5 37, 38] Hipparchus 41 



matics,* which enabled processes of numerical calculation 

 to be applied to geometrical figures, whether in a plane or 

 on a sphere.,? -He made an extensive series of observations, 

 taken with all the accuracy that his instruments would 

 permit^.- He systematically and critically made use of old 

 observations for comparison with later ones so as to 

 discover astronomical changes too slow to be detected 

 within a single lifetime. Finally, he systematically employed 

 a particular geometrical scheme (that of eccentrics, and to 

 a less extent that of epicycles) for the representation of the 

 motions of the sun and moon. 



38. The merit of suggesting that the motions of the 

 heavenly bodies could be represented more simply by com- 

 binations of uniform circular motions than by the revolv- 

 ing spheres of Eudoxus and his school ( 26) is generally 

 attributed to the great Alexandrine mathematician Apol- 

 lonius of Perga, who lived in the latter half of the 3rd 

 century B.C., but there is no clear evidence that he worked 

 out a system in any detail. 



On account of the important part that this idea played 

 in astronomy for nearly 2,000 years, it may be worth 

 while to examine in some detail Hipparchus's theory of 

 the sun, the simplest and most successful application of 

 the idea. 



We have already seen (chapter i., 10) that, in addition 

 to the daily motion (from east to west) which it shares with 

 the rest of the celestial bodies, and of which we need here 

 take no further account, the sun has also an annual motion 

 on the celestial sphere in the reverse direction (from west 

 to east) in a path oblique to the equator, which was early 

 recognised as a great circle, called the ecliptic. It must 

 be remembered further that the celestial sphere, on which 

 the sun appears to lie, is a mere geometrical fiction 

 introduced for convenience ; all that direct observation 

 gives is the change in the sun's direction, and therefore 

 the sun may consistently be supposed to move in such a 

 way as to vary its distance from the earth in any arbitrary 

 manner, provided only that the alterations in the apparent 

 size of the sun, caused by the variations in its distance, 

 agree with those observed, or that at any rate the differences 



* Trigonometry. 



