Si] 



The Almagest 



As in the case of the moon, he used as deferent an 

 eccentric circle (centre c), but instead of making the 

 centre j of the epicycle move uniformly in the deferent, he 

 introduced a new point called an equant (E'), situated at 

 the same distance from the centre of the deferent as the 

 earth but on the opposite side, and regulated the motion of 

 j by the condition that the apparent motion as seen from the 

 equant should be uniform; in other words, the angle A E' J 

 was made to increase uniformly. In the case of Mercury 

 (the motions of which have been found troublesome by 

 astronomers of all periods), 

 the relation of the equant to 

 the centre of the epicycle was 

 different, and the latter was 

 made to move in a small 

 circle. The deviations of the 

 planets from the ecliptic 

 (chapter i., 13, 14) were 

 accounted for by tilting up 

 the planes of the several 

 deferents and epicycles so 

 that they were inclined to the 

 ecliptic at various small angles. 



By means of a system of this 

 kind, worked out with great 



care, and evidently at the cost of enormous labour, Ptolemy 

 was able to represent with very fair exactitude the motions 

 of the planets, as given by the observations in his possession. 



It has been pointed out by modern critics, as well as by 

 some mediaeval writers, that the use of the equant (which 

 played also a small part in Ptolemy's lunar theory) was a 

 violation of the principle of employing only uniform circular 

 motions, on which the systems of Hipparchus and Ptolemy 

 were supposed to be based, and that Ptolemy himself 

 appeared unconscious of his inconsistency. It may, how- 

 ever, fairly be doubted whether Hipparchus or Ptolemy 

 ever had an abstract belief in the exclusive virtue of such 

 motions, except as a convenient and easily intelligible 

 way of representing certain more complicated motions, 

 and it is difficult to conceive that Hipparchus would have 

 scrupled any more than his great follower, in using an 



FIG. 35. 1 hi: equant. 



