Astronomical Images : Axes, poles and equant of the superior planets

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 is a slightly revised and reduced copy of a diagram in the original (c. 1474) edition of Peuerbach's treatise. It shows the axes and poles of the movements of the three superior planets. The outermost circle represents the zodiac and the next circle the convex limit, concentric to the World, of the most exterior orb of the planet. The interior circle is the eccentric deferent. FE is the axis of the ecliptic, F being its south pole (polus eclipticae Meri[dianus]), and E its north pole (polus oppositus Sep[tentrionalis]). The vertical line perpendicular to this axis represents the ecliptic plane (superficies plana eclipticae). The axis and the plane of the ecliptic intersect at D, the centre of the World. AB is the axis of the deferent, A being its south pole (polus deferentis Meridionalis) and B its north pole (polus deferentis Septentrionalis). Perpendicular to this, the line marking the plane of the deferent (superficies plana deferentis, misspelled 'deferente' on the diagram), shows at one end the apogee (aux) and at the other end the perigee (oppositum [augis]). It coincides with the line of the apogee (linea augis). The axis and the plane of the deferent intersect at the centre of the eccentric deferent. On the diagram, this centre of the deferent is apparently marked H, and H, according to the legend, is 'the centre of the equant' (H Punctus est centrum aequantis), which is absurd. In the diagram representing the orbs of the superior planets (fol. 13r), the centre of the deferent is labelled C. We presume that on the present diagram, H and C are inverted; H ought to be below and C above. The origin of the error is probably in the preceding diagram, where the equant point is erroneously placed between the centre of the deferent and the centre of the World. The intersection between the axis of the ecliptic (FE) and the axis of the eccentric deferent (AB) is not labelled, although its place is relevant to the demonstration. For Peuerbach says that the eccentric deferent 'moves eastward on its axis, which intersects the axis of the ecliptic, and its poles are separated from the poles of the zodiac by unequal distances' (super axe suo axem zodiaci secante secundum successionem Signorum movetur, et poli eius distant a polis zodiaci distantia non aequali). The diagram actually shows that A, the south pole of the deferent, is more distant from EF (the axis of the ecliptic), than B (the north pole of the deferent) is from the same axis; the reason being that the axis of the eccentric and the axis of the deferent do not intersect at D, the middle of the World. Peuerbach adds that for this reason, 'the apogees of the eccentrics never pass through the ecliptic but always remain away from it toward the north, and the perigees toward the south, in such a way that the apogees of the deferent orbs of the epicycles [auges deferentium epicyclos], like the perigees, centres and poles of [these] eccentric deferents [opposita atque centra, et poli deferentium eccentricorum], describe circumferences parallel to the plane of the ecliptic [circumferentias superficiei eclipticae â?¦ aequidistantes]', as the orbs are carried by the motion of the eighth sphere (virtute motus octavae sphaerae). These rotations are represented in the diagram by four lines parallel to the plane of the ecliptic (superficies plana eclipticae) drawn from the two poles of the eccentric deferent (A and B) and the points of the apogee (aux) and the perigee (oppositum), at the intersection between the circumference of the deferent and the line that defines the plane of the deferent (superficies plana deferent[is]). However, the draftsman has probably not understood that the axis of symmetry is the axis of the ecliptic (EF): the lines from B and from aux ought to be longer, and the line from oppositum shorter. According to Peuerbach, 'the planes of the eccentrics will be cut unequally by the plane of the ecliptic, and the greater part will be left toward the apogee, the smaller toward the perigee'. For clearer diagrams of the axes and poles of the superior planets, see the commentaries by Reinhold (1553, fol. 42r) and Schreckenfuchs (1556, plate after p. 98). The spatial relations of the axes of the superior planets 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). The right-hand woodcut is a reduced copy of the diagram representing the orbs of the superior planets, with an addition: the equant circle that intersects the eccentric deferent is drawn. As in the diagram on fol. 13r, point h, the centre of the equant circle (H Punctus est centrum aequantis), is not in the correct place; it ought to be as distant from the centre of the deferent as the deferent is from the centre of the World, so that the centre of the deferent would be in the middle of the centre of the equant and the centre of the World. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).