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IV. TlefleSHons on the Theory of the Infinitesimal Calculus. Br 

 C. Car NOT, E.v-Direclor of the French Republic, Minifc.A 

 tfWar, and Member of the National Infitute, Paris 1797. 

 Tranjlatcd from the French, and illuflratcd with Notes,, 

 bji William Dickson, LL.D. 



To' the Editor of the Phikfophical Magazine. 



DEAR SIR, 



X HE mathematical readers of your excellent publication 

 ijeed not be told of the importance of the infinitclimal calcu- 

 lus, or of the afiiftance it lends to every part of natural phi-, 

 lofophy, which falls not within the province of chemiftry. 

 That calculus is practically the fame with what we call the 

 method of fluxions, except in name and notation. But the 

 theories of the two methods are different; or, rather, thole 

 theories are only different ways of illulirating one and the 

 fame method under different names and fymhols. The flux- 

 ionary theory, as delivered hv its inventor, the incomparable 

 Newton, is confeffedly the molt accurate; but the infinitefi- 

 fnal, otherwife called the differential theory, is generally 

 thought, I know not for what reafon, to. be the moft eafily 

 underftood *, As it is often advantageous to confider a fub- 

 jeci in different points of view, it was perhaps fortunate that 

 M. Leibnitz claimed this difcoverv, as he was, of courfe, 

 obliged to give it a new explanation; and thus we have the 

 ideas of two of the moft acute men who ever exifted, on one 

 of the moft extraordinary and fublime {peculations which ever 

 exercifed the human intellect. 



* " We truft/'faid the excellent apoflle, with infinitely more depth ancjl 

 propriety than appears at firfl light; " wt t:t>j/ Eha.1 \vc have a good con- 

 science." I tru.fi that I undcrftand fcmething of Newton's lluxionary 

 theory ; but I never could underftand the differential, as delivered by 

 Leibnitz, in the Afia '.uutitorum of Lejpfic, for October 1684. of 

 which the' learned and ingenious Mr. Rr.phion has infertcd a tfanllation, 

 in his Hirtory of Fluxions. 1 believe moft impartial perfoos, who try to 

 jrad that perplexed and perplexing piece, will be far from accufing the hi'fr 

 toiian of feveiity. when he fays, that it contains " far-fetched, fymbolifing, 

 infignificant novelties,"' and that the notation is ' ; lefs apt and mere labq« 

 rious" than that of the real inventor. 



In 



