Astronomical Images : Axes and poles of the Moon's motion

Georg von Peuerbach

Astronomical Images

Georg Peuerbach (Georgius Aunpekh) was born in Peuerbach, near Linz. He studied at the University of Vienna, obtaining his BA in 1448 and MA in 1453. He held positions as court astrologer to the king of Hungary, and then to Emperor Frederick III. At the request of Cardinal Johannes Bessarion, Peuerbach began an abridgement of Ptolemy's Almagest, which was incomplete when he died in 1461. Peuerbach had also compiled Theoricae novae planetarum, a revision of the Theorica planetarum attributed to Gerard of Cremona. This originated as lectures given in Vienna in 1454, which were attended by Johannes Regiomontanus, who published the first edition in Nuremberg around 1474. This is the 1482 edition by Erhard Ratdolt, which contains copies of the original diagrams. As in the original edition, some woodcuts were coloured. Ratdolt was active in Venice and Augsburg, and was particularly interested in astronomical subjects. He also produced editions of Johannes Engel's Astrolabium planum in tabulis ascendens and G. Julius Hyginus' Poetica astronomica. Peuerbach's text was printed in a compilation that also included Johannes Sacrobosco's Sphaericum opusculum and Johannes Regiomontanus' Contra Cremonensia in planetarum theoricas delyramenta disputationes. This collection of astronomical treatises, and other similar ones, together comprised the main elementary texts available in the late fifteenth century. This woodcut shows the axes and poles of the orbs of the Moon that define its motion. According to Peuerbach, 'the deferents of the apogee of the eccentric move westward together, uniformly (contra successionem Signorum simul regulariter) about the centre of the World, by about eleven degrees and twelve minutes beyond the diurnal motion in a natural day (ultra motum diurnum in die naturali)'. Thus, they follow the diurnal revolution (360 degrees in twenty-four hours), but, being slightly faster, they overtake it by eleven degrees and twelve minutes every twenty-four hours. 'The axis of this motion intersects the axis of the ecliptic (or zodiac) in the centre of the World', the constant measure of the declination of its poles from the poles of the ecliptic being five degrees. The eccentric deferent of the epicycle 'moves eastward uniformly [secundum successionem Signorum regulariter] about the centre of the World', so that in every twenty-four hours the centre of the epicycle covers about thirteen degrees, eleven minutes. The axis of this movement of the deferent moves parallel to the axis of the deferent orbs of the apogee, the poles of these two axes being distant according to the size of the eccentricity. Five consequences follow: 1. The eccentric deferent of the epicycle does not move uniformly about its axis. 2. The centre of the epicycle of the Moon moves so much the faster as it is closer to the apogee, and so much the slower as it is closer to the perigee. 3. The centre of the eccentric deferent describes uniformly a small circle around the centre of the World, and the axis of the same deferent orb revolves uniformly about the axis of the deferents of the apogee (its poles also describing small circles around the poles of the axis of the deferents of the apogee). The movement of all the small circles is westward (circumferentias contra successionem describendo). 4. The apogee of the eccentric moves likewise uniformly westward and crosses over the ecliptic (eclipticam praeteribit). Hence the apogee is sometimes in the plane of the ecliptic, sometimes away from this plane, either toward the south or the north; and the centre of the eccentric also sometimes recedes from this plane in opposite directions. 5. The plane of the ecliptic does not cut the plane of the eccentric in equal parts, except when the apogee of the eccentric is in the nodes. In this woodcut, the poles of the ecliptic (po[lus] ecl[ipticae]), and the poles of the axis of the deferent orbs of the apogee (po[lus] augem def[erentis]) are marked on the outermost circle, which represents the eighth sphere. The axis of the ecliptic and part of the axis of the deferent orbs of the apogee are drawn. The arcs of circles on the second outermost circle indicate that the poles of the axis of the deferent orbs of the apogee describe circles around the poles of the ecliptic. Parallel above the axis of the deferent orbs of the apogee is the axis of the deferent orb of the epicycle of the Moon, which rotates around this axis of the deferents of the apogee: three arcs of circles - one around the centre of the World, two on the second innermost circle - indicate this rotation. Also marked on the diagram are the lines indicating the plane of the ecliptic (superficies plana eclipticae), and the plane of the deferent orbs of the apogee (superficies plana deferentis). These two lines, each perpendicular to its own axis, intersect at the centre of the World. The spatial relations of these orbs and their motion 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. 38. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).