SEQUEL TO THE EPOCH OF HIPPAECHUS. 171 



order to apply this theory to the sun, moon, and planets, and of the 

 other calculations which are requisite, in order to deduce the conse- 

 quences of this theory, the work is a splendid and lasting monument 

 of diligence, skill, and judgment. Indeed, all the other astronomical 

 w r orks of the ancients hardly add any thing whatever to the informa- 

 tion we obtain from the Almagest ; and the knowledge which the 

 student possesses of the ancient astronomy must depend mainly upon 

 his acquaintance with Ptolemy. Among other merits, Ptolemy has 

 that of giving us a very copious account of the manner in which Hip- 

 parchus established the main points of his theories ; an account the 

 more agreeable, in consequence of the admiration and enthusiasm with 

 which this author everywhere speaks of the great master of the astio- 

 nomical school. 



In our present survey of the writings of Ptolemy, we are concerned 

 less with his exposition of what had been done before him, than with 

 his own original labors. In most of the branches of the subject, ho 

 gave additional exactness to what Hipparchus had done; but our 

 main business, at present, is with those parts of the Almagest which 

 contain new steps in the application of the Hipparchian hypothesis. 

 There are two such cases, both very remarkable, that of the moon's 

 Evcction, and that of the Planetary Motions. 



The law of the moon's anomaly, that is, of the leading and obvious 

 inequality of her motion, could be represented, as we have seen, either 

 by an eccentric or an epicycle ; and the amount of this inequality had 

 been collected by observations of eclipses. But though the hypothesis 

 of an epicycle, for instance, would bring the moon to her proper place, 

 so far as eclipses could show it, that is, at new and full moon, this 

 hypothesis did not rightly represent her motions at other points of her 

 course. This appeared, when Ptolemy set about measuring her dis- 

 tances from the sun at different times. "These," he 52 says, "some- 

 times agreed, and sometimes disagreed." But by further attention to 

 the facts, a rule was detected in these differences. " As my knoAvledge 

 became more complete and more connected, so as to show the order oi 

 this new inequality, I perceived that this difference w r as small, or noth- 

 ing, at new and full moon; and that at both the dichotomies (when 

 the moon is half illuminated) it was small, or nothing, if the moon was 

 at the apogee or perigee of the epicycle, and was greatest when she 

 was in the middle of the interval, and therefore when the first inequal- 



32 Synth, v. 2. 



