Close — Mipparchus and the Precession of the Equinoxes. 455 



Similarly, either the title of Hipparchus' tractate, or his language 

 therein respecting the stars, is to he taken in a non-literal sense. 



"We shall now consider Ptolemy's treatment of the title of the 

 tractate, which, as we have said, is equivalent to " Concerning the retro- 

 gradation of the tropical and equinoctial jjoints.^'' 



Be it always rememhered that Ptolemy had the tractate hefore 

 him, which we unfortunately have not ; and he would douhtless know 

 whether the title of it, or the expressions in the text respecting the 

 stars, were to be taken literally. But if Ptolemy knew that that title 

 was intended hy Hipparchus to be taken literally, he would not treat 

 it as he does in the following instances. In chap. 2 of Book vn., 

 not far from the beginning, Ptolemy mentions, from himseli, that the 

 sphere of the fixed stars has its own proper motion according to the 

 succession of the signs, that is progressively. He then proceeds 

 immediately to quote without comment the title of Hipparchus' 

 tractate, which implies the retrogression of the equinoctial points. 

 Again, in chap. 3, Ptolemy quotes the title of Hipparchus' tractate on 

 the precession, without comment. He then speaks himself, and makes 

 Hipparchus speak, of the progression of the stars. ISTow if Ptolemy 

 knew that Hipparchus intended the title to be taken literally, all this 

 would be like a disrespectful slighting of the words of his revered 

 master. It would be a passing-by of Hipparchus' expressions without 

 any notice, as though they were not worthy of correction. A similar 

 remark may be made respecting the passage already alluded to near the 

 end of chap. 2. Ptolemy there quotes another tractate of Hipparchus, 

 ^^ Concerning the Length of the Year,''^ in which Hipparchus writes thus : — 

 " Eor if, for this cause, the solstices and equinoxes might be moved 

 backwards, not less than xo-oth part of a degree per annum," &c. 

 Then Ptolemy immediately after, without comment, speaks of Spica 

 Virginis and the brightest stars of the zodiac as having progressed, by 

 that amount, according to the succession of the signs. 



We might confidently conclude, even from all this alone, that 

 Ptolemy did not take literally the title of the tractate, which implies the 

 retrogi'adation of the equinoctial points, nor the expression, just quoted 

 from the text, in which Hipparchus speaks of the equinoctial points as 

 being moved backwards ; any more than we should take literally the 

 words of a modern astronomer when he speaks of the rising of the Sun. 

 There is no arg-ument corresponding to this which can be advanced on 

 the other side. 



K"ow we turn back to chap. 1 of this Book vn. of the Almagest ; 

 and we there find Ptolemy's own direct statement that Hipparchus 



