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The afhes of this foflil, when burnt, being boiled 
in water, and the water evaporated, there remained 
no fait behind. 
I am, my Lord, &c. 
Grofvenor-Street, Feb. 28, 1760. 
Read Feb. 28, 
1760. 
LIV. A new Method of cojnputing the Su?ns 
of certain Series ; by Mr. John Landen : 
Communicated by Mr. Thomas Simplon, 
F. R . S. 
A S the improving the analytic art, 
efpecially any branch of it that re- 
lates to the fummation of feries, may, by facilitating 
computations, conduce to the improvement of feveral 
branches of fcience; it is prefumed, that this paper, 
which exhibits a new and eafy method of computing 
the fums of a great number of infinite feries, may be 
acceptable to the mathematical world, and deemed 
worthy to be inferted in the Britifh Philofophical 
Tranfadtions. 
1. 
Suppofing x to be the fine of the circular arc z. 
whofe radius is 1, 
x 
Vi — . 
X 
will be = Z'j and, con- 
From whence, by 
fequently, • — , 
J Vx'—i V—\ 
taking the correct fluents, we have hyp. log. 
x + V x % — T 
z 
Hence* 
V — 1 
