Astronomical Images : The third motion of the eighth sphere according to the Alphonsine Tables

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 Wittenberg edition of Peuerbach (1535), itself copied, with some changes, from the Apian edition of Peuerbach (Ingolstadt, 1528; see fol. 35r in our 1537 edition). The changes in the diagram were inspired by a figure in the edition by Oronce Fine of the <i>Theoricae planetarum</i> (Paris, 1525). In particular, the Wittenberg editors adopted the lettering of the Fine diagram and plagiarised its legend. At the beginning of the last section of his treatise, 'On the motion of the eighth sphere' (<i>De motu octavae sphaerae</i>), Peuerbach expounds the theory applied in the <i>Alphonsine Tables</i>. He explains that the eighth sphere (that of the fixed stars) has three movements: its own proper movement and two movements transmitted by two superimposed invisible spheres ' the ninth sphere and, above it, the tenth sphere, also called first movable sphere. This threefold motion is itself transmitted to the orbs carrying the apogees of the planets. The first movement, transmitted by the first movable sphere, is the revolution around the poles of the World once in a natural day, westward (<i>diurnus motus</i>). The second movement comes from the ninth sphere, called the 'second movable' (<i>secundum mobile</i>), 'which always moves uniformly on the poles of the zodiac eastward, against the first motion' (<i>qui semper est secundum successionem Signorum contra motum primum super polis zodiaci regularis</i>). This movement is very slow: 'every two hundred years it advances nearly one degree and twenty-eight minutes' (<i>in quibuslibet ducentis annis per unum Gradum et viginti octo Minuta fere progrediatur</i>), which amounts to one complete revolution in 49,000 years. 'In the tables, it is called the [mean] motion of the apogees and the fixed stars' (<i>hic motus augium et stellarum fixarum in tabulis appellatur</i>). The third movement is shown in the diagram. It is the proper motion of the eighth sphere, 'called the motion of trepidation or approach and recession of the eighth sphere' (<i>motus trepidationis vocatur, sive accessus et recessus octavae sphaerae</i>): the first degrees of Aries and Libra of this sphere describe two equal small circles around the corresponding points of the ninth sphere. The revolution of these circles is completed in 7000 years. Thus, the ecliptics of the two spheres are two different great circles that intersect at the first degrees of Cancer and Capricorn of the ninth sphere (<i>in capitibus Cancri et Capricorni nonae</i>). When one of the equinoctial points of the eighth sphere is in the southern half of its small circle, the other point is in the northern half. The consequence is that the first degrees of Aries and Libra of the eighth sphere are not always 90 degrees distant from the intersection between both ecliptics. These first degrees of Aries and Libra are the only points of the eighth sphere that have a circular motion. In particular, the first degrees of Cancer and Capricorn 'complete as it were conical figures that have for their bases curved lines on both sides' from the corresponding points of the ninth sphere (<i>capita vero Cancri et Capricorni octavae sphaerae quasi figuras conoidales habentes pro basi lineas curvas utrinque a capitibus Cancri et Capricorni nonae peragere</i>). In clearer terms, each of these points of the eighth sphere describes (approximately) two vertically opposite spherical cones, a kind of elongated infinity sign, whose middle point is the corresponding point of the ninth sphere. On the diagram, circle ABCD is the ecliptic of the ninth sphere, or ecliptic 9 (<i>nona</i>), also called fixed ecliptic (<i>ecliptica fixa</i>). A is the beginning of Aries, B the beginning of Cancer, C the beginning of Libra and D the beginning of Capricorn on this ecliptic. E is its pole. The two other great circles represent the ecliptic of the eighth sphere, or ecliptic 8 (<i>octa[va]</i>), also called the mobile ecliptic (<i>ecliptica mobilis</i>), in the two positions where it is most separated from the fixed ecliptic. Points A and C (the first degrees of Aries and Libra of the fixed ecliptic) are the centres of the small circles, FGHI (I resembles an L) and KLMN, described by the corresponding points on the mobile ecliptic. We must understand that, as specified in the legends of the Fine edition and repeated in the Wittenberg edition, when the beginning of Aries in the eighth sphere is at F, the beginning of Libra is at K, the beginning of Cancer at B, the beginning of Capricorn at D, and the pole of the ecliptic of the eighth sphere at S. When the beginning of Aries in the eighth sphere is at G, then the two ecliptics are joined; the beginning of Libra is at L, the beginning of Cancer at O, and the beginning of Capricorn at P. The pole of ecliptic 8, then joins the pole of ecliptic 9 at E (the two legends say, '<i>et polus S cum polo E</i>'). When the beginning of Aries in the eighth sphere 'goes down' in H (<i>descendente capite Arietis in H</i>), the beginning of Libra is at M, the beginning of Cancer at B, the beginning of Capricorn at D, and the pole of the ecliptic of the eighth sphere at T. When the beginning of Aries in the eighth sphere is at I, then the two ecliptics are joined again (their poles being at E); the beginning of Libra is at N, the beginning of Cancer at Q, and the beginning of Capricorn at K. Thus, when the eighth and ninth ecliptics are most separated, the first degrees of Cancer and Capricorn of both ecliptics are joined, and when these ecliptics are joined, the first degrees of Cancer and Capricorn of ecliptic 8 are at their maximal distance from the corresponding points of ecliptic 9, this distance being equal to the radius of the small circle (<i>nimirum secundum semidiametri parvi circuli distantiam</i>, according to the Wittenberg editors). The arcs of the approach and recession of the first degrees of Cancer and Capricorn are OBQ and PDR (<i>arcus accessus et recessus capi[tis] Cancri OBQ Capricorni PDR</i>). The arc of the approach and recession of the pole of ecliptic 8 is SET. Reinhold specifies in his commentary that the right line AEC represents a great circle, the colure of the equinoxes of the ninth sphere, passing through the poles of the equator, the poles of the 'fixed ecliptic', and the equinoctial points of the same ecliptic. It intersects ecliptic 9 at right angles and both circles divide the 'small circles' into four equal quarters. The four points delimiting these quarters can be called the northern (F), southern (H), eastern (G) and western (I) points, 'as the author says afterwards that the mean motion of the eighth sphere is measured from the northern point following the order of the Signs, that is toward the eastern point' (<i>quemadmodum postea dicit autor medium motum 8 sphaerae numerari a puncto Septentrionali in consequential, id est, versus punctum Orientale</i>). Reinhold adds that the first degrees of Cancer and Capricorn of the eighth sphere describe 'according to the description of Peuerbach, conical figures that are somehow distorted' (<i>schemata [in Greek:] konoeidè juxta Purbachii descriptionem, quae utcunque deformata sunt</i>). But in the diagram this figure, similar to an elongated infinity symbol, is no longer visible as it was in the Apian diagram (see Apian (1537), fol. 35r). As for the poles of ecliptic 8, they 'go up and down in the same plane, as in line SET that corresponds to an arc of a great circle' (<i>in eodem plano ascendant et descendunt, ut in linea SET, quae arcum magni circuli refert</i>). This great circle is the colure of the equinoxes: Peuerbach says that the movement of approach and recession of the poles of the mobile ecliptic 'are always along the great circle passing through the poles of the zodiac of the ninth sphere and the centres of the small circles'. Translated quotations of Peuerbach's <i>Theoricae</i> are from Aiton (1987). Quotations from the Paris 1525 edition and the Wittenberg 1535 edition of Peuerbach, and from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>