Astronomical Images : Orbs of the three superior planets and Venus

Peter Apian

Astronomical Images

This Venetian edition of Peuerbach's Theoricae novae was copied from Apian's 1528 edition, printed in Ingolstadt. Subsequently, the work went through several further editions. Apian's edition added new woodcuts as well as notations to some of those from earlier editions. Some errors in the woodcuts in the 1528 edition were repeated in this Venetian edition of 1537. This diagram is a reduced and slightly revised copy of a diagram in Peuerbach's original (c. 1474) edition. The three superior planets (Jupiter, Mars and Saturn) and Venus each have three orbs, similar to the orbs of the Sun except that their middle eccentric orb contains an epicycle (the epicycle is not visible on this diagram, though it is represented in the original diagram). A, 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 (its centre is point D), while the centre of its concave surface is the centre of the eccentric deferent (point C, according to the legend). E, the innermost orb printed black, is also 'deformed': the centre of its interior concave surface is point D, while the centre of its exterior convex surface is point C. 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 vertical line is the axis of the deferent orbs of the apogee, also called the line of the apogee (linea augis). 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 (not represented on this diagram) is attached to the circle in the middle of this orb. 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 (fols. 13v-14r), 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. The legend also mentions that 'Point H is the centre of the equant circle' (Punctum H est centrum aequantis). The equant circle is not represented on the diagram and its centre, point H, is not in the correct place; it ought to be as distant from the centre of the deferent as the deferent is from the centre of the World, so that the centre of the deferent would be in the middle of the centre of the equant and the centre of the World. In the original diagram the equant circle is not drawn, but its centre is in the correct place. 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. 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). Other quotations (translated by Isabelle Pantin) are from Pedersen (1973).