27 



47. Every quantity may be considered positively, as an 

 identity determined by. its contents: every quantity may be con- 

 sidered relatively, or in comparison of its contents with those of 

 another. The two quantities, though different, agree in the cir- 

 cumstance of an infinite divisibility, which is the positive property 

 of each ; but they differ relatively in the proportion of their parts. 



43. Infinite divisibility is a property common to all quanti- 

 ties; but, for purposes of convenience, it is necessary that we 

 should make a suppositions ultimate quantity of the lowest per- 

 ceptible minuteness : thus in numbers we have an unit, in sub- 

 stances a particle. Now the largest bulks are made up of those 

 particles, and by them the largest bulks possess the property 

 which they themselves possess. If the particle be an ultimate 

 quantity, the divisibility of the bulk, it being reducible into par- 

 ticles, and made up of the repetitions of finite quantities, must be 

 finite; but if the particle be divisible in infinitum^ then the bulk, 

 being composed of the repetitions of infinite quantities, must itself 

 be infinitely divisible, the whole possessing the quality of the 

 parts, and the parts of the vyhole; the whole being more than the 

 parts, because the whole contains more of the infinitely divisible 

 particjes. 



49. It is possible to pursue these thoughts much further, and 

 to start many other difficulties: but to do so would only be to ex- 

 hibit some subtile reasoning, by which they must at last be recon- 

 ciled, and the argument would terminate with something like the 

 following conclusion, viz. that every quantity is made finite by 

 synthesis, and is infinite in analysis; that divisibility is a property 

 common to all quantities, and therefore belongs to the least as 

 well as to the largest; that the difference between quantities con- 

 sists in the various repetitions of infinitely divisible minute quan- 

 tities, whjch compose the respective masses. 



50. The closest definition of the facts will not permit our con- 

 sidering a given quantity as infinite. But when we use this term, 

 \ve speak of its contents: thus, if the body of a man or a horse 

 were the given quantity, when the analysis had proceeded so far 

 as to have divided him into four or eight parts, we should scarcely 

 say that, pursuing the analysis, upon cutting one of the legs in two 

 we had made another division of the man, the quantity composing 

 the man having ceased; nor should we imagine ourselves making 

 a further division of the leg when we were about the fourth section 

 of a toe-nail. The quantity which belongs to an identity is divisi- 

 ble, this being a common property: that quantity reduced to halves, 

 the former identity, so far as depends upon quantity, has ceased; 

 then the parts come to be divided and lose their identity, then 

 other parts; a common property of all things being divisibility. 

 Thus, it is not an infinite divisibility of things identified by quan- 

 tity; but the term infinite is applicable only tq their contents. 

 In this account I am scarcely aware of having digressed at all 

 from the enumeration, of facts : or if I have, it is only in making u 



