INDUCTIVE EPOCH OF HIPPARCHUS. 195 



somehow connected, that is, in order that we may 

 have any theory of the motions ; and no assumption 

 more simple than the one now mentioned can be 

 selected. The merit of the theory is this; that 

 obtaining the amount of the eccentricity, the place 

 of the apogee, and, it may be, other elements, from 

 a fere observations, it deduces from these, results 

 agreeing with all observations, however numerous 

 and distant. To express an inequality by means of 

 an epicycle, implies, not only that there is an in- 

 equality, but further, that the inequality is at its 

 greatest value at a certain known place, diminishes 

 in proceeding from that place by a known law, 

 continues its diminution for a known portion of the 

 revolution of the luminary, then increases again ; 

 and so on : that is, the introduction of the epi- 

 cycle represents the inequality of motion, as com- 

 pletely as it can be represented with respect to 

 its quantity. 



We may further illustrate this, by remarking 

 that such a Resolution of the unequal motions of 

 the heavenly bodies into equable circular motions, 

 is, in fact, equivalent to the mosf recent and im- 

 proved processes by which modern astronomers 

 deal with such motions. Their universal method is 

 to resolve all unequal motions into a series of 

 terms, or expressions of partial motions ; and these 

 terms involve sines and cosines, that is, certain 

 technical modes of measuring circular motion, the 

 circular motion having some constant relation to 



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