On t%e Theory of the Infinite/imal Calculus. 323 



In the eflay, of which the following is a tranflation, the 

 two theories are blended, and Co clearly explained, that thofe 

 who think the fare tiuxionary theory, even as facilitated by 

 Mr. T. Simpfon, in his excellent " Selecl Mathematical 

 Exerciies," ftill fomewhat difficult, may derive inftru&ion 

 from the author's new and perfpicuous way of treating the 

 fubjeel:. This theory, like other mathematical theories, being 

 of an abftracl nature, may perhaps, after all, be more tafily 

 conceived than exprefied. And, as happens in the practice 

 of arithmetic, there may be perfons who are expert in the 

 application of fluxions, but who have never been able fully 

 lo fatisfy themfelves as to the demonftrable validity of the 

 theory. It fhould however be remembered, that all rational 

 praelicc entirely depends on found theory ; and, to ufe the 

 words of the great Maclaurin *, in proportion as the u gc - 

 ncral methods are valuable, it is important that they be e(ta- 

 blithed above all exception; and fince they fave us fo much 

 time and labour, we may allow the more for illuftrating the 

 methods themfelves." 



Thofe who, with a competent knowledge of geometry, al- 

 gebra, and the conic feclions, attentively perufe the following 

 eflay, will perhaps wonder why a fubjeel; capable of fuch. 

 clear illuftration has been reprefented as fo difficult. The 

 performance, though obvioufly not without faults, is, upon the 

 whole, well worthy of the attention of fuch mathematician* 

 as I have alluded to. The tranflation is as literal as the 

 idioms of the two languages would bear; and I have annexed 

 notes where I thought they would be ufeful. Though I de- 

 cidedly prefer the fluxionary notation, as well as theory, to 

 the differential ; yet in the text I have retained, among the 

 other fymbols of the original, all the d's, and the dd's, and 

 the ddd's and the dddd's, to which the foreign mathemati- 

 cians are fo partial, as being moft congenial with the inge- 

 nious author's manner of eonfidering his fubjeel:. 



I am, 



Dear Sir, 

 Sincerely and refpeclfully yours, 



W.D. 



* II ;\,': Jjitrodudion Co his TreatiH: of Fluxions. 



Ad'jer- 



