Astronomical Images : Orbs and centres of the superior planets and Venus

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. In the original version (c. 1474), the equant circle is not drawn. It has been added in the Margarita philosophica (see Reisch (1512), sig. Q8v), and in the editions by Oronce Fine of the commentary on Peuerbach by Franciscus Capuanus (Paris, 1515) and of the Theoricae novae (Paris, 1525). However, the Apian edition (Ingolstadt, 1528) and the Wittenberg edition (1535) follow the original version (see Apian (1537), fol. 13r). In the 1551 Wittenberg edition of the Theoricae novae, this Reinhold diagram has been introduced. The superior planets and Venus have three orbs, similar to the orbs of the Sun except that their middle eccentric orb contains an epicycle. The outermost orb, printed black, is said to be 'deformed' (its two surfaces are not concentric): its exterior convex surface is concentric with the World, while the centre of its concave surface is the centre of the eccentric deferent. The innermost orb, printed black, is also 'deformed': the centre of its interior concave surface is the centre of the World, while the centre of its exterior convex surface is the centre of the eccentric deferent. These two deformed orbs are the deferent orbs of the apogee (orbes augem deferentes). They move 'by virtue of the motion of the eighth sphere on the axis and poles of the ecliptic' (virtute motus octavae sphaerae super axe et polis eclipticae moventur). The white orb sandwiched between these orbs is eccentric to the centre of the World on both its inner and outer surfaces (its centre is C). The centre of the epicycle is attached to the circle in the middle of the eccentric orb, ABFG. Both orb and circle are called the eccentric deferent of the planet. 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). As is explained later (fol. 42r), the intersection between the axis of the eccentric and the axis of the deferent is not at the centre of the World, and the north poles of the deferent and ecliptic are closer together than the corresponding south poles. AKFL is, according to the legend, 'the circumference of the eccentric equant described around the centre of the equant, H. Its radius is equal to the radius of the eccentric deferent, and, for this reason, the circles themselves are equal' (circumferentia eccentrici aequantis descripta super centro aequantis H. Huius semidiameter est par semidiametro eccentrici deferentis, ac propterea etiam ipsi circuli existunt aequales). Its centre (H) is above the centre of the deferent (C), as distant from it as the deferent is from the centre of the World, so that C is between H and the centre of the World (D), and equally distant from each. Reinhold notes that the two eccentric circles (the equant and the deferent) intersect at points A and F, but that 'the planes themselves do not intersect, but constitute a kind of continuous plane' (ipsae superficies non scindunt sese, sed sunt unum quoddam continuum planum). Peuerbach defines this equant only later in the treatise, when he deals with the movements of the eccentrics and of the epicycles of the superior planets. In the fifteenth-century glossary of astronomical terms edited by Olaf Pedersen, the 'eccentric equant' (eccentricus equans) is defined as 'a circle in relation to whose centre the centre of the epicycle moves regularly and describes equal angles in equal times; its centre is as distant from the centre of the deferent, as the centre of the deferent from the centre of the Earth' (quidam circulus supra cuius centrum equaliter movetur centrum epicycli, et in temporibus equalibus equales angulos describit, cuius centrum tam distat a centro deferentis quam centrum deferentis a centro Terrae). 'Equans' is a term used only in the theory of Mercury, Venus, and the three superior planets, not in the theory of the Sun nor even the theory of the Moon, in which the term 'opposite point' (punctum oppositum) is used for the point corresponding to the centre of the eccentric equant. Peuerbach specifies that the movement of the centre of the epicycle (which is uniform in relation to the centre of the equant), is slower (in relation to the centre of the deferent) near the apogee of the deferent and faster near the perigee, which is 'the opposite of what happens in the case of the Moon'. Translated quotations of Peuerbach's Theoricae are from Aiton (1987). Quotations from Reinhold's commentary and from Pedersen (1973) are translated or paraphrased by Isabelle Pantin.