On the Fundamental Principles of Mathematics. 341 





 of the symbol 7: 







ed by primary considerations. 



[In the case now described the symbol or form jj presented 



itself, because the terms were zero in comparison with a standard 

 unlimited in at least one respect. In the instance of a fraction 

 such as that represented in the equation, 



fx ~ Qi{x-a) n 



which, when x—a, becomes, 



Fx PxO 

 fx ~ QxO = ; 







the form or symbol q appears, because the particular value of x 



reduces each of the ^multipliers, (:r-a) m and (x-a) n , to zero. 

 Hence no product can, in effect, result, whatever may be the 

 value of the multiplicand; i.e., (14.), nothing will be found in 

 the place of the numerator as well as that of the denominator : 



or the value of the fraction, in its form of ^ , becomes indeter- 

 minate, not as in the former case, because of the character of the 

 standard of reference, but because of the actual disappearance of 

 every thing from both terms of the fraction, which under other 

 circumstances, could render them definite.] 



Another Application of Preceding Principles, 



(25.) [The relations of things being, as already maintained in 

 (4.), constituted relations; — and they also being constituted in 

 some respects alike, as appears from the comparisons between 

 those of space and time in (22.) — we may even reverentially pro- 

 ceed a step farther, and conclude, that, as any finite (or even in 

 some respects boundless) space is worthless, or to be regarded as 

 good for nothing j in comparison with the absolute infinite of 

 space; and as, again, any finite portion of duration is also a rela- 

 tive zero, in comparison with the absolute infinite of duration ; 

 so, also, must the highest created intelligence and lowest among 

 men be alike tvorthless or regarded as nothing in comparison with 

 the alone infinite one : or man, placed as it would seem lowest 

 in scale of such intelligences, must be represented, in comparison, 

 as being as it were " less than nothing.' 7 This truth has impor- 



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J 



be 



