194 THE GREEK ASTRONOMY. 



for another reason, much more important to the 

 purpose of this work; namely, that we may see how 

 theories may be highly estimable, though they con- 

 tain false representations of the real state of things, 

 and may be extremely useful, though they involve 

 unnecessary complexity. In the advance of know- 

 ledge, the value of the true part of a theory may 

 much outweigh the accompanying errour, and the 

 use of a rule may be little impaired by its want 

 of simplicity. The first steps of our progress do not 

 lose their importance because they are not the last; 

 and the outset of the journey may require no less 

 vigour and activity than its close. 



That which is true in the Hipparchian theory, 

 and which no succeeding discoveries have deprived 

 of its value, is the Resolution of the apparent 

 motions of the heavenly bodies into an assemblage 

 of circular motions. The test of the truth and rea- 

 lity of this Resolution is, that it leads to the con- 

 struction of theoretical Tables of the motions of the 

 luminaries, by which their places are given at any 

 time, agreeing nearly with their places as actually 

 observed. The assumption that these circular mo- 

 tions, thus introduced, are all exactly uniform, is the 

 fundamental principle of the whole process. Thi& 

 assumption is, it may.be said, false; and we have 

 seen how fantastic some of the arguments were, 

 which were originally urged in its favour. But 

 some assumption is necessary, in order that the 

 motions, at different points of a revolution, may be 



