330 



On the Fundamental Principles of Mathematics. 



Thus —2 indicates the subtraction, or at least the negative re- 

 lationship, of neither more nor less than -f 2 (the negation of 

 neither 3 nor 1 would answer the purpose) and -Q, indicates 

 the subtraction, or at least ihe negative relationship of as much 

 as 4-Q,, and no more. Tn neither case can one of these quantities 

 produce in a like combination a greater or a less effect than its 

 own negative would produce ; but that negative in such a com- 

 bination (because it is negative) will be destructive to precisely 

 the same extent to which the positive quantity is constructive. 

 Hence, a negative quantity ( - Q,) cannot be regarded < 



fact 



effect 



*r 



cies, in one particular respect ; viz. that very respect, in which 

 the other quantity ( +0,) is positive. For the zero is nothing- in that 



ifi 



CI) is precisely 



as great indeed as + &, but of an opposite character in the very 

 respect in which -f d is positive; insomuch that -f Q, would be 

 precisely destroyed by ~Q; i. e., annihilated or reduced to the 

 zero of the species. Or (as viewed in the opposite direction) 4- CI 

 would be precisely adequate to the destruction of - &, reducing 

 it to the zero ; and a second similar introduction of 4-Ci would, 

 in place of this last result of the zero, give +& itself: or, it ap- 



that — Q,. in the vpth rpsnprt in whirh 4 "* 



pears 



in effect 



positive sense, is above it. 



a 



the 



>f 



Similar principles will be applicable to the results of like com- 

 binations of other quantities with the respective quantities; +Q, 

 Q, and the zero ; the respective results being represented by -\-JQi 



)f the same species with +fGL 



■fa 



In the determination of the position of a point in space, reference, 

 as is well known, is made to three coordinate axes, all meeting 



A M ft ■ M» A 



at one point 



the origin. 



If from 



Ficr. 1. 



P 



this origin O, we measure out- 

 ward upon any of the three axes, 

 we naturally mark the measured 



th as positive ; since it m- 



ses as we proceed in that di- 

 rection in space. If we measure 

 from P toward O or P', any dis- 

 tance less than PO, the quantity 

 thus measured will thereby be 

 taken from PO or will have an 

 effect, the negative of the previ- 

 ous increase. If we thus meas- 

 ure from P a distance equal to PO ; this distance will extend to 

 the origin ; and PO will be subtracted from itself, leaving no re- 



or the zero of 



mainder 



i. e. 



point 



