This Venetian edition of Peuerbach's 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 is a crude reduced copy of a diagram in the original edition of Peuerbach's treatise (c. 1474). It is related to a section of the treatise that examines the consequences of the eccentricity of the Moon. It concerns a device for the calculation of the equation of the argument of the Moon (aequatio argumenti Lunae<\/i>), measured on the zodiac (it is defined as the arc of the zodiac lying between the mean and true longitudes of the Moon), and dependent on the true argument of the Moon (argumentum Lunae verum<\/i>), measured on the circumference of the epicycle, as it 'extends from the true apogee of the epicycle up to the centre of the body of the Moon'. As the distance of the centre of the epicycle from the centre of the World varies, the diameter of this epicycle, measured on the zodiac from the centre of the World, also varies. Therefore, to the same value of the true argument (measured on the epicycle) correspond unequal arcs of equations (measured on the zodiac): they are smaller near the apogee of the eccentric (and minimal at the apogee), larger near the perigee (and maximal at the perigee). The epicycle is called by Peuerbach 'the small circle' (circulus brevis<\/i>), and the variation of the equations, for the same given argument, 'the variations of the diameter of the small circle' (diversitates diametri circuli brevis<\/i>). In the diagram, the outermost circle is drawn around the centre of the World; its radius extends from this centre to the apogee of the deferent. The innermost circle is also drawn around the centre of the World, and its radius extends from the centre of the World to the perigee of the deferent. The space between these two circles is divided into six orbs by five concentric equidistant circles. From the one next to the outermost circle to the innermost circle they are numbered from 10 to 60 along the vertical line that represents the axis of the deferent orbs of the apogee (linea augis<\/i>). The circle that marks the exterior limit of the blackened zone is the eccentric deferent of the epicycle (the centre of the lunar epicycle is attached to it, and rotates with it). Peuerbach explains that 'the line taken from the centre of the World to the apogee of the deferent is longer than the line extended from the same centre to the perigee. Moreover, the excess of the former over the latter, divided into sixty equal parts, is called proportional parts, and is twice the eccentricity' (Linea vero a centro mundi ad augem deferentis protracta, longior est linea ab eadem centro ad oppositum augis extensa. Excessus autem illius super istam divisus in 60 particulas aequales, minuta proportionalia dicitur, et duplus est ad excentricitatem<\/i>). In other words, the portion of the linea augis<\/i> divided into sixty proportional parts (proportionalia minuta<\/i>) is twice the distance between the centre of the World and centre of the eccentric. The blackened zone shows that at the apogee the eccentric deferent encompasses all the proportional minutes, that it encompasses none of them at the perigee, and that in other places it encompasses some of them: fewer near to the perigee and more, in proportion, near to the apogee. We see that when the centre of the epicycle is at the perigee, it is on line 60, and that it is on line 0 at the apogee. The lines radiating from the centre of the World are meant to meet the successive intersections of the eccentric deferent with the other lines, in order to mark the places where the centre of the epicycle is at 10, 20, 30, 40 and 50 proportional minutes. But they are so clumsily drawn that they miss their target. As for the use of this diagram, in Peuerbach's words, 'the equations of the arguments that are written in the tables are those that come about when the centre of the epicycle is in the apogee of the deferent' (Aequationes autem argumentorum, quae scriptae sunt in tabulis, sunt, quae contingunt, dum centrum epicycli in auge deferentis fuerit<\/i>). The tables do not give the values of the equation when the centre of the epicycle is in other places, but it is possible to reckon them. If we know the centrum Lunae<\/i> (the angle formed, at the centre of the World, by the lines drawn respectively to the apogee and to the centre of the epicycle), the tables indicate the proportional parts; and if we know the true argument, they indicate the value of the diversitas diametri<\/i> when the centre of the epicycle is at the perigee of the eccentric (that is, when the proportional minutes are 60); then we calculate the diversitas diametri<\/i> corresponding to the exact position of the centre of the epicycle (10, 15, 25 proportional minutes, and so on), and this value is added to the equation of the argument taken from the tables. The right-hand woodcut is a new version of a diagram in the original edition of Peuerbach's treatise. It aims at explaining the movement of the ascending and descending nodes, the Head and Tail of the lunar Dragon. The plane of the eccentric of the