Astronomical Images : Axes and poles of the motion of the superior planets

Erasmus Reinhold

Astronomical Images

This Parisian edition was copied from the first edition of the commentary of Peuerbach by Erasmus Reinhold, printed in Wittenberg by Hans Lufft in 1542. Subsequently, in 1556, Charles Perier published a new edition, copied from the revised edition printed by Lufft in 1553, which contained additions to the theory of the Sun ([Theoricae] auctae novis scholiis in theoria Solis ab ipso autore). This diagram is an improved version of a traditional figure. The original edition of Peuerbach's Theoricae (c. 1474) contains a similar figure, as did the subsequent editions; see for example those of Apian (1537), fol. 13v, and Reisch (1512), sig. R1r. The outermost circle represents the ecliptic; EDF is the axis of the ecliptic and of the deferent orbs of the apogee. EDF intersects at right angles, at the centre of the World (D), the line indicating the plane of the ecliptic (superficies eclipticae). The interior circle is the eccentric deferent; its centre is C and its axis MCN. The two axes intersect at G. BCDL, the line indicating the plane of the eccentric deferent (super[ficies] eccen[trici]) is also the line of the apogee: 'aux' (apogee) and 'oppos[itum augis]' (perigee) are marked at its extremities. This line crosses at right angles, at the centre of the eccentric (C), the axis of the eccentric, MCN. N, one of the poles of the eccentric deferent, is less distant from the axis of the ecliptic EDF than M, the other pole, as G, the point of intersection, is nearer to N than to M (eo quod punctum sectionis vergit ad N non ad M). Reinhold enumerates the consequences of these intersections of the axes: 1. 'The apogees of the eccentrics of the three superior planets do not progress along the ecliptic, as does the apogee of the Sun, nor approach it and recede from it, as in the case of the Moon, but keep always the same distance from the ecliptic in the same parts: at the apogees in the northern part, and at the perigee in the southern part' (Quod apogia eccentricorum, nec incedant sub eclipti ca, ut Solis apogion, nec ad eam accedant, ac recedant ut in Luna, sed perpetuo retineant eandem distantiam ab ecliptica seu via Solari, atque in eandem partem, ut apogia versus Boream, perigia autem in Austrum). 2. 'The apogees, perigees, centres and poles [of the eccentrics of the three superior planets] describe circles parallel to the [plane of the] ecliptic, as they follow the movement of the eighth sphere, like each fixed star and point [of the eighth sphere] describe circles parallel to the equator, as they follow the movement of the Prime Mover. â?¦ These circles are not finished before the eighth sphere has accomplished its own period' (Quod apogia, perigia, centra, atque poli deliniant circulos parallelos eclipticae motu sphaerae octavae, quemadmodum ad motum primi coeli, singulae stellae ac puncta designant parallelos circulos aequatori. â?¦ nec absolvuntur hi circuli priusquam ipsa octava sphaera confecerit suam periodum). The last section of the treatise, De motu octavae sphaerae, explains that the rotation of the eighth sphere is extremely slow. These rotations are represented in the diagram by five lines parallel to the plane of the ecliptic (superficies eclipticae) drawn from M and N, the two poles of the eccentric deferent, from E and L, the points of the apogee (aux) and perigee (oppos[itum augis]) of the eccentric deferent, and from C, the centre of the eccentric, to points symmetrical in relation to the axis of the ecliptic, which is the axis of rotation. 3. 'The planes of the eccentrics are always cut by the plane of the ecliptic in unequal parts, not in parts that are sometimes equal, as in the case of the Moon. For the centres of the eccentrics never encounter the plane of the ecliptic, but they always remain at the same distance from it. But the portions of the planes of the eccentrics are larger about the apogee, for there the portion of the circle that contains the centre of the same circle is larger' (Superficies eccentricorum a plano seu superficie eclipticae perpetuo secantur per inaequalia, non etiam interdum per aequalia, ut in Luna. Quia centra eccentricorum nunquam ingrediuntur planum eclipticae, sed ab hac semper distant eadem quantitate. Maiores autem portiones superficierum eccentricorum existunt versus apogion, quia major est circuli porti, quae continent centrum eiusdem circuli). The spatial relations of these axes 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. 98. Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.