Mr. maseres’s Method of 
■204 
= rx [1.388, 034, 187, 034, -.633, 766, 233, 765, 
-rx .754,267,943,269; which agrees with the value- 
of the whole feries r- -j+y-y +y~n + &c - onl y in the 
higheft figure 7, the more exact value of that feries 
being .785,398,163,397, Sec. But, if we compute eight 
terms of the differential feries which is equal to the 
feries r-—+— — -+—-77+ Sec., we fhall thereby obtain 
its value exadt to three places of figures; which is as 
great a degree of exadtnefs as would be attained by 
computing about five hundred terms of the feries 
r + + + + 8cc. itfelf. The computation 
3 S 7 9 11 J 3 *5 1 
of the eight firft terms of the faid differential feries is as 
follows. 
Art. 13. Since t is in this cafe = r, tt will be = rr, 
and confequently or x, will be = 1. Therefore xx, x 3 , 
x^^ x ^ , and all the other powers of x, will in this cafe be 
equal to 1, and 1 +x will be equal to 1+ 1,. or 2, and the 
powers of 1 +# to the powers of 2. Therefore the frac- 
tion and its powers will be equal in this cafe to the 
fradlion 4 and its powers. Therefore the general differ- 
ential feries in art. 8. to wit, 
i- 
