A ‘Treatise of Algebra. i6i

9.9987814 -f- 2.7224/= 10 ; from which / comes out-= 000447, 2nci therefore * = 3.020 47 ; which is trueto the last Place. Again, let it be proposed to find the

20.V

Root of the Equation

\/i 6-f 5*+* :

25

Put 2o -f- / = .*•; then, by procee ding as bef re,we lhall

400 + 20/ 20 + f X v/405 + 40/ r, .

have ——-—+ -Z-J—= 34: But

^5*6+ 45/(by Theorem III.)

_

25

r 1

■ ■= is nearly = — —^^516 + 45/ 4/516

1032x4/516

:, and (by Theorem II.) y'4O5-|-40i

ioe

— 4/405 4- —= ; wherefore, these Values being4/405

substituted above, our Equation will stand thu»

400-I-20/X

45'

4/516 1632x4/516

204/ _ 20/

--~X4/4bj4--r=t

25 4/405

— 34, that Is, 400 -f- 20/ X .044022 — .00192/ -4.

20 + t X .804984 4- .0398/= 34 ; whence, by re-jecting e 2 , &c. as before, we have 1.7 13/ = ,19:5, andConsequently e— .1118.

Thirdly, let there be given 4/r — x -f- 4/1—■ 2^ -s-4/1 — 3*3 = 2. Then if 0.5 -j- / be substituted there-in instead of x , it will become 4/0.5 —z -f- 4/0.5 — 2/-f 4/0.625—2.25/ = 2; or 4/0.5 — 4/0T5X/ -f 4/0.5

— . - 4Z.625x2.25/

—-4/0.5 x 2/ + 4/.625-= 2 (vid. The-

2/0.625

orem second) whence 3.545/= .204; therefore /= .057,and x =0.557 ; with which the Operation being re-peated, the next Value of * will come out = .5516.

Lastly, let there be given 1 4-*' -j" i+* 2 'l 3 "I - 1 ••

= 6,5, to find x. Here, by writing 3 -}- / for x, and

M proceeding