236 Car not on the Theory of 



the difference between RS and MP, is what we call an in- 

 finitely fmall quantity. 



20. On the other hand, we call every quantity Infinitely 

 great, or (imply Infinite, which is equal to unity divided by 

 an infinitely fmall quantity : confequently the quantity 



IT? or "Fv — Wp iS ' n ^ mte J or infinitely great. 



But, fince MP is the limit, or ultimate value, of PS, it 

 is evident that o is the ultimate value of RZ, or RS — MP, 



and that ~ is the ultimate value of — . 



RZ 



21. Thus we may affirm, in general, that An infinitely 

 fmall quantity is a quantify ivbofe limit is o ; and on the 



contrary, that An infinitely great, or fimply an infinite, quan- 

 tity is a quantity ivhofc limit is c ' . 



22. Under the name of Infinitejimal quantities, we com- 

 prehend quantities which are infinite, or infinitely great, as 

 well as thofe which are infinitely fmall. All other quantities 

 are called finite. 



23. To fav, in conformity with common ufage, that In- 

 finity is that which has no bounds, or is that which is 

 without limit, or is that whofe limit does not cxifr, is a 

 mode of expveffion which conveys a fimple idea of what is 

 meant, and which is by no means deftitutc of propriety ; be- 

 caufe in fact, the limit of one kind of infinitefimal quantities 

 is o, and that of the other - c ; and o and i are not real quan- 

 tities *. 



24. But, 



: ' This kind of notation, which is in general ufe, is very apt and figni- 

 ficanr. But we are under no neceility of making o always reprcfent abfo- 

 lule nothing. We are at liberty, when our fubjeft requires it, to make 

 o ftand for relative nothing, or that which may be considered as nothing 

 relatively to fome other quantity. Thus any very fmall fraction 

 •oooooooocooi, (prefixing cyphers at pleafure) though not abfolutely 

 nothing, may be fafely cpnfidered as nothing, relatively to, or compared 

 with 1, and, a fortiori, with any other whole number, and accordingly 



may be reprefented by o. And, if fo, r^~,. ~, i or 1 00000000000 



(annexing cyphers at pleafure) though by no means abfolutely infinite, 

 may be accounted infinite relatively to 1, or any moderate given number, 

 and accordingly may he reprefented by '.—Thus the diameter of the 



earth 



