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5- It is convenient that they difFer in their loweft terms only; 

 otherwife the quote found upon dividing their fum by their 

 difFerence (by the increafe or dccreafe of which the convergency 

 of the feries is accelerated or retarded) would be of a lower 

 dimenfion than cither produd; fo that we would be at the 

 trouble of finding produ£ls of a higher dimenfion, when perhaps 

 produds might be found of the fame dimenfion with the quote 



-J, differing only in their loweft terms. 



Besides, if this compound difference (or fome compound quan- 

 tity which Is of the fame dimenfion with this difference and 

 an aliquot part of it) do not meafure either produd, there is 

 this additional inconvenience, namely, that the numerator of the 

 fradion is uncertain, being aft'eded by the variable quantity x ; 

 whereas if the difference of the produds be the fame with the 

 difference of their abfolute terms, it is in no manner affeded 



by the variation of ;>?, and the numerator of the fradion — may 

 fometimes be reduced to unity, which is convenient in the ap- 

 plication of the feries to pradice. 



If the compound difference (or fome aliquot part of it, and of 

 the fame dimenfions with it) meafure either produd, it is a 

 fore fign that there are produds of an inferior dimenfion every 

 v.hit as advantageous for the conftrudtion of logarithms. From 



all 



