Astronomical Images : Lines and motions of the superior planets

Peter Apian

Astronomical Images

<p style='text-align: justify;'>This Venetian edition of Peuerbach's <i>Theoricae novae </i>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. Although it represents three positions of the centre of the epicycle, instead of two, this diagram closely resembles the diagram in Gregor Reisch's <i>Margarita philosophica</i> that shows the meaning of the terms concerning the superior planets, Venus and Mercury in the astronomical tables (sig. o3r). It shows the three orbs of the superior planets. The outermost circle represents the zodiac. Point x, marked outside the circle, top right, is the beginning of Aries. The vertical line is the line of the apogee (<i>linea augis</i>), which passes through the apogee of the eccentric deferent of the planet, the three aligned centres of the equant circle, the eccentric deferent and the World (although only two centres are visible on this diagram), and the perigee of the deferent. The line that crosses it at right angles at the centre of the World indicates the points of the eccentric deferent that are at middle distance from the Earth (between the apogee and perigee), called mean longitudes. According to the legend, the mean motion of the planet (<i>medius motus planetae</i>) is arc xb, measured on the zodiac from the beginning of Aries to the line of the mean motion (<i>linea medii motus</i>), drawn from the centre of the World to the zodiac, parallel to the line drawn from the centre of the equant to the centre of the epicycle. From this we may infer that point c is the centre of the equant, though everywhere in this section of the book, c is the letter for the centre of the eccentric deferent. The legend does not mention the true motion of the planet (<i>verus motus planetae</i>), but the lines of the true motion (<i>lineae veri motus planetae</i>), which come from the centre of the World (point g) and pass through the body of the planet, are drawn on the diagram. The true motion of the planet, that is the arc of the zodiac measured eastward from the beginning of Aries to the line of the true motion, is thus easily spotted on the diagram: for instance, when the planet is at t, its true motion is arc xd. The lines of the true motion of the epicycle (<i>lineae veri motus epicycli</i>), drawn from the centre of the World to the zodiac and passing through the centre of the epicycle, are also visible on the diagram (gf, gk, gn, for the three positions of the epicycle), but not mentioned in the legend. The mean centre of the planet (<i>centrum medium planetae</i>), kb according to the legend, is the arc of the zodiac measured eastward from the line of the apogee (<i>linea augis</i>) to the line of the mean motion (<i>linea medii motus</i>). The true centre of the planet (<i>centrum verum et aequatum planetae</i>), kf according to the legend, is measured on the zodiac from the line of the apogee to the line of the true motion of the epicycle (<i>linea veri motus epicycli</i>). The equation of the centre in the zodiac (<i>aequatio centri in zodiaco</i>), fb according to the legend, is the arc of the zodiac between the line of the true motion of the epicycle and the line of the mean motion. This equation is null when the centre of the epicycle is on the line of the apogee, as is the case with the epicycle in the middle of the diagram. The equation of the centre in the epicycle (<i>aequatio centri in epicyclo</i>) is arc re according to the legend, which is somewhat puzzling as the letter r is nowhere visible, and e is apparently marked on the zodiac. The equation of the centre in the epicycle is the arc of the epicycle between the true and mean apogee of the epicycle. The mean apogee of the epicycle (<i>aux epicycli media</i>) is the point of the epicycle marked by the line drawn from the centre of the equant and passing through the centre of the epicycle, while its true apogee (<i>aux epicycli vera</i>) is shown by the line drawn from the centre of the World and passing through the centre of the epicycle. Thus, on the diagram, the equation of the centre in the epicycle is the arc of the epicycle corresponding to the letters ef marked above near the zodiac. These ambiguities in the lettering stem from the fact that the Venetian edition exactly copies the legend of Apian's original edition, but introduces some variants in the lettering. The equation of the argument of the planet (<i>aequatio argumenti planetae</i>) is the arc of the zodiac lying between the line of the true motion of the planet and the line of the true motion of the epicycle: arc df on the diagram. The true argument of the planet (<i>argumentum verum planetae</i>) is the arc of the epicycle from the true apogee of the epicycle (the point of the epicycle that corresponds to f on the zodiac) to the centre of the body of the planet (point r that corresponds to d on the zodiac). Thus, the diagram shows obviously the correspondence between the equation of the argument of the planet and the true argument of the planet. The proportional minutes (<i>minuta proportionalia</i>) are also represented, as in the <i>Margarita</i> diagram, by the graduation marked along the line of the apogee in the inferior part of the eccentric orb (between the perigee and the exterior limit of the interior deformed orb). For a more complete clarification, see Apian (1537), fol. 17r.</p>