4-0 Mifcellanea Curiofa. 



fuffice to affume an- Index of a Figure or two 

 more than your intended Logarithm is to have, 

 as Mr. Briggs did, who to have his Logarithms 

 true to 14 places, by continual extraction of 

 the Square Root, at laft came to have the Root 

 of the i4°7374^83$5328f^ Power; but how 

 operofe that Extraction was,will be eafily judg- 

 ed by whofo lhall undertake to examine his 

 Calculus. 



Now, though the Notion of an Infinite Pow- 

 er may feem very ftrange, and to thofe that 

 know the difficulty of the Extraction of the 

 Roots of High Powers, perhaps impracticable ; 

 yet by the help of that admirable Invention of 

 Mr. Newton, whereby he determines the VncU 

 or Numbers prefixed to the Members compo- 

 iing Powers (on which chiefly depends the Do- 

 ctrine of Series) the Infinity of the Index con- 

 tributes to render the Expreffion much more 

 eafie : For if the Infinite Power to be refol- 

 ved be put (after Mr. Newton's Method) 



H-W f|P^ or T+i > inftead of + 



r , r — rn. i—im^-imm ^ i- — 6m-j-i imm — 6m* 

 ^TmrH Mi" 6wTF 24^ ^ 



&c. (which is the Root when m is finite)becomes 



m 1 2m^ J 1 3m J 4^ 5^ 

 m m being infinite infinite, and confequently 

 whatever is divided thereby vanifhing. Hence 



it follows that \ multiplied into q—iqq^f 



7/1 



of our mean Proportionals between Unity and 

 i~l and is therefore the Logarithm of the 

 ratio of 1 to 0 and whereas the Infinite In- 

 dex 



