34° Carnot on the Theory oj" 



Is ft may be fuppofed as fmall as we pleafe, without afTeftuTg 

 the quantities in the fir ft term ; beeaufe we may fuppofe R$ 

 to be as near as we plea'c to l\IP. Agreeably, therefore, to 

 the theory of indeterminate quantities, each of the terms 

 of tins equation, taken feparateiy, mull deftroy itfelf, or 'be 

 equal to nothing; that is, this equation may be refolved or 

 «fccampofed into two others, namely, 



tp , y __ ] 7 ^£._^ 2 y z -( RZ : MZ ±±* *& z yR L^ . 



y ~ a ~ x~ ' y (a — .:) . (2a — 2.v — MZ) 



the firft of which equations contains only afligned quantities, 

 3nd the fecond none but arbitrary ones. But affigned quan- 

 tities alone are neceffary to our purpofe; for they give us the 

 required value of TP, the fame that We before found it. 

 When, therefore, we have even committed errors in the 

 Kourfe of the calculation, the exactnefs of the refult will not 

 fee affected, provided that thofe errors are confined to the fe- 

 cond equation. And this, in fait, is the fame thing which! 

 would have happened if we had confxlercd MZ, RZ, and 

 T'T, as nullities, in comparifon with the quantities a, a?, and 

 y. We fhould, indeed, have committed errors in expreffing 

 the conditions of the problem ; but thefe errors would have 

 deftroyed each other by compenfation, and the required refult 

 U-ould not, in any rcfpect, have been altered- 



Thc Iitfmifejimal Analyjis is only an Application or Extenjion 



of the Method of proceeding in Indeterminate Problems. 



37. From what has been {aid, it will be eafy to perceive 

 that the Infmitefimal AnalyfTs is nothing elfe than an appli- 

 cation, or, if you will, an cxtenfionof the Method of Inde- 

 Scrmiiutes. For, agreeably to that method, I fay, that when 

 we neglect an infinitely fmall quantity, we (}q nothing more, 

 jiropertv fpeaking, than underjland it, and do not fuppofe it 

 to be nothing. Thus, when inftead of the two exact equa- 

 1:0ns,. found in article £, namely, 



RZ> RZ ~ %a - a* -MZ* 



I employ the two imperfect equations, 



^ = MP - a „ d - 



I kno«( 



