Astronomical Images : Motions 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. The left-hand woodcut represents the 'small circle' that the centre of the deferent describes. The four centres are drawn as aligned, at equal intervals, as indicated by Peuerbach: when the centre of the deferent is at the apogee of the small circle, it 'will be twice as far from the centre of the equant as the centre of the equant from the centre of the World' (in duplo plus distabit a centro equantis quam centrum equantis a centro mundi). They are labelled 'c[entrum] deferen[tis]', 'c[entrum] parvi cir[culi]', 'c[entrum] equante' (sic), 'c[entrum] mundi'. The right-hand woodcut is a new version of a diagram from the original edition of Peuerbach's treatise (see sig. f6r in our 1482 edition). It shows the movements of the centre of the epicycle of Mercury and of the apogee and perigee of its eccentric deferent as the centre of the eccentric rotates on the small circle. The elements of the original diagram have been enclosed in a large circle representing the ecliptic. This addition is not really useful, except to suggest that the motions, in the last instance, have to be measured on the ecliptic. The two large intersecting circles represent the eccentric deferent and the eccentric equant. The small circle is drawn in the middle. As the proportions have been changed, the circle representing the eccentric deferent passes through the blackened circle marked 'Terra', which is rather surprising. 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 (see fol. 19v), the centre of the deferent is at the apogee of the small circle and the four centres are aligned, as in the left-hand diagram. However, the point marking the centre of the World is replaced by the blackened circle, Terra. The epicycle is shown in four different positions. Even in the main position shown by the diagram (when the centre of the deferent is at the apogee of the small circle and the centre of the epicycle on the apogee of the eccentric deferent), the centre of the epicycle is not exactly on the eccentric deferent, as required by the theory; but, in this case, it is certainly a mistake of the draughtsman. In the three other positions of the epicycle, we must understand that the centre of the epicycle is still on the eccentric deferent, but that 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 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 equant and the eccentric deferent have merged into one and the same circle. The small circle is divided into four parts by four points: two on the vertical diameter and two at the points marked by the tangent lines intersecting at the centre of Terra. 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 each point. The top quarters, right and left, are 120 degrees each, the bottom quarters 60 degrees each. The drawn lines tangential to the small circle and intersecting at the centre of the World 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. The outline of the bottom crescent is clear, that of the top is not: the draughtsman has failed to distinguish what belongs to the crescent, and what to the eccentric circle. 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 shown on the diagram (this is the case illustrated by the top epicycle). 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 encounters 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 at 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 at its bottom eastern (left) position. The diameter of the eccentric deferent, passing through the centre of the World and indicating the apogee and perigee of the deferent, coincides with the above mentioned tangent line. 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 that the apogee of the eccentric is at its greatest possible distance westward from the vertical line (at the right extremity of the upper crescent), while the perigee is at the eastern (left) extremity of the lower 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: 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 the centre of the epicycle in any other position than those represented in the left and right bottom of the diagram. 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 the perigee both 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 meets 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).