Astronomical Images : Terms and practical rules for computing the equations of the centres (superior planets)

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 Reinhold diagram has no model in the original (c. 1474) edition of Peuerbach's treatise. It first appeared in the commentary on Peuerbach by Franciscus Capuanus (Venice, 1495), then in the Fine edition of the treatise (Paris, 1525), and in the Wittenberg edition (1535). It can be used as a visual glossary or a mnemonic tool for an easy calculation of the movements of the planets, with the aid of astronomical tables. The exterior circle (AEKO) represents the ecliptic. The interior circle is the eccentric. The vertical line is the line of the apogee, passing through the centre of the equant (H), the centre of the eccentric (C), the centre of the World (D), and the perigee (G). A is the beginning of Aries. AB is the 'apogee in second signification' (<i>apogion in secunda significatione</i>). If the centre of the epicycle is at F, line HF is part of the line of the mean apogee of the epicycle. Line DO, parallel to HF, is the line of the mean motion of the epicycle and of the planet (<i>linea DO parallelas [sic] ipsius HF, linea medii motus epicycli et planetae</i>). DFE is the line of the true motion, not of the planet, but of the epicycle only (<i>linea veri motus, non planetae, sed tantum epicycli, DFE</i>). Arc AEO is the mean motion or longitude of the planet or the epicycle (<i>medius motus planetae vel epicycli arcus AEO</i>). Arc ABE is the true motion, not of the planet, but only of the epicycle (<i>verus motus non planetae, sed tantum epicycli arcus ABE</i>). Arc BEO is the mean centre (<i>centrum medium</i>). Arc BE is the true centre (<i>centrum verum</i>). Arc EO is the equation of the centre, measured on the ecliptic (<i>aequatio centri in zodiaco, arcus EO</i>). Angle EDO is the angle of the equation at the centre of the World (<i>angulus aequationis super centro mundi EDO</i>). As HF and DO are parallel, so angle EDO is equal to angle HFD at the centre of the epicycle, commonly called 'coalternate' according to Euclid, <i>Elements</i> I.29 (<i>huic autem angulo aequalis est angulus, ut vulgo vocant, coalternus, HFD, super centro epicycli consistens. Id constat partim per hypothesin aequidistantiae linearum HF, et DO partim per 29 primi Elementorum</i>). Obviously, this equation of the centre (arc EO) must be subtracted from the mean centre and the mean motion of the planet when the centre of the epicycle is in the first half of the eccentric (BEK), that is when the true centre of the planet is less than 180 degrees. And the equation must be added when the centre of the epicycle is in the last half of the eccentric (KOB). For more explanation about these additions and subtractions, see fol. 54r. For the definition of all these terms, see Reisch (1503), sig. o3r and Apian (1537), fol. 16v. Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>