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Astronomical Images : Lines and motions of the Sun, and linea medii motus

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. The left-hand woodcut defines the mean motion of the Sun. A is the beginning of Aries on the ecliptic of the eighth orb (called <i>zodiacus</i> in Apian's text). C is the centre of the eccentric deferent. D is the centre of the World. The line of the mean motion of the Sun (<i>linea medii motus</i> on the diagram) is DB, the line drawn from the centre of the World to the ecliptic and parallel to the line drawn from the centre of the eccentric deferent to the centre of the body of the Sun. These two lines merge with one another twice a year: when the Sun is at the apogee (<i>aux</i>) or at the perigee (<i>oppositum augis</i>). For the line of the apogee (<i>linea augis</i>) passes through C and D, and the two lines always make equal angles with respect to the line of the apogee: when the Sun is at the apogee or perigee, this angle is null. The line of the mean motion of the Sun intersects with the ecliptic of the eighth orb at B, and the mean motion of the Sun (<i>medius motus Solis</i>) is arc AB of the ecliptic. The diagram does not show the line of the true motion of the Sun (<i>linea veri motus Solis</i>), which is extended from the centre of the World to the ecliptic, passing through the body of the Sun. All distances are measured <i>secundum Signorum successionem</i>, that is from Aries to Taurus and so on (from west to east). The right-hand woodcut shows more clearly and completely the lines according to which the different positions or motions (<i>motus</i>) of the Sun can be measured. It is derived from a diagram of the original edition of Peuerbach's treatise (c. 1474), but with several additions: the three orbs of the Sun (comprised of the two black orbs, called the deferent orbs of the aux or apogee of the Sun, and the white orb of the deferent of the body of the Sun), were not represented in the 1474 diagram, and the latter showed only the lines for five different positions of the Sun (in Apian's version, we have them for eight positions). The arcs of circles above the outermost orb of the Sun, which serve to measure the motions, are also additions. Although they are represented as superimposed for the sake of legibility, they are all meant to be portions of the same circle: the ecliptic of the eighth sphere (called <i>zodiacus</i>). The centre of the eccentric deferent is c, and d the centre of the World. The line marked '<i>Principium</i>' (for <i>principium Arietis</i>) is extended from the beginning of Aries to the centre of the World, d. The line of apogee (<i>linea augis</i>) is the vertical line extending through the centre of the eccentric and the centre of the World. Its intersection with the eccentric orb of the Sun shows the furthest distance from the centre of the World (<i>longitudo longior</i> or <i>aux</i>), and the closest distance, that is the perigee (<i>longitudo proprior</i> or <i>oppositum augis</i>). The apogee of the Sun (<i>aux Solis</i>) in its secondary meaning (<i>aux in secunda significatione</i>) is the arc of the zodiac (more exactly of the ecliptic of the eighth sphere) reckoned eastward from the beginning of Aries up to the line of the apogee. On the diagram it is marked (in abbreviated form) '<i>ef aux in secunda significatione</i>'. The argument of the Sun (<i>argumentum Solis</i>), shown here as dh, is the arc of the ecliptic between the line of the apogee and the line of the mean motion of the Sun (<i>linea medii motus Solis</i>), reckoned eastward. (As shown in the left-hand woodcut, <i>linea medii motus</i> is the line drawn from the centre of the World to the ecliptic, and parallel to the line drawn from the centre of the eccentric deferent to the centre of the body of the Sun.) The argument is always equal to the arc of the eccentric deferent between the apogee of this eccentric deferent and the centre of the body of the Sun, reckoned eastward (<i>semper est similis arcui eccentrici inter augem eccentrici et centrum Solis secundum successionem</i>). As a consequence, when you subtract the arc of the ecliptic between Aries and the line of the apogee (<i>aux in secunda significatione</i>) from the mean motion of the Sun (that is the arc of the ecliptic from the beginning of Aries to the <i>linea medii motus</i>), the argument of the Sun remains. This simple subtraction is sufficient when the <i>linea medii motus</i> is east of the <i>linea augis</i>; but when it is west of this line, you must also add 360 degrees. The line of the true motion of the Sun (<i>linea veri motus Solis</i>) is the line from the centre of the World, d, extended through the centre of the body of the Sun to the zodiac at point b in this woodcut. The true motion of the Sun (<i>verus motus Solis</i>) is the arc of the ecliptic between a (Aries) and this <i>linea veri motus Solis</i>; here, it is shown as the arc marked '<i>ab verus motus</i>'. When the Sun is at the apogee or perigee (on the <i>linea augis</i>), the line of the mean motion merges into the line of the true motion and the mean and true motions are equal. As clearly shown in the diagram, three lines are necessary to measure each position of the Sun, except when it is on the line of the apogee: the <i>linea veri motus</i> and the two parallel lines defining the <i>linea medii motus</i>. We can observe that, on the diagram, the same point (the beginning of Aries on the ecliptic) apparently corresponds to two letters: e (in <i>ef aux in secunda significatione</i>) and a (in <i>ab verus motus</i>). The equation of the Sun (<i>aequatio Solis</i>) is the arc of the zodiac falling between the lines of the mean and true motions. This equation is null when the Sun is at the apogee and perigee (see above). It is maximal when the Sun is at its mean longitudes (as illustrated by the previous diagram in this work, on fol. 5r). On the diagram, the equation is indicated for one position of the Sun: the arc bh, also marked (with abbreviations and almost illegibly) '<i>aequatio</i>'. The text adds a rule: when the argument is less than 180 degrees (six Signs), the equation must be subtracted from the mean motion to obtain the true motion; when it is greater than 180 degrees, it must be added.</p>


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