Astronomical Images : Orbs, axes and poles of Mercury's motion

Erasmus Oswald Schreckenfuchs

Astronomical Images

<p style='text-align: justify;'>This unique edition of Oswald Schreckenfuchs' massive commentary contained, for the first time in the <i>Theoricae novae</i> printed tradition, a series of three-dimensional diagrams intended to complement the ordinary diagrams of the orbs, circles, axes and poles of the planets and the eighth sphere. These diagrams are printed on one side of two <i>bifolia</i>. In some copies the <i>bifolia</i> form one gathering b (four folios), bound after the preface; in others the figures have been cut, and each is inserted in the appropriate place in the treatise. They are not lettered and have no legend, though some of their elements are labelled, as they must be used in association with the diagrams in the text. This diagram corresponds to the figure of the orbs, axes and poles of the motion of Mercury. The five orbs of the planet are seen from above, in latitudinal section. The exterior and interior black 'deformed' orbs are the 'deferent orbs of the apogee of the equant', which move with the motion of the eighth sphere on the axis of the zodiac. They are labelled '<i>exterior deferens augem aequantis</i>' and '<i>interior deferens augem aequantis</i>'. The shaded 'deformed' orbs, between which the white orb is placed, are the 'deferent orbs of the apogee of the eccentric', which, according to Peuerbach, move uniformly westward on the centre of the small circle described by the centre of the eccentric deferent, '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>tali velocitate, ut praecise in tempore, quo linea medii motus Solis unam facit revolutionem, et orbes isti in partem oppositam similiter unam perficiant</i>). They are labelled '<i>exterior defer[ens] augem excen[trici]</i>' and '<i>interior defer[ens] augem excen[trici]</i>'. The white eccentric orb between them is labelled '<i>deferens epicyclum Mercurii</i>'. There is a 'hole' in it where the epicycle and the axis of its movement is visible. The poles of the main axis (the axis of the ecliptic) are visible. The one at the bottom is labelled '<i>polus 8 sphaerae</i>'. The part of this axis that is visible inside the sphere is labelled '<i>axis defer[entiu]m au[gem] aequantis</i>', as the axis of the 'deferent orbs of the apogee of the equant' coincides with the axis of the ecliptic. It is the axis more towards the right. The next axis behind it, whose upper part is visible, is labelled '<i>[axis deferentium] au[gem] excen[trici]</i>' (axis of the deferent orbs of the apogee of the eccentric). The last axis behind, whose upper part is also visible, is the axis of the eccentric deferent, labelled '<i>axis defer[entis]</i>'. Above these poles, a small circle probably suggests the rotation of the exterior deferent of the apogee of the eccentric; the pole that emerges in the middle of it must be the axis of the deferent orbs of the apogee of the eccentric, although it is not drawn quite in line with it. Just beneath this small circle, another small circle probably suggests the rotation of the deferent orb of the epicycle. Further beneath, a line (that is a third small circle viewed in profile) is crossed by the three axes. It is probably related to the movement of the axis of the deferent around the axis of the deferent orbs of the apogee of the eccentric, as the centre of the eccentric deferent moves around the 'small circle' (see below), except that, in principle, the third axis (that of the ecliptic and of the deferent orbs of the apogee of the equant) ought to remain exterior to this movement. The middle of the diagram is barely legible. A transversal line is labelled '<i>ostensor augis exc[entrici]</i>', evidently meant to indicate the direction of the apogee of the eccentric. This <i>ostensor</i> is linked to a kind of mechanism confusedly drawn inside the innermost orb. There we read (with difficulty) '<i>axis mob[ilis] exce[ntrici]</i>'. That must be understood in relation to the following passage of Peuerbach: 'Now the motion of the orb of this planet which carries the epicycle is made about an imaginary axis whose extremities, as appeared in Venus, on account of the other motion that is in latitude, similarly approaches the poles of the zodiac and recede from them. However, this axis as a whole is mobile following the motion of the centre of the deferent in the small circle' (<i>huius autem orbis epicyclum deferentis motus sit super axe imaginario, cuius extremitates (sicut apparuit in Venere) propter motum alium quem habet in latitudinem, similiter accedunt ad polos zodiaci, et ab eis recedunt. Axis autem iste secundum se totum mobilis est secundum motum centri deferentis in parvo circulo</i>). In his commentary (Wittenberg, 1542), Erasmus Reinhold explains that the axis of the deferent of the epicycle of Mercury is called 'imaginary' because it is mobile, and that its motion is not really similar to the motion in latitude of Venus, for it is caused by the rotation of the centre of the deferent of the epicycle of Mercury on the small circle. Thus, the axis of the eccentric deferent of the epicycle 'sometimes will be nearer to the axis of the ecliptic than the axis of the deferent orbs of the apogee of the eccentric, and sometimes it will be more distant, depending on the position of the centre of the deferent of the epicycle' (<i>axis deferentis epicyclum interdum propior erit axi zodiaci, quam axis deferentium apogion eccentrici, interdum vero distantior, videlicet pro situ centri deferentis epicyclum</i>) ' given that the axis of the deferent orbs of the apogee of the eccentric and the axis of the eccentric deferent of the epicycle always remain parallel. Thus, what is drawn in the middle of the sphere is related to the small circle described by the centre of the eccentric deferent of the epicycle. Translated quotations of Peuerbach's <i>Theoricae</i> are from Aiton (1987). Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>


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