Astronomical Images : Lines of the motions and equations of the Moon

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 figure that first appeared in the edition of the Theoricae novae printed in Wittenberg in 1535. It has no equivalent in the original (c. 1474) edition of the treatise, nor in the edition procured by Peter Apian (Ingolstadt, 1528). In the 1551 Wittenberg edition of the Theoricae novae, this Reinhold diagram has been introduced. It is the last of the diagrams conceived to explain the motion of the epicycle of the Moon (see also fols. 29r, 31r and 33r). In this diagram, which shows clearly that the line of the mean motion of the Moon coincides with the line of the true apogee, the relationship between the measurement of the longitude of the Moon on the zodiac and the movement of the epicycle becomes obvious. The outermost circle, whose centre is the centre of the World (T), represents the ecliptic. The middle circle is the eccentric deferent of the epicycle of Moon. The apogee of this eccentric is at H, the perigee at K. The axis of the deferent orbs of the apogee is line HSTVK. The 'first half of the eccentric' (prima medietas eccentrici) is its eastern part, HLMN; its 'other half' (altera medietas) is its western part, KNOH. The epicycle of the Moon is shown in four positions (one in each quarter of the eccentric deferent). In the two first positions (in the prima medietas) the body of the Moon, at F, is situated on the tangent to the epicycle, drawn from the centre of the World. The line of the mean motion, or longitude, of the Moon is drawn from T, the centre of the World, to B, on the ecliptic, passing through the centre of the epicycle (L in its first position, then successively M, N, and O, in its other positions). The legend adds that part of it, here line TD, which ends at the circumference of the epicycle, is the line of the true apogee (cuius pars, ut linea TD semper est linea verae augis epicycli), as D is the true apogee of the epicycle. The mean motion or longitude (medius motus), measured eastward on the ecliptic from the beginning of Aries, is arc AB. The line of the true place, motion, or longitude (linea veri loci seu motus) is drawn from T, the centre of the World, to C on the ecliptic passing through F, the centre of the body of the Moon. The true motion or longitude (verus motus), measured eastward on the ecliptic from the beginning of Aries, is arc AC. The equation of the argument of the Moon (aequatio argumenti) is arc CB of the ecliptic (not CE as the legend erroneously calls it), determined by the lines of the true and mean motions of the Moon. E, on the circumference of the epicycle, determined by the line from the 'opposite point' that passes through the centre of the epicycle, is the mean apogee of the epicycle (aux media). The equation of the centre (aequatio centri) is arc DE of the epicycle (between its true and mean apogees). The true argument (argumentum verum) is arc DF of the epicycle (from the true apogee of the epicycle to the centre of the body of the Moon). The mean argument (argumentum medium) is arc EF of the epicycle (from the mean apogee of the epicycle to the centre of the body of the Moon), although the legend erroneously calls it EB. The arcs of circles drawn above the epicycle measure the mean argument: in the second and third positions of the epicycle (when its centre is at M or N, in the inferior part of the eccentric), these arcs measure more than 180 degrees. It is also quite visible that in the latter cases, the line of the true motion of the Moon precedes the line of the mean motion, reckoned eastward, whereas when the argument is less than 180 degrees (in the superior part of the eccentric), the reverse occurs. On these points, arcs and lines, see the 1482 edition of Peuerbach (sig. e6r) and Apian's 1537 edition (fol. 10v). Reinhold specifies that when the centrum Lunae (the angle formed at the centre of the World by the lines drawn respectively to the apogee of the eccentric and to the centre of the epicycle) is less than six Signs (180 degrees), as at L and M, the equation of the centre is added to the mean motion of the Moon; when the centre is more than six Signs, as at N and O, the equation of the centre is subtracted from the mean motion of the Moon. Similarly, when the true argument contains more than six Signs, as at M and N, the equation of the argument is added to the mean motion. And when the same argument contains less than six Signs, as at L and O, the equation of the argument is subtracted from the mean motion. Translated quotations of Peuerbach's Theoricae are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.