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Astronomical Images : The motion in latitude of the eccentrics of Venus and Mercury

Erasmus Reinhold

Astronomical Images

<p style='text-align: justify;'>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 (<i>[Theoricae] auctae novis scholiis in theoria Solis ab ipso autore</i>). This image of the intersection of the plane of the eccentric of Venus with the plane of the ecliptic (and of the eccentric of the Sun) is an improved copy of a figure of the Apian edition of Peuerbach (see Apian, 1537, fol. 19r). It originated in a figure of the first edition of Sylvester de Prierio's commentary on Peuerbach (Milan, 1514). Oronce Fine reproduced it in his own edition of the commentary of Sylvester de Prierio (Paris, 1515). Apian then introduced a clumsy imitation of it in his own edition. The Wittenberg edition of Peuerbach (1535) did not copy or imitate it. In De Priero's commentary and in the Apian edition the figure is found in the first section of the treatise, in the short chapter <i>De Venere</i>; Reinhold transferred it in the second section, <i>De passionibus planetarum diversis</i>, in the chapter devoted to the latitudes of Venus and Mercury, to illustrate a <i>scholion</i>. In the original De Prierio figure there are two images of the intersecting planes transfixed by their axes. In the first image the axis of the plane facing the reader is low in front and high behind, while the axis of the other plane is high in front and low behind. In the second image, this is the reverse. Thus, the swinging to and fro of the plane of the eccentric is suggested. In the Apian edition there is only one image, no explanation is given, and the axes do not seem to be perpendicular to their planes. In the Reinhold diagram, the perspective has been rectified, so that each axis appears perpendicular to its plane, and letters have been added to link the diagram to the accompanying demonstration. C represents the centre of the World, and FCG the diameters of the World that are the lines of intersection between the plane of the ecliptic and the planes of the eccentrics of Venus and Mercury. 'Let us suppose that K is the apogee of the eccentric of Venus, L the perigee. If we place the centre of the epicycle of Venus in K, the plane of the eccentric will be FKG, crossed at right angles, at the centre of the World, C, by line ACD. According to Euclid, <i>Elements</i> XI.6, ACD will be parallel to the axis of the eccentric. Similarly, if we place the centre of the epicycle in L, the perigee, the plane of the eccentric will be HGL, crossed at right angles by line BCE, also parallel to the axis. Thus the axis swings to and fro, as wide as angle ACB. This angle is twenty minutes in Venus, but ninety minutes in Mercury. It is obvious that the plane of the eccentric is divided into unequal parts by the plane of the ecliptic. The larger part is that which has the centre [of the World], that is which has the apogee in the middle, etc. Consequently, when, in the case of Venus, the centre of the epicycle moves in the larger part, the intersection of the axes of the eccentric and of the ecliptic will decline northward, and [the declination will be] southward in the other part. In the case of Mercury the reverse occurs. Lastly, when the centre of the epicycle crosses the nodes, the same axes are parallels, etc.' (<i>Sit enim K apogion ecc[entrici] Veneris, L perigion. Iam si ponamus centrum epicycli Veneris in K, erit planum ecc[entrici] FKG super quod per centrum mundi C transeat orthogonalis linea ACD, ideo per 6 undecimi El[ementorum] erit aequidistans axi ecc[entrici]. Ita si centrum epi[cycli] ponamus in L perigio, erit planum eccentrici HGL, super quod orthogonalis BCE aequidistans rursum axi ecc[entrici]. Ad quantitatem igitur anguli ACB, nutat seorsum ac deorsum axis ecc[entrici]; qui angulus in Venere est 20 Scrup[ulis] in Merc[urio] autem 90 Scrup[ulis]. Constat autem planum ecc[entrici] in segmenta inaequalia dirimi a plano eclipticae. Maius enim est segmentum quod centrum habet, hoc est, in cuius medio apogion existit, etc. Ideoque dum centrum epi[cycli] peragrat maius segmentum, intersectio axium ecc[entrici] et eclipticae in Venere declinabit in Boream, alias vero in Austrum. Contrarium sit in Mercurio. Denique dum centrum epi[cycli] transit nodos, iidem axes sunt paralleli etc.</i>) Translated quotations of Peuerbach's <i>Theoricae</i> are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>


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