C 60 ) 
>Jow, though the Notion of an Infinite Power may feem 
very ftrange, and to thofe that know the difficulty of the 
Extra(5kion of the Roots of High Powers, perhaps impradi- 
cable ; yet by the help of that admirabie Invention of Mr. 
J<lewtony whereby he determines the Unaa or Numbers pre- 
fix: to the Members compofmg Powers (on which chiefly 
depends the Dodrine of Series) the Infinity of the Index con- 
tributes to render the Expreffion much more eafte : For if the 
Infinite Power to be relbived be put (after Mr. Newton's Me- 
t V ; , S L I 
thod) p + fq, p-rP^l i + "^r.inftead of 1 + ^^+ 
I — m . I — ^m'\-2 m m i — Sm-^ii mm — 6m^ 
&c. ( which is the Root when m is finite, ) becomes 
being infinite infinite, and confequently whatever is divided 
thereby vanifliing. Hence it follows that ~ multiplied into 
f — H 1^ +■ H ^ ? — \t augment of the 
firft of our mean Proportionals between Unity and i + f , 
and is therefore the Logarithm of the ratio of i to i 
and whereas the Infinite Index m may be taken at pleafure, 
riie feveral Scales of Logarithms to luch Indices will be as 
^ or reciprocally as the Indices. And if the Index be. taken 
m 
10000 &c. as in the cafe of N<a/j«r's Logarithms^they will be 
Again, if the Logarithm of a decrcafing ratio be fought. 
I 
I I 
the infinite Root of i — or i — ^K'* is i — — a — —a* 
~ ^ ~ r^^' - 6ln ^^e^ce ^he 
decrement of the firft of our infinite Number of Propor- 
tionals wiU be ~ int0 5f+ 1 jj+f q' + 1 + +J q^ &a. 
which therefore will be as the Logarithm of the ratio of 17- 
nity to I — .^. But if m be put 10000 &c. then the faid Lo- 
garithm will be + +? 3' + 5?^ + I f + &c. 
Hence 
