Astronomical Images : Motion of the three superior planets in the epicycle

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 has no model in the original (c. 1474) edition of Peuerbach's treatise. The corresponding diagram in this edition is quite different. The woodcut aims to show that, in Peuerbach's words, the body of the planet on its epicycle 'revolves once precisely in as much time as it takes from the mean conjunction of the Sun and the planet to the next following' (semel precise in tanto tempore, quantum est a media conjunctione Solis et istius planetae ad proximam sequentem revolvatur), so that the body of the planet is always in the mean apogee of its epicycle in every mean conjunction with the Sun, and always in the mean perigee of its epicycle when the Sun and the planet are in mean opposition. Moreover, 'the centre of the body of the planet is always as many degrees and minutes distant from the mean apogee of the epicycle as the line of mean longitude of the Sun is distant from the line of mean longitude of the planet'. Two planets are in mean conjunction (conjunctio media) when their mean motion or longitude on the zodiac (motus medius) coincide; they are in mean opposition when their mean motion or longitude on the zodiac are distant by 180 degrees. The mean motion of the Sun is the arc of the zodiac from the first degree of Aries to the line of the mean motion of the Sun (linea medii motus Solis), that is the line drawn from the centre of the World to the ecliptic and parallel to the line drawn from the centre of the eccentric deferent to the centre of the body of the Sun. The mean motion of another planet is the arc of the zodiac from the first degree of Aries to the line of the mean motion of the planet that extends from the centre of the World to the zodiac, passing through the centre of the epicycle. According to the fifteenth-century astronomical glossary edited by Olaf Pedersen, the mean apogee of the epicycle of a superior planet (aux media epicycli) is 'the point in the superior part of the epicycle that determines the line drawn from the centre of the equant and passing through the centre of the epicycle' (punctus in superiore parte epicycli, quem terminat linea exiens a centro equantis per centrum epicycli), whereas the true apogee of the epicycle (aux vera) is 'the point that determines the line drawn from the centre of the Earth and passing through the centre of the epicycle' (punctus quem terminat linea exiens a centro Terrae per centrum epicycli). On the diagram, the outermost circle probably represents the zodiac, the next circle is the eccentric deferent of the epicycle of a superior planet, and the innermost circle is the eccentric deferent of the Sun. The vertical line is the line of the apogee (linea augis), on which the centres of the World (D), of the eccentric deferent (C) and of the equant are aligned. As in all the diagrams concerning the superior planets in Apian's edition, the equant point (H) is misplaced: it ought to be above C, rather than below. When the Sun and the centre of the epicycle are in mean conjunction on the line of the apogee, we see that the body of the planet is at the mean apogee of its epicycle (on the line drawn from the centre of the equant and passing through the centre of the epicycle). When the Sun and the centre of the epicycle are in mean opposition, also on the line of the apogee, we see that the body of the planet is at the mean perigee of its epicycle (on the line drawn from the centre of the equant and passing through the centre of the epicycle, but in the inferior part of this epicycle). Other lines radiating from the centre of the equant (H, though this point is misplaced on the diagram) indicate the successive positions of the mean apogee of the epicycle when the centre of this epicycle circulates around the centre of its deferent, while the body of the planet circulates around the centre of its epicycle. The diagram also gives a hint that at the same time the Sun circulates around the centre of its own eccentric deferent and occupies successively the positions marked by the intersections of the radiating lines with its eccentric deferent. Thus, the correspondence between the movement of the Sun and the movements of every superior planet is suggested, although the diagram not only is inaccurate, but could even be quite misleading. The motion of the centre of the epicycle and the motion of the body of the planet on its epicycle seem to go in opposite directions, and, above all, the impression is conveyed that the movement of the Sun on its deferent and the movement of the centre of the epicycle of the superior planet are synchronised, which is absurd as the period of Mars is approximately two solar years, that of Jupiter twelve years, and that of Saturn nearly thirty years. That is perhaps the reason why a reader has struck through this figure and the one on the opposite page with a pen. The right-hand woodcut show the true (point b) and the mean (point A) apogees of the epicycle, the former being defined 'by the line from the centre of the World through the centre of the epicycle', the latter 'by the line drawn from the centre of the equant through the centre of the epicycle', but again H, assumed to be the centre of the equant, is misplaced. The third epicycle, the centre of which is on the line of the apogee (linea augis), that is at the apogee or the perigee of the eccentric deferent, shows that in this case the lines of the mean and of the true apogees coincide. For a similar diagram concerning the epicycle of the Moon, see fol. 9r. Translated quotations of Peuerbach's Theoricae are from Aiton (1987). Other quotations (translated by Isabelle Pantin) are from Pedersen (1973).