the Infinitcfimal Calculus. 2»7 



periocular MO upon NQ, which is parallel to MP, artd 

 put a for the radius of the circle. We (hall then evidently 



have 



, . MO TP 

 MO : NO::TP : MP; that is, — - . 



On the other hand, the equation of the curve for the point 

 M being yy = lax — xx*, the equation for the point IV 

 will be 



(y + NO) 1 = %a (x + MO) — (.v + MO) 1 ; 

 and fubtra&ing the former equation from the latter, and re- 

 ducing, we have 



M9. = __±I±Jl — \ but we before found 

 NO ia — 2x — MO 



MO TP :, - TP 2j + NO 



. = ; therelore — - = ^i 



JV'O y ' je 2a ~ - x ~ MU 



y (2 y + NO) 



and multiplying by y, we have TP - ■~Z~~£rZ~M& 



If, then, MO and AT) were known, we fhould have the 

 value of TP, the fubtangent required. Now the quantities 

 MO and NO are very fmall, being each of them lefs than the 

 fide MX, which, by'the fuppofition, is itfelf very fmall. We 

 may therefore, without any fenfible error, rejeft thofe quan- 

 tities, in com pari fon with the quantities xy and ix — za, 

 wherewith they are connected. The equation will then be 



reduced to TP = — ~- — = ~~ri the value of the fuljtan - 



za — ix a — x 



gent fought. 



The Infinitefimal Calculus may, in this View, he conjldcred 

 as ajirwple Method of Approximation. 

 4. If this refult be not abfolutely cxaA, it is at leaft evident 

 that, in practice, it may pafs for fiich, becaufe the quantities 

 MO and NO are extremely fmall. But a perfon who has no 

 idea oi' the doctrine of infinites, will perhaps be furpriled to 



be told that tfie equation TP - ——, does not barely make 

 1 a — x 



a near approach to the truth, but that it is really and perfc&ly 



Accurate. Of this, however, he may eafily fatisfy himfelf by 



' lor, in the circle. ?a — .v :y : : y : x. 



G g z invef- 



