[ 414 ] 



The invefiijation of produds of five dimensions may be at 

 prefent omitted. — For tlie difference of the produds of five 

 dimenfions, which feem moft commodious for the conftrudion 

 of logarithms, is fo great as to deflroy a confiderable part of the 



advantage arifing from the greatnefs of their fum. -Befides 



the very invention of thefe produ£ts, efpecially when the fadors 

 are large, is troublefome. — Not to mention the number of ad- 

 ditions and fubtradions neceffary to find the logarithm required, 

 after the logarithm of the ratio, as direded by the feries, has been 

 found. 



This laft objedion indeed, would be of much lefs weight 

 were produds found whofe difference {hould bear fo fmall a ratio 

 to their fum, as to preclude the neceflity of ufing a fingle term 

 of the feries. 



If x+_a, x+ l>,xjl^, denote the rcfpedive fadors of two pro- 



duds 5 thefe produds will be /if' ^ — a6. x ^ ab. a-\- b. 



— b' 



— a- 



Their arithmetical mean x* ^ — ab. x, will be refolvable into 



— b^ 



three fimple and rational fadors j if a^ + «3 +^% be a perfcd 



fquare. 



