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Astronomical Images : The motion in latitude of Venus, orbs and axes of Mercury

Georg von Peuerbach

Astronomical Images

<p style='text-align: justify;'>This 1515 Parisian edition, which contained the commentaries on Peuerbach by Franciscus Capuanus (first edition 1495) and Sylvester de Prierio (first edition 1514), and Jacques Lefevre d'Etaples' <i>Astronomicon</i>, was supervised by Oronce Fine, who redrew and improved all the diagrams of the preceding editions. Folio 73v belongs to the second part of the volume that contains the commentary of Sylvester de Prierio, OP, first published in Milan by Gotardus de Ponte in 1514, with abundant illustration. The left-hand diagram explains the movement in latitude of the eccentric of Venus. According to Peuerbach the movement eastward of the eccentric of Venus 'is made about its imaginary axis, whose poles approach and recede from the poles of the zodiac on each side, on account of the other motion of the eccentric in latitude' (<i>sit autem motus huius deferentis in longitudinem super axe eius imaginario, cuius poli accedunt et recedunt a polis zodiaci in utranque partem propter motum alium in latitudinem</i>). As a consequence, 'the apogee of the eccentric does not cross the ecliptic, but â?¦ sometimes declines to the south, and sometimes to the north' (<i>aux eccentrici non eclipticam non transeat, verum â?¦ quandoque ad Meridiem, quandoque ad Septentrionem declinat</i>). The diagram is a copy of a figure that first appeared in the original edition of the commentary of Sylvester de Prierio (1514). It consists of two successive images of the intersecting planes of the eccentric of Venus and of the ecliptic, crossed by their axes. In the first image the axis of the plane facing the reader is low in front and high behind, while the axis of the other plane is high in front and low behind. In the second image, this is the reverse. Thus, the swinging to and fro of the plane of the eccentric is suggested. The right-hand diagram shows the orbs and axes of Mercury, at the beginning of the chapter devoted to this planet. In the original editions of Peuerbach (c. 1474) and in the commentary of De Prierio there is one diagram for the orbs of Mercury (<i>Theorica orbium Mercurii</i>), and one for the axes (<i>Theorica axium et polorum</i>). Fine has preferred to follow a diagram of the <i>Margarita philosophica</i> that combines both diagrams. Besides, Fine has introduced an important innovation: the diagram is labelled with letters that are referred to in the text. This diagram is also used in the first part of the 1515 volume (the commentary of Capuanus) and in the Fine edition of Peuerbach (Paris, 1525). In the latter, it is accompanied by a legend. Mercury has five orbs and one epicycle. The outermost orb is said to be 'deformed' or 'relatively eccentric' (<i>eccentricus secundum quid</i>), as its convex surface is concentric to the World, while its concave surface is eccentric. This orb is contiguous to another orb, whose two surfaces have different centres, both distinct from the centre of the World: in the diagram, these orbs are printed black and separated by a white circle. The two innermost orbs constitute a similar system, except that the innermost surface is concentric to the World, while the outermost surface is eccentric. The eccentric white orb sandwiched between the two pairs of black orbs is the deferent orb of the epicycle (whose centre is attached to the circle in the middle). Peuerbach calls it 'the fifth orb' (<i>orbis quintus</i>). We could, then, number the interior deformed orbs 1 and 2, and the exterior ones 3 and 4. The commentary accompanying the diagram explains that, 'for an easier understanding, the five orbs will be designated by letters: b for orbs 4 and 3, k for orb 5, the eccentric deferent, i for orb 2, and g for the last and innermost orb' (<i>vocentur autem brevitatis et facilioris intelligentiae gratia superior orbis b et reliquus b, et deferens: k et alius: i et ultimus: g</i>). It is worth noting that in the original edition the commentary already mentions letters (a, b, c, d, e), but these letters are not used in the diagram. Like the superior planets and Venus, Mercury has an eccentric equant (a circle in relation to whose centre the centre of the epicycle moves regularly). As a consequence, Mercury's <i>theorica</i> has four primary centres (what concerns the epicycle being left aside): first the centre of the World (c), second the centre of the eccentric equant (labelled 'd', according to the legend in the 1525 edition of Peuerbach), third the centre of the eccentric deferent (f), and fourth the centre of the concave surface of the outermost orb (orb 4) and of the convex surface of the most interior orb (orb 1), and also of the contiguous surfaces of orbs 3 and 2. This fourth centre (labelled 'e') is 'as distant from the centre of the equant as the centre of the equant is from the centre of the World' (<i>tantum a centro aequantis, quantum centrum aequantis a centro distat</i>). It is itself 'the centre of the small circle, which the centre of the deferent describes, as will be seen' (<i>et ipsum est centrum parvi circuli, quem centrum deferentis, ut videbitur, describit</i>). The vertical line passes through the apogees of the eccentric deferent and of the equant, the centre of the World, the centre of the equant, and the centre of the 'small circle'. The centre of the deferent is also on this line, at the two points where the small circle crosses it, at the apogee or at the perigee (where it coincides with the centre of the equant): on the diagram it is at the apogee. The four centres (c, d, e, f) are thus aligned on the line of the apogee, from the centre of the World to the centre of the deferent, at equal intervals. The outermost orb (orb 4) and the innermost orb (orb 1), which have the same centres, 'are called the deferent orbs of the apogee of the equant, and they move with the motion of the eighth sphere on the axis of the zodiac' (<i>vocantur autem deferentes augem aequantis, et moventur ad motum octavae sphaerae super axe zodiaci</i>). Orbs 3 and 2, whose centres coincide, respectively, with the centre of the eccentric deferent of the epicycle and with the fourth centre (that is, as noted above, the centre of the concavity of the fourth orb, and centre of the small circle), are called 'the deferent orbs of the apogee of the eccentric; they move uniformly on the centre of the small circle westward with such speed that exactly in the time that the line of mean motion of the Sun makes one revolution, the orbs likewise complete one in the opposite direction' (<i>augem eccentrici deferentes vocantur, et moventur regulariter super centro parvi circuli contra successionem Signorum tali velocitate, ut praecise in tempore, quo linea medii motus Solis unam facit revolutionem, et orbes isti in partem oppositam similiter unam perficiant</i>). The fifth orb, the deferent orb of the epicycle, moves eastward uniformly about the centre of the equant with 'such speed that the centre of the epicycle revolves once in the same time that the line of mean longitude of the Sun completes one revolution' (<i>hanc tamen habet velocitatem, ut centrum epicycli in eo tempore semel revolvatur, in quo linea medii motus Solis unam complet revolutionem</i>). In other words, Mercury has the same mean motion as the Sun and Venus. Therefore, the fifth orb and the deferent orbs of the apogee of the eccentric move at the same speed, but in opposite directions. Line mcn, passing through the centre of the World (c), is the axis of the ecliptic (also the axis of the deferent orbs of the apogee of the equant). Line peq, passing through the centre of the small circle, is the axis of the deferent orbs of the apogee of the eccentric. Line ofr (r is barely legible), passing through the centre of the deferent (f), is the axis of the eccentric deferent orb of the epicycle. All these axes are parallel, and perpendicular to the line of the apogee. The spatial relations of the orbs of Mercury and their movements are more clearly shown in the three-dimensional diagram provided in Erasmus Oswald Schreckenfuchs' <i>Commentaria in novas theoricas planetarum Georgii Purbachii</i> (Basel: Henricus Petri, 1556), plate after p. 204. Translated quotations of Peuerbach's <i>Theoricae</i> are from Aiton (1987). Quotations from the commentary of Sylvester de Prierio are translated or paraphrased by Isabelle Pantin.</p>

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