418

PrOB. II.

GEOMETRIA

quantitatem b pro lubitu aflumens, prodibit jr — ; fa$&fi uef

divifione = -^ - ~ ^ 8tc. Et inde Regula, ut in fa-

perioribus, dabit y - ~ - ~ + yr _ 8cc. relationem inte fx et y.

38. Sic etiam habita aequatione + 3 - vv ; fi, proptei

— 2 4-2—2A'—^’ ;

terminum j, fcribam 14 -a: pro a:, emerget ^ ^

terminoque in infinitam feriem, 2- zx+ %x~- 2 X Z + 2X 4 , & c ’reda£to,erit - =^-^.x+x z - zx^ + ix*, 8cc. Adeoque juxta regula^ 1obtinebitur ^=4^- 2x z +jx 3 -jx*+fx 5 , &c. relatio inter at et /.

39. Atque ita fi proponitur 4 - x~*+x~ l -x^, quia terminun 1

x ~ 1 (five inefie video, tranfm-uto x; quemadmodum pro e °fubftituendo i-at; et oritur 4 ~

4-

n/i-a?. Termini

x y/1 — X I — x

autem — b- valet i+at + a^ + at 3 , &c. Et \/i—x valet i—^x—^x 1 '-'^

1 — x ' z 8

&c. adeoque —J= five —-— A — - valet 1 +\x+\x 1 +-^rx' i ,

^ y/l-X i-{x-\x - T \xl, &c. 1 S 1 6

^ ^ « * 3

Lee. Quamobrem (valoribus bilbe fubfiitutis) erit ^ = 1 + ix + v

+-4 a- 3 , (S) Lee. Et inde per regulum Ut y=x+x z +jX 3 + ^;X*-,(&) ^ c 'Et fic in aliis.

40. Hujufmodi etiam transmutatione Fluentis quantitatis &quatio in aliis cafibus nonnunquam commode reduci potet lf '

Quemadmodum fi exponitur i = ^ 5 ^-.—. pro « fcribo ,

r, etinde per regulam- y— -A + *

et obtineo 4 =

y _ f3 -^’

, fi ve

x

L

C

At harum transmutationum ufus in fequentibus magis elucet'

S O b

0 -

( 2 ) Haec ad Calculorum fidem emendata promo : Codices M 3 S. habent i 4 - ix-\-%x* +- = i + 2x-\- jx z + \~x l &cc. y — x 4- x 1 + \ x 3 + .£.£ x* &c. Vitiose quidem. Nam

— 1 F * x + 4^t& * 3 + j

id rc-r

V i — i

—, i 4" x -p x "|* i" 4- j

I — X