Astronomical Images : Orbs, axes and poles of the motion of Venus

Erasmus Oswald Schreckenfuchs

Astronomical Images

This unique edition of Oswald Schreckenfuchs' massive commentary contained, for the first time in the Theoricae novae 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 bifolia. In some copies the bifolia 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 Venus. The three orbs of the planet are seen from above, in latitudinal section: the exterior and interior black 'deformed' orbs (the deferent orbs of the apogee of the eccentric, labelled 'deferens augem eccen[trici] exterior' and 'def[erens] augem eccen[trici] interior'), and the white eccentric orb sandwiched between them (labelled 'deferens epicyclum Veneris'), with a 'hole' where the epicycle (epicyclus Veneris) and the axis of its movement is visible. The main axis is that of the ecliptic (axis octavae sphaerae), which coincides with the axis of the deferent orbs of the apogee of the eccentric. Up to this point, this three-dimensional diagram of Venus is similar to that of the superior planets (see plate after p. 98), as the flat diagram of its orbs is similar to the flat diagram of theirs. But in other respects, it is quite different. Indeed, only a three-dimensional figure could illustrate the description by Peuerbach of the movements of Venus. This is probably why there is no diagram of the axes and poles of the movement of Venus in the first editions of the Theoricae novae. According to Peuerbach, the movement eastward of the eccentric of Venus (which is uniform in relation to the centre of the equant, as for the superior planets), '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, concerning which something will be said later [see Reinhold (1553), fol. 152v]' (sit autem motus huius deferentis in longitudinem super axe eius imaginario, cuius poli accedunt et recedunt a polis zodiaci in utranque partem proter motum alium in latitudinem, de quo post dicendum erit). In his 1542 commentary, Reinhold notes that the axis of the eccentric is called 'imaginary' by Peuerbach 'because it is not fixed, but mobile, and as if it swung on both sides [northward and southward]' (vocat autem imaginarium axem, quia non fixus est, sed mobilis, et quasi nutans in utranque partem). As a consequence, Reinhold adds, the apogee of the eccentric of Venus also swings to and fro (nutare ultro citroque), and the angle of intersection between the plane of the eccentric and the plane of the ecliptic (of which the plane of the eccentric of the Sun is a part) varies. 'The planes of the eccentrics of the Sun and of Venus even unite completely at certain moments' (imo plana eccentricorum Veneris et Solis interdum prorsus uniri). In his own commentary (fol. 182v), Schreckenfuchs asks his reader to imagine, in a material three-dimensional sphere (in sphaera materiali), the fixed plane of the ecliptic, transfixed by its perpendicular axis, also immobile, as its poles. Then the reader must conceive a kind of 'mobile equator passing through the first degrees of Aries and Libra, which could represent, for example, the eccentric deferent of the epicycle' (intelligatur aequator mobilis super capitibus Arietis et Librae, qui exempli gratia repraesentet deferentem epicycli). The plane of this imagined eccentric is also transfixed by a perpendicular axis, whose poles approach and recede from the first imagined poles (cuius poli ad polos prius imaginatos accedunt et recedunt). On account of this movement in latitude of its eccentric deferent, Venus much differs from the three superior planets, 'whose apogee does not decline sometimes southward, and sometimes northward from the ecliptic, and sometimes unites to it, but is always northward' (quorum aux non modo ad Meridiem, modo ad Septentrionem declinet ab ecliptica et modo uniatur cum eo, imo sit semper Septentrionalis). In the diagram, the swinging to and fro of the plane of the eccentric is only suggested, but its mobile axis is drawn (axis imaginarius et mobilis): it is slightly oblique in relation to the axis of the ecliptic. According to Peuerbach, the epicycle of Venus also has a movement in latitude (which is described in the second part of the treatise, De passionibus planetarum diversis), suggested in the diagram by the obliquity of the axis of the epicycle. Translated quotations of Peuerbach's Theoricae are from Aiton (1987). Quotations from the commentaries by Reinhold and Schreckenfuchs are translated or paraphrased by Isabelle Pantin.