£J4 ..Camot on the Theory of 



13. To enable us to extend thefe remarks to other pro- 

 blems of the fame kind, let us now put the cafe, That any 

 fyftem whatever of quantities is propofed, in onier that the 

 relations which exift between them may be injveftigated *. 



14. And iirft, 1 (hall comprehend under the name of 

 aJJigned quantities (quantitis dejignees} not only all the 

 quantities propofed in the very enunciation of a problem, but 

 a-ifo all thofe which depend on thofe quantities, that is, 

 which are functions of thofe quantities, and of none elfe. * 



15. On the other hand, I l'hali give the names of un- 

 aligned, or auxiliary quantities, to all thofe which make no 

 part of the fyftem of afiigned quantities, and which confe- 

 qnently do not effentially enter into the calculation, but are 

 introduced folely to facilitate the comparifon of propofed 

 quantities. 



Thus, in the preceding example, MP, MC, MT, DP, 

 See. are qffigned quantities ; becaufe they depend only on 

 the pofition of the point M, to which the tangent is to be 

 drawn. But RS, and all its dependent lines, MZ, RZy 

 T'T, T'P, &c. are auxiliary quantities ; becaufe we mould 

 not have thought of drawing them, except their afiiflanc* 

 had been wanted in the folution of the queftion, the obje6fe 

 of which is to difcover the proportion, or relation, of MP 

 to MT. 



* I here fuppofc that, in any problem propofed, the relations which exift 

 between fucli 01 fuch propofed quantities has been previoufly difcovcrcd. 

 If, for example, the problem be, to find a curve which has a certain de- 

 tcrminate propi rty, I fuppofe that the relation between an ordinate of that 

 curve and the correfponding abfcilTc is already known. In like manner 1 , 

 if it were required to draw a tangent to any indeterminate point of th;ft 

 curve, I be<j;in by arbitrarily fixing on the point to which I wifh to draw 

 the tangent, and I limit the problem torhe inveftigationof the relation which 

 fubfifts, for inftance, between the fubtangent and the abfeiffe, or between 

 the ordinate and the correfponJing fubnormal at that point. But if it 

 fho'jld be afked how I apply the definition of infinity to fuch queftions as 

 t : :efe: Is matter diviJiUle ad infinitum ? Is the /pace in which all created 

 beings exijl infinite? I fay, if fuch queftions fnould be put to me, I lhoultl 

 anfwer, that my definition is reftricted' to mathematical infinity, and that 

 it can only lie applied co problems whofe objeft is the difcovery of the re- 

 lations which exift between different mathematical quantities, and that the 

 mctaphyfical queftions juft ftatcd «~an by nof leans be referred to the theory > 

 of which I here propofe to eltablilh theprij :ip>ies. 



Hence 



