I 393 1 



I PROPOSE now to fliew, how produds of this nature may- 

 be found — and firft, when they rife to tv/o dimenfions only, 

 or confift each of two fadlors. 



Let the two fadors of one produd be x -I- a, and x -{- b ; 

 that produd will then be x* , x + al> ; if we affume for 



two other fadors, the quantities x and x , we get the pro- 

 dud X* T / ^' which differs from the firft produd by ab, the 

 lowefl term of that produd. — Here it is obvious, 



1. That the nearer ab approaches to o, castcris paribus, the 

 fafter will the ferics converge. 



2. That \£ a + b be made equal to o there will be but three 

 different fadors, for x ]f f will then be equal to x. 



3. It may be obferved with refped to produds of any di- 

 menfions whatever, that the fame fador mufl not enter both 

 produds, for this would ferve only to raifc the terms of the 



d ,. . -n . 



fradion — ; not to dimmifh its value. 

 s 



4. Hence it follows, that in fcarching for thefe produds, 

 we mufl.fuppofe one of them to confifl entirely of compound 

 fadors. 



Vol. VI. 3D 5. It 



