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Astronomical Images : Orbs, axes and poles of the Sun's motion

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 diagram copies, with some corrections, the Apian diagram of the orbs, axes and poles of the motion of the Sun. This woodcut, with the same lettering, had also been used in the edition of the <i>Theoricae novae</i> (without commentary) printed in Wittenberg by Hans Lufft in 1551. In this figure, the outermost circle represents the ecliptic. The three orbs of the Sun are comprised of the two orbs printed black and the white orb sandwiched between them and divided in two by a circle. The black orbs are said to be 'deformed' because their two surfaces are not concentric: one of them is concentric with the World (in the diagram its centre is point B), while the other has the same centre as the eccentric or deferent of the body of the Sun (point A). These orbs are called the deferent orbs of the aux (or apogee) of the Sun (<i>orbes augem Solis deferentes</i>), because the aux of the Sun varies according to their motion; they move together in that the narrower part of the larger orb is always above the wider part of the smaller orb. The white orb is eccentric to the centre of the World on both its inner and outer surfaces. It is called the deferent orb of the body of the Sun (or the deferent orb of the Sun). The Sun is attached to it (the centre of its body is shown on the circle in the middle of the orb, also called <i>deferens corporis Solis</i>) and moves according to its motion. The points of the deferent where the Sun is at its apogee and perigee are marked on the diagram: <i>aux Solis</i>, <i>opo[situm] au[gis]</i>. The poles of the ecliptic of the eighth sphere (each marked <i>polus eclip[tice]</i>) are at the extremity of the axis of the ecliptic, or axis of the World. The poles of the motion of the deferent orbs of the apogee (G and H) are situated on the same axis, 'for the apogee of the eccentric deferent of the Sun continually revolves in the plane of this ecliptic'. According to the legend, line GBH is 'the axis of the deferent orbs of the apogee of the eccentric, which is a part of the axis of the ecliptic of the eighth sphere'. Points E and F are the poles of the motion of the eccentric deferent orb of the body of the Sun (each marked <i>polus defe[rentis]</i>), at the extremity of line EAF, the axis of the deferent orb (<i>axis deferentis</i>). This axis is 'parallel to the axis of the deferent orbs of the apogee' (<i>axi orbium augem deferentium aequidistans</i>), that is to the axis of the ecliptic. 'The axis of the solar deferent orb with the centre of the eccentric circle [A], and also the poles of the solar deferent orb [E and F], describe the circumferences of small circles about the axis of the deferent orbs of the apogee [line GBH that coincides with the axis of the World (<i>axis mundi</i>), or the axis of the ecliptic of the eighth sphere], according to the size of their eccentricity.' This motion is represented by three small semicircles (EK, AL and FI), which are to be considered to be in parallel planes perpendicular to the plane of the sheet. The legend specifies that line AB (between the centre of the eccentric deferent and the centre of the World) is the eccentricity of the Sun (<i>eccentricitas</i>), which according to the Alphonsine astronomers (<i>juxta Alphonsinos</i>) is about 2,266/60 parts of the radius of the eccentric circle (<i>duarum Partium ac 16 Minu. fere, qualium semidiameter eccentrici continet 60</i>), whereas according to Albategnius it amounts to 38 radii of the Earth. Reinhold adds that the rotation of the small circles is very slow: it is 'not accomplished before the fixed stars have achieved their period, that is after 49,000 years, if we are to trust in the Alphonsine astronomers' (<i>hi circuli non integrantur aut absolvuntur prius quam stellae fixae conficiant suam periodum, id est, post annos 49000 si Alphonsinis credendum est</i>). Besides, 'the observations show that the eccentricity of the Sun varies gradually' (<i>porro observationes docent paulatim variari Solis eccentricitatem</i>). In 1542, when Reinhold had written this text, he already mistrusted the <i>Alphonsine Tables</i>, but he had not yet completed his own <i>Prutenic Tables</i> (Tuebingen, 1551). The line of the apogee, perpendicular to the <i>axis deferentis</i> and the <i>axis mundi</i>, passes through the centre of the deferent (A), the centre of the World (B), and the points of the apogee (C) and perigee (D). In Peuerbach's original (c. 1474) diagram, it is marked as 'the plane of the ecliptic and the deferent' (<i>superficies plana eclipticae et deferentis</i>). It signifies that the axis of the deferent and the axis of the ecliptic are always on the same plane, as the former revolves around the latter. The spatial relations of these orbs and their motion are more clearly shown in the three-dimensional diagram provided in Erasmus Oswald Schreckenfuchs' <i>Commentaria in novas theoricas planetarum Georgii Purbachii</i> (Basel: Henricus Petri, 1556), plate before p. 1. 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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