[ 8« ] 



and thus it becomes the fubjedl of mathematical calculation, in 

 the fame manner as the degrees of heat. 



The ratio of thofe quantities which confift of parts, cannot 

 always be accurately afligned ; neverthelcfs, fince the quantities 

 are finite, they muft have fome finite, determina:te ratio to each 

 other. Thus the area of a circle to the circumfcribed fquare 

 cannot be accurately exhibited: in thefe cafes we can, in general, 

 proceed by continual approximations, and aflign limits within 

 Y>^hich the true ratio muft fubfift. 



If there be two things, one of which is greater or lefs than the 

 other, they are quantities of the fame fpecies : thus when a cannon 

 ball is faid to be greater than an orange, the abftrad magnitudes 

 of both are quantities of the fame fpecies. 



If two things be of the fame fpecies, and one of them' can be 

 reprefented by an exponent of a given kind, the other is in its 

 nature capable of being expreffed by an exponent of the fame 

 kind. Thus if the area of a fquare be reprefented by a given right 

 line, the area of the infcribed circle is capable of being reprefented 

 by another right line, though no mathematician has yet been able 

 to fhew what that line is, by any geometrical conftruflion. 



If the velocity of a ray of light incident on a piece of cryftal 

 be expreffed by a given number, there is a number which will 

 alfo exprefs its velocity within the cryftal. 



Vol. VII. L The 



