Astronomical Images : Motions of Mercury

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. 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 volume's printer, Erhard 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. This woodcut, a slightly reduced copy of a diagram of the original edition of Peuerbach's treatise (c. 1474), shows the movements of the centre of the epicycle of Mercury and of the apogee and perigee of its eccentric deferent. These movements are complex, due to the fact that the centre of the eccentric of Mercury rotates on a 'small circle'. The diagram is not easy to read and this is probably why some of its elements are labelled, which is unusual in the early editions of Peuerbach. However, the letters are not referred to in the text. The letters are the same as in the original edition (which likewise does not mention them in the text). The two large intersecting circles represent the eccentric deferent and the eccentric equant. The 'small circle', mentioned above, is drawn in the middle. The vertical line is the line of the apogee of the equant, which is also the line of the apogee of the eccentric deferent when the centre of this eccentric deferent is on it (either at the apogee or the perigee of the small circle). Here, as in the diagram of the orbs and axes, the centre of the deferent is at the apogee of the small circle and the four circles are aligned, at equal intervals, as in the text above: '[in this disposition] the centre of the deferent will be twice as far from the centre of the equant as the centre of the equant from the centre of the World' (et centrum deferentis in duplo plus distabit a centro equantis quam centrum equantis a centro mundi). They are labelled '[centrum] defer[entis]', 'c [centrum] parvi circuli' (with abbreviations), '[centrum] equantis', 'b [centrum] mundi'. The epicycle is shown in four different positions. We see that only in one of these is the centre of the epicycle on the eccentric deferent, as required by the theory: in the upper position, when the centre of the epicycle is on the line of the apogee. This corresponds to the position of the eccentric deferent shown on the diagram (with the centre of the deferent at the apogee of the small circle). In the other positions of the epicycle, the centre of the epicycle is still on the eccentric deferent, but this circle is no longer in the position shown by the diagram, as its centre has circulated on the small circle. Thus, in two cases (bottom right and bottom left) the centre of the epicycle is on an invisible eccentric circle, and in the third case (marked l) it is on the equant circle: at this moment the centre of the eccentric deferent is on the centre of the equant, and the eccentric deferent and the eccentric equant have merged into one and the same circle. The small circle is divided into four parts by the vertical diameter and two radii. The diagram, following the text of Peuerbach, is meant to show what happens to the centre of the epicycle and to the apogee of the eccentric when the centre of the deferent eccentric arrives at the limit of each quarter. The top quarters, right and left, are 120 degrees each, the bottom quarters 60 degrees each. The drawn radii of the small circle terminate at two lines, tangential to this circle and intersecting at the centre of the World. These lines also mark the limits of two crescent-shaped figures, drawn at the top and at the bottom of the diagram, which are meant to represent the movement of the apogee and of the perigee of the eccentric deferent. In other words, the tangent lines show the limits that the line marking the apogee of the eccentric will never pass beyond, westward or eastward. According to Peuerbach, 'when the centre of the deferent moves by the motion of the two secondary orbs from the apogee of its circle toward the west, the centre of the epicycle will move by the motion of the deferent â?¦ just the same amount toward the east' (cum centrum deferentis per motum orbium duorum secundorum movebitur ab auge sui circuli versus Occidentem, centrum epicycli per motum deferentis movebitur tantumdem versus Orientem). The 'secondary orbs' are the 'deferent orbs of the apogee of the eccentric', contiguous to the eccentric deferent orb. On their movement, westward, on the centre of the small circle, and on the movement of the eccentric deferent eastward but with the same speed (the period of both movements being one mean solar year), see entries on the orbs and axes of Mercury. First, the centre of the deferent is at the apogee of the small circle, and the centre of the epicycle at the apogee of the eccentric deferent, which is also on the line of the apogee of the equant, as clearly shown on the diagram. Then, as the centre of the eccentric deferent moves westward (to the right in the diagram) from the apogee of the small circle, 'the centre of the epicycle will move by the motion of the deferent from the apogee of the equant just the same amount toward the east â?¦ and the apogee of the deferent recedes continually from the [line of the] apogee of the equant toward the west' (centrum epicycli per motum deferentis movebitur ab auge aequantis tantumdem versus Orientem â?¦ et aux deferentis ab auge aequantis versus Occidentem recedit continue). When the centre of the deferent meets the western tangent line (120 degrees distant from the apogee of the small circle), 'then similarly the centre of the epicycle will be four Signs [= 120 degrees] distant from the [line of the] apogee of the equant toward the east. Furthermore, the apogee of the deferent will be in its greatest separation from the [line of the] apogee of the equant toward the west' (et tunc similiter centrum epicycli ab auge aequantis versus Orientem distabit quattuor Signis. Aux autem deferentis erit in maxima sua ab aequantis auge versus Occidentem remotione). On the diagram, the centre of the eccentric deferent then meets the western (right) tangent to the small circle, while the epicycle is in its bottom left position. The diameter of the eccentric deferent, passing through the centre of the World and indicating the apogee and perigee of the deferent, is the tangent line labelled kb. Peuerbach has previously demonstrated that the line marking the apogee of the eccentric cannot pass beyond the tangents to the small circle (see Reinhold, 1553, fol. 68r). As the centre of the eccentric is on this tangent, we see on the diagram that the apogee of the eccentric is at its greatest possible distance westward from the vertical line (at the right extremity of the top crescent), while the perigee is at k (the left extremity of the bottom crescent). Besides, 'in this position, the centre of the epicycle will be in the closest approach it is accustomed to make to the centre of the World. However, it will not then be in the perigee of the deferent' (atque in hoc situ centrum epicycli fiet in maxima sua, quam solet habere ad centrum mundi, accessione. Non tamen tunc erit in opposito augis deferentis). Of this, no other demonstration is given than the visual evidence of the diagram: we see that the radius drawn from the centre of the equant to the centre of the epicycle is of too small a circle to encompass either k or l. In the next position, the centre of the deferent is at the centre of the equant, at the perigee of the small circle, and then the centre of the epicycle is at l, at the perigee of the eccentric deferent and of the eccentric equant (for the eccentric deferent and the eccentric equant are united). Then the centre of the deferent encounters the eastern (left) tangent line, 120 degrees distant from the apogee of the small circle. The centre of the epicycle is at the bottom right position of the diagram, also 120 degrees from the line of the apogee of the equant, but measured against the sequence of the Signs. The apogee of the deferent, indicated by the tangent to the small circle, is at its greatest distance eastward from the line of the apogee of the equant (at the left extremity of the top crescent), and the perigee at its greatest distance westward from the same line (at the right extremity of the bottom crescent). The centre of the epicycle is again at its nearest to the Earth. Peuerbach later enumerates the consequences of these motions, noting that 'the centre of the epicycle of Mercury â?¦ does not, as in the cases of the other planets, describe the circular circumference of the deferent, but rather the periphery of a figure that resembles a plane oval' (centrum epicycli Mercurii â?¦ non ut in aliis planetis sit, circumferentiam deferentis circularem, sed potius figurae habentis similitudinem cum plana ovali peripheriam describere). Translated quotations of Peuerbach's Theoricae are from Aiton (1987).