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Astronomical Images : The mean motion and the equation of the eighth sphere

Erasmus Reinhold

Astronomical Images

<p style='text-align: justify;'>This Parisian edition was copied from the first edition of the commentary of Peuerbach by Erasmus Reinhold, printed in Wittenberg by Hans Lufft in 1542. Subsequently, in 1556, Charles Perier published a new edition, copied from the revised edition printed by Lufft in 1553, which contained additions to the theory of the Sun (<i>[Theoricae] auctae novis scholiis in theoria Solis ab ipso autore</i>). This diagram is a reuse or a close copy of a woodcut in the 1535 Wittenberg edition of Peuerbach, itself inspired by a figure in the Fine edition of Peuerbach (Paris, 1525), rather than by the corresponding diagram in the Apian edition (Ingolstadt, 1528; see fol. 37r in our 1537 edition). The lettering is the same as in the Fine diagram. After describing the proper movement of the eighth sphere, Peuerbach explains how it is measured: 'the mean motion of approach and recession of the eighth sphere is the arc of the small circle reckoned from the uppermost point of the quadrant eastward up to the beginning of Aries of the eighth sphere' (<i>medius motus accessus et recessus octavae sphaerae est arcus circuli parvi a puncto supremo quartae secundum successionem Signorum usque ad caput Arietis octavae sphaerae computatus</i>). As indicated in the legend, ABI represents the ecliptic of the Prime Mover (<i>ecliptica primi mobilis ABI</i>). We know that the ecliptics of the ninth and tenth spheres are in the same plane and can be represented by the same circle. Both ecliptics can be called the 'fixed ecliptic'. A is the beginning of Aries of the Prime Mover (<i>principium Arietis eiusdem A</i>) and B the beginning of Aries of the ninth and the centre of the small circle on which the beginning of Aries of the eighth sphere rotates (<i>initium Arietis nonae, id est centrum circelli B</i>). The order of the Signs (the direction eastward) is ABI (<i>series Signorum ABI</i>). The small circle described by the first degree of Aries of the eighth sphere is DKEI, D being the 'Boreal point' (<i>circellus, cuius circuncurrentem lineam caput Arietis octavae describit DKEI, estque D punctum circelli Boreale</i>). The pole of the fixed ecliptic is C (<i>polus zodiaci fixi C</i>). Thus AB represents the proper motion of the ninth sphere (<i>motus igitur nonae sphaerae arcus AB</i>), which is called the 'motion of the apogees and of the fixed stars' (<i>motus augium et stellarum fixarum</i>) in the astronomical tables. Three arcs of circle are drawn from C. The middle one passes through B, the first degree of Aries of the ninth sphere, and through D and E on the small circle. The other arcs from C, CLNG and CFHM, pass through other points of the fixed ecliptic and of the small circle. The mean motion of the eighth sphere is measured eastward from D. 'If we suppose that the first degree of Aries of the eighth sphere is at F, the mean motion of approach will be arc DF' (<i>iam si ponamus caput Arietis octavae in F, erit medius motus accessus arcus DF</i>). According to Peuerbach, 'the equation of the eighth sphere is the arc of the ecliptic of the ninth sphere intercepted between the centre of the small circle and the great circle from the poles of the ecliptic of the ninth passing through the beginning of Aries of the eighth' (<i>aequatio autem octavae sphaerae est arcus eclipticae nonae sphaerae centrum parvi circuli et circulum magnum a polis eclipticae nonae per caput Arietis octavae transeuntem interiacens</i>). When the first degree of Aries is at F, the equation is BH. Some rules are added by Peuerbach: the equation is null when the mean motion of approach and recession is 0 degrees or 180 degrees; it is maximal when the mean motion is 90 degrees or 270 degrees. When the mean motion is less than 180 degrees, the equation is added to it; when it is more than 180 degrees, it is subtracted. Reinhold notes that when the equation is BH, it must be added to AB, the motion of the ninth sphere (<i>aequatio vero arcus BH hic addenda super motum nonae sphaerae etc.</i>). 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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