Astronomical Images : The third motion of the eighth sphere

Peter Apian

Astronomical Images

This Venetian edition of Peuerbach's Theoricae novae was copied from Apian's 1528 edition, printed in Ingolstadt. Subsequently, the work went through several further editions. Apian's edition added new woodcuts as well as notations to some of those from earlier editions. Some errors in the woodcuts in the 1528 edition were repeated in this Venetian edition of 1537. At the beginning of the last section of his treatise, 'On the motion of the eighth sphere' (De motu octavae sphaerae), Peuerbach expounds the theory applied in the Alphonsine Tables. 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 (diurnus motus). The second movement comes from the ninth sphere, called the 'second movable' (secundum mobile), 'which always moves uniformly on the poles of the zodiac eastward, against the first motion' (qui semper est secundum successionem Signorum contra motum primum super polis zodiaci regularis). This movement is very slow: 'every two hundred years it advances nearly one degree and twenty-eight minutes' (in quibuslibet ducentis annis per unum Gradum et viginti octo Minuta fere progrediatur), 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' (hic motus augium et stellarum fixarum in tabulis appellatur). The third movement is the proper motion of the eighth sphere, 'called the motion of trepidation or approach and recession of the eighth sphere' (motus trepidationis vocatur, sive accessus et recessus octavae sphaerae): 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 (in capitibus Cancri et Capricorni nonae). 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 (capita vero Cancri et Capricorni octavae sphaerae quasi figuras conoidales habentes pro basi lineas curvas utrinque a capitibus Cancri et Capricorni nonae peragere). In clearer terms, each of these points of the eighth sphere describes (approximately) two vertically opposite spherical cones, a kind of elongated infinity symbol, whose middle point is the corresponding point of the ninth sphere. This third motion is shown in the above diagram, which is an improved version of a figure in the original (c. 1474) edition of the Theoricae novae, most probably copied from a figure in the edition of the Theoricae novae by Oronce Fine (Paris, 1525). However, the Fine diagram is labelled and accompanied by a legend, whereas the Apian diagram is not. We see the ecliptic of the ninth sphere, or ecliptic 9 (nona) between the ecliptic of the eighth sphere, or ecliptic 8 (octa[va]), represented in the two positions where it is most separated from the said ecliptic of the ninth sphere. The points on the ecliptic of the ninth sphere marked with the symbols of Aries and Libra are the centres of the small circles described by the corresponding points (the first degrees of Aries and Libra) of the eighth sphere. The straight line that joins the first degrees of Aries and Libra of the ninth sphere 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' (the ecliptic of the ninth sphere that is in the same plane as the ecliptic of the tenth sphere), and the first degrees of Aries and Libra of the ninth sphere. The middle point is the pole of ecliptic 9. We see that the first degrees of Aries and Libra of the eighth sphere are also on this circle in the two positions of the ecliptic of the eighth sphere represented on the diagram. The particular figure (similar to an elongated infinity symbol) described by the first degrees of Cancer and Capricorn of the eighth sphere is also drawn. The diagram also suggests a movement of approach and recession of the pole of ecliptic 8 either side of the pole of ecliptic 9: according to Peuerbach, the poles of the ecliptic of the eighth sphere 'sometimes approach the poles of the ecliptic of the ninth, sometimes are under them, and sometimes recede from them'. For an improved version of the same diagram, and more precise explanations, see Reinhold (1553), fol. 164v. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).