mundi), second the centre of the eccentric equant (c[entrum] equantis), third the centre of the eccentric deferent (c[entrum] def[erentis]), 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 (c[entrum] parvi circuli) 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 marked 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, at equal intervals. The apogee of the deferent (aux deferentis) and of the eccentric equant (aux equantis) are on this line. 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. The line perpendicular to the apogee at the centre of the World is the axis of the ecliptic (also the axis of the deferent orbs of the apogee of the equant). Its poles are each marked 'polus eclipticae'. The line perpendicular to the apogee at the centre of the small circle is the axis of the deferent orbs of the apogee of the eccentric. Its poles are each marked 'polus augem deferentium'. The line perpendicular to the apogee at the centre of the deferent is the axis of the eccentric deferent orb of the epicycle. Its poles are each marked 'polus deferentis'. 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).