ISO On the Fundamental Principles of Mathematics. 



inherent properties of the things themselves; i. e., those which 

 render the things to which they belong what they are. 



For while the form, size, &c, of a body can in many cases 

 be accurately ascertained, and the supposable mathematical form 

 which that of the body may closely resemble, may have perfectly 

 definite and well ascertained properties, we, as yet, can know very 

 little of the atoms which compose that body, and cannot even 

 assert that, in the strict sense of the word, it is composed of atoms 



at all. 



It cannot then be a legitimate objection to the conclusions of 



mathematics, that there are no such things, as those to which 



they refer ; since those conclusions have not to do with things as 



such, but with their relations, and as stated at the outset, (1.) it 



is sufficient that even these be supposable, constituted as things 



now are 



The Relations of Things are Matters of Constitution and Ar- 



rangement. 



(4.) The relations of things already designated are themselves 

 not mere figments of the human mind, but — as all experience 

 teaches us — they are constituted relations : i. e., in so far as we 

 have to do with them, their connexion with things actual is a 

 matter of arrangement dependent upon the constitution of the 

 things, or else the things themselves are in some measure consti- 

 tuted in subordination to those relations: or both. 



Thus, one part of space is not diverse from another, nor does 

 one day of the week of course succeed another, because we may 

 choose to think so, but because the Creator has formed (or con- 

 formed) them so. For "of" Him not merely are all things, but 

 "by" Him they also consist: or, in other words, He has not 

 merely made those things with which we are familiarly conver- 

 sant, what they are, but also, in certain respects, as they are. Any 

 similarity in the relations of things must therefore also be a mat- 

 ter of constitution or arrangement ; and we may safely make use 

 of it in the illustration of one class of relations, by a comparison 

 with another. 



Of Quantity and its Distinctions and Ratio. 



(5.) Quantity is the general term employed to designate all 

 those relations of things which are the subjects of investigation 

 in mathematics. In so far as it is thus employed, it denotes what- 

 soever admits of the distinction of greater and less. 



(6.) Two quantities are of the same species, if each, in itself 

 exceeds its less, in the selfsame respect in which the other, in it' 

 self, exceeds its less; i. e., the terms greater and less must be ap- 

 plicable, in the case of each, in the self same sense. They 

 must, moreover, be thus applicable to the quantities themselves, 

 and not merely to their boundaries or limits. 



