[ '4-6 ] 



denomiiiater exceeds, by i, half the product, whofe fadors arc 

 the fiift or leaft term of the progrefTion, and the fquare of the 

 fourth term ; if the common difference be any other number, 



fuppofe m ; — will be equal to that aliquot fradion above de- 



fcribcd, multiplied by m'^ . The general feries will then cxprefs 

 the logarithm of the ratio which the produdt of the firH term 

 into the fquare of the fourth, bears to the product of the fifth 

 term into the fquare of the fecond. This, fince the arithmetical 

 progreifion is an increafing one, will be a ratio of leffer in- 

 equality. 



It alfo appears, that there is no reflridion fet on finding the 

 moft convenient produds, by the fuppofition that one of them 

 is defedive in its lowcft term. And that, in the inveftigation 

 of produds, if we find fecond terms which (all of them being 

 equally diminifhed fo that one may vanifh) will then admit a 

 common mcafure, the produds may then be reduced to a fmaller 

 difference. 



Let X* + qx'^ + rx" + jx + / reprefent a produd of four dimen- 

 fions, and let s be = o, two fadors are to be found, whofe product 

 ftiall be x"' I yx + r ; this being multiplied by x' will give the pro- 

 dud x" + qx^ ■\-rx\ differing from the firft produd by / thelowefl 



term 



