for computing Logarithms . 
3ii 
talk : and although the work be much fhortened by help 
of the converging feries invented by the illuftrious Sir 
redtly computed without many figures by any theorem 
I have yet feen. The eafielt computation of it that has 
come to my hands is in page 44. of the late ingenious 
Mr. thomas simpson’s pamphlet on Trigonometry and 
logarithms. His feries confifts of the powers of f 
If now we put n — x in the theorem (log. n -^tl 
2 log. | + log. |. Here then the fractions, whofe odd 
powers are to be ufed, are y and confequently, in the 
feries formed from y, about one half of the number of 
terms taken by Mr. simpson will give the refult true 
to as many places of figures as his; and, from the frac- 
tion f, much fewer terms will fuffice. To Ihow how 
fall thefe feries converge I will fet down of each terms, 
enough to give the logarithm of 1 true to ten places of 
figures. 
Isaac newton, ftill the logarithm of 2 has not been di- 
^ we fhall have log 
