93 
Appendix to a Method of extending 
odd powers of the fraction — , to wit, — itfelf, — j or 
A ee ' 7 ee ' ee I 
?> ec 1 ’ ° r «-> 
zz)7 
or 
i T4 zista 
eel ’ 
or 
,ib 3 
8cc. are marked 
with the fign + , or are to be added to the fir ft term 2 a, 
or 2, and all the other terms are marked with the fign 
— , or are to be fubtradted from the former. 
Thefe are the conclufions obtained in the faid former 
paper, which is printed in. the Philofophical Tran fac- 
tions for the year 1778, Number xlii. pages 902 — 
049. The conclufions obtained in this paper are as 
follows. 
Art. iq. If - is lefs than — , but greater than its 
half, or — , and e be put, as before, = — and zz tjL _ 
’54’ 1 ’2’ 21 
-, it is fhewn in the prefent paper, Art. 5 and 7, that 
4 
the root of the equation x^-qx-r will be equal to the 
mixed expreflion \/ 3 1 e + z + v /3 p - z + /\s/ l e x the infinite 
feries -+A+ + &c . or v/ 3 77 I + 
gee 65616? 4,782,969? 8,135,830,269? 4 
\/ 3 e — z + \\/ l e x the infinite feries .111,111,111, 8cc. 
x^+. 023, 472, 031, 8 cc. x ^+.011,690,017, See. Xjrs + 
.007,414,542, &c. x — + &; C . or v/ 3 |^ + z + y/ l \e — z + 
A.\/ Z e x the infinite feries — + — + + &c ; in 
which feries the capital letters c, g, l, p, &c. denote the 
4 fame 