Moon intersects the plane of the ecliptic, as the axis of the orbs that carry the lunar apogee intersects the axis of the ecliptic at the centre of the World. Thus, the line of intersection is a diameter of the World. One part of the plane of the eccentric declines from the plane of the ecliptic towards the north, the other towards the south. The Head and Tail of the lunar Dragon are situated at the points where the eccentric circle intersects the plane of the ecliptic. The ascending node, or Head of the Dragon, is the intersection that the centre of the epicycle passes by when, carried along by the movement of the eccentric deferent, it enters the half of its path that declines northwards. For the descending node, or Tail of the Dragon, it is the reverse. E. J. Aiton gives the following translation of this passage of Peuerbach: the intersection 'that begins to move towards the north when the centre of the epicycle is on it, is called the Head of the Dragon' (Illa igitur intersectio ... in qua cum centrum epicycli fuerit, versus Aquilonem incipit ire, Caput Draconis nuncupatur<\/i>). This translation is absurd because the intersections cannot move northwards or eastwards, as they mark the points of the eccentric deferent that are exactly on the ecliptic. They effectively move, but along the ecliptic. They 'move daily beyond the diurnal motion about three minutes towards the west' (moventur autem hae intersectiones quotidie ultra motum diurnum versus Occidendem tribus minutis fere<\/i>), as they are carried along by the outermost orb of the Moon, also called the 'deferent of the Head of the Dragon' (deferens Caput Draconis<\/i>). The mean motion of the Head of the Dragon (medius motus Capitis Draconis<\/i>) is the arc, measured westward (contra successionem<\/i>) on the ecliptic, from the beginning of Aries to the line drawn from the centre of the World passing through the Head of the Dragon. The true motion of the Head (verus motus Capitis<\/i>) is the arc of the ecliptic from the beginning of Aries to the same line passing through the Head, but measured eastward (secundum successionem Signorum<\/i>). The same measurements can be made for the Tail. Of course, if we add the mean and true motions of the Head, the sum is 360 degrees, and 'by subtracting the mean longitude of the Head from twelve Signs [= 360 degrees], its true longitude is the remainder. And thus the common maxim, that the Head of the Moon goes as much with the mean motion against the firmament as in reality it goes with the firmament, is understood to mean that the mean longitude of the Head of the Moon extends westward to the point to which the true longitude extends eastward' (Ex his manifestum est, quod subtracto medio motu Capitis a duodecim Signis, verus eius motus remanet. Unde commune dictum dicens, Caput Lunae tantum medio motu ire contra firmamentum quantum in veritate vadat um firmamento, ita intelligitur medius motus Capitis Lunae contra successionem Signorum in eum punctum protenditur, in quem verus secundum successionem Signorum<\/i>). Peuerbach later explains, in the middle section of the treatise (Passiones planetarum<\/i>), that solar and lunar eclipses occur only when the Sun and the Moon are near the nodes, either at New Moon or at Full Moon. In the diagram, the outermost circle is a zodiacal limb partially graduated (the thirty degrees of Aries and the beginning of Taurus are visible). Inside, the two intersecting circles are the eccentric deferent and a circle in the plane of the ecliptic. The symbol of the 'Head of the Dragon' (Caput Draconis<\/i>), or ascending node, with the belly [venter<\/i>] of the curve upwards, is near the right intersection, and the symbol of the 'Tail of the Dragon' (Cauda Draconis<\/i>), or descending node, with the belly downwards, is near the left intersection. Both intersections are, of course, diametrically opposed and situated on the line of intersection between the two planes. The epicycle is also represented with the Moon in two different positions. We should take note that at the top of the eccentric deferent it is at its maximal declination northwards in relation to the ecliptic and at its closest position to our zenith, whereas at the bottom of the eccentric it is at its maximal declination southwards in relation to the ecliptic and at its remotest position to our zenith. Unlike the original c. 1474 diagram, Apian's diagram does not clearly show the radius that defines the 'true position of the Head' (verus locus Capitis<\/i>), extended from the centre of the World to the zodiac and passing through the ascending node. A clearer diagram of the Head and Tail of the Dragon is given in the commentary of Erasmus Reinhold (fol. 40r). Translated quotations of Peuerbach's Theoricae<\/i> are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.<\/p>" }, { "label": "Date of Creation", "value": "1537" }, { "label": "Title", "value": "Proportional parts of the Moon and the lunar Dragon" }, { "label": "Material", "value": "paper" }, { "label": "Classmark", "value": "Te.52.111" }, { "label": "Note(s)", "value": "
