and Infinite Series. 
•Now x = yb+c*fi/b-c-'tyi 3 + J/g = 4*431,4186 = 
the root of the equation x 3 -* 3V 7 117 .x = 22. And 
the terms of the two feries being found as in Art. 1 17, 
we have the firft = a - c - 8cc. = 1 - *0000450 = 
*9999550, and the fecond = b + d + &c. = *0036731 + 
*0000008 = *0036739. Alfo 4 tyb - 4^1 1 — v 7 704- 
Hence, . ■ • 
By the id feries 
• 9-99955° - lo g* "1*9999805 
^704 - 0-9491909 
feries := -f- 88955200 - 0^949 17 14 
X ~ — 4-4314186 
-f- 4-4641014 greatefl root 
By the 2d feries 
’0036739 - log. 3*5651273 
^704 - - - 0*9491909 
feries = 4- -0326827 2*51431 82. 
X 22 -f- 4-43 142 86 
4- 4-4641013 the fame root 
Which nearly agree with the fame root found in 
Art. 1 17. 
138. But in Art. 64, the fame root was found to be 
1 + v 7 1 2 — 1 + 2-v 7 3, hence we obtain tliefe two firft 
•equations following, and their fum. and, difference give 
the other two : 
2.^.8. 1 1 .14. 17.20. 2 6 
I 4- 12-1 - I 3 4- 9 J 2. 5 8; ;2 4 
4^1 1 3 . 6.9.12.1 1 + 3^6.9.12 . 15 . 1 8.2 1.24. 1 1 8 
1 4- V 7 12 — A^I3 — A^9 2 . 2 * ^ 2 . 5 . 8 . I I . 14 . 2 6 
3. 6. 1 1 2 3.6.9 .12 . 15. is . 11 
v / i 3 4 -v / 9 __ T 2.2" 2.5.8. 2 4 2.5.8. 11. 14.2 6 
2 *y 1 1 
- I - 
x 4- f/12 
2*y 1 1 
~ I 4. 
3.6. if 
2 .2 2 
3.6.9. 12. 1 I 4 3.6.9. 12. I5.18.I I 
s + &C. 
s* — See, 
2. 3.8.2^ 
4- 
2 3.8.11.14. 
3.6.H 2, 3.6.9. 12. 11 4 3. 6. 9. 1 2.1 3.18. 11 
— -i- 8cc. 
The laft of which agrees with one found in Art. 1 r 9. 