Links to other items:<\/p>
Peuerbach's planetary theories: CUL Te.52.111 (Motion of the three superior planets in the epicycle)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Orbs of Venus)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Adams.5.58.2 (Lunar motion according to Copernicus)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Inc.5.B.3.23c[1460] (Orbs of the Moon)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Inc.5.B.3.23c[1460] (Axes and poles of the Moon's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.b.14 (The motion in latitude of Venus, orbs and axes of Mercury)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.b.14 (How to find the true centre and true motion of a superior planet)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.b.14 (Orbs, lines and motions of Venus)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Inc.5.B.3.23c[1460] (Lines and motions of the Moon)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.b.14 (Orbs of Venus)<\/a><\/p> Peuerbach's planetary theories: CUL Hanson.c.180 (Motions of Mercury, and the proportional parts of Mercury)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Orbs of the three superior planets and Venus)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Line of mean motion of the superior planets)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Lines and motions of the superior planets)<\/a><\/p> Corresponding image in a different edition: CUL Inc.5.B.3.23c[1460] (Proportional parts of the Moon)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Axes, poles and equant of the superior planets)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (The motion in latitude of the eccentric of Venus)<\/a><\/p> Peuerbach's planetary theories: CUL Inc.5.B.3.23c[1460] (Orbs of the Sun)<\/a><\/p> Peuerbach's planetary theories: CUL Inc.5.B.3.23c[1460] (Motions of Mercury)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.c.32 (The meaning of terms concerning the superior planets, Venus and Mercury in astronomical tables)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Orbs and motion of Venus in relation to the motion of the Sun)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Orbs, axes and poles of the Sun's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.c.32 (Orbs and axes of Mercury's motion)<\/a><\/p> Peuerbach's planetary theories: CUL P*.10.45(D) (Basic elements of the Theorica<\/em> tradition in natural philosophy)<\/a><\/p> Peuerbach's planetary theories: CUL Norton.c.32 (Orbs, axes and poles of the Sun's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Proportional parts of Mercury)<\/a><\/p> Peuerbach's planetary theories: CUL Syn.6.51.5 (Orbs, axes and poles of the Sun's motion)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Syn.6.51.5 (Orbs, axes and poles of the Moon's motion)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Te.52.111 (Orbs, axes and poles of the Moon's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Lines and motions of the Sun, and linea medii motus<\/em>)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Te.52.111 (Mean and true apogees of the epicycle of the Moon)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Orbs and axes of the motion of Mercury)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Te.52.111 (Variations in speed of the motion of the Moon's epicycle)<\/a><\/p> Peuerbach's planetary theories: CUL Syn.6.51.5 (Orbs, axes and poles of the superior planets)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Te.52.111 (Axes, mean and true apogees of the epicycle of the Moon)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Proportional parts of the superior planets)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Lines and motions of the Sun)<\/a><\/p> Peuerbach's planetary theories: CUL Syn.6.51.5 (Orbs and axes of Mercury's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Motions of Mercury)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Norton.c.32 (Orbs, axes and poles of the Moon's motion)<\/a><\/p> Peuerbach's planetary theories: CUL Te.52.111 (Title-page: lines and motions of the superior planets)<\/a><\/p> Peuerbach's planetary theories - the Moon: CUL Te.52.111 (Orbs of the Moon)<\/a><\/p> Peuerbach's planetary theories: CUL Syn.6.51.5 (Orbs of Saturn)<\/a><\/p> Peuerbach's planetary theories - the Moon: Wren S.3.117 (Orbs, axes and poles of the Moon's motion)<\/a><\/p> Peuerbach's planetary theories - the Moon: Wren S.3.117 (Motion of the epicycle of the Moon )<\/a><\/p> Peuerbach's planetary theories - the Moon: Wren S.3.117 (Mean and true apogees of the epicycle of the Moon)<\/a><\/p> Peuerbach's planetary theories - the Moon: Wren S.3.117 (Variations in speed of the motion of the Moon's epicycle)<\/a><\/p> Peuerbach's planetary theories - the Moon: Wren S.3.117 (Lines of the motions and equations of the Moon)<\/a><\/p> Corresponding image in a different edition: Wren S.3.117 (Proportional parts of the Moon)<\/a><\/p> Corresponding image in a different edition: Wren S.3.117 (The lunar Dragon)<\/a><\/p>