474

Caput IX.

GEOMETRIA

Et

fic ^

I+ r ^j - z, per debitam redudtionem dat d- I -ti b x 2 +j b' x 4 &c. unde (per Prob. i.) z=x+± b x 3 +^ b* x 5 ' &c-

Ar — Clb

-~aa

6

+ TS**

~h aa

Sic denique z-ffa^+x 1 , per extractionem Radicis Cubicae, datr—s Lee. Indeque z-ax + dL. _ _i.

9«' di« -*■ I2a bzs'

z-a +

a 3

3 a

JL _Scc.

162^

+ 8ec. Indeque t?x + dL. - -A- +

8l« * l2S

adb. Vel etiam z=x + — _ _fL+ ifl 8ec. Indeque L-

3* 2 9*= 81^ * 2

+- 5 lj? &c = HDEH (')-

19. EXEMPLA QUINTA.

Ubi pravi a reducito per aquationis affecta refolutionem requirit

Si Curva per aequationem 'z % + alz+axz - ia^-x^-0 definiat# 1 *extrahe radicem, et proveniet z=a— — + d— -1- dddL (h 8ec. tl#

± 4 64 a 51 zaa v '

de, ut in prioribus, obtinebitur z~ax- L + dL- + diiL- 8ec.

' x o 192« 2048^“

Sin s' 3 - cz z - 2X z z-c z z+ 2x 3 + c 3 = o Iit aequatio ad Curva# 1 ’

relblutio dabit triplicem radicem ; nempe z-c+x- - +

4 c 1 6 c*

Scc-

Et z-C-

ZX zx*

■X-r ---

8cc. Et Z——-C-

X

2 C

X S X y

-- + 4 T.

zcc

&c. Et i#

de

4 c 16 c'

trium correfpondentium arearum valores,^= cx+ y -x z - ,

Z — CX-jX +

2 4 C- b\c

X 4 ■T 6

ac z--cx-- - 5 -t+--'4

6c 8c 2 24 C

5 cc-

20. De Curvis Mechanicis hic nihil adjicio, Equidem red## 10ad formam Geometricam poft oftendetur.

21. Caeterum cum fic inventi valores z areis quandoquebafis finitam partem ab, quandoque ad partem eh infinitefus h produdtam, et quandoque ad utramque partem fit#

cond##

(y) Sit cdii curva cujus naturam haec aquatio indicat *

<* 3 + .y 3 t, defignante x indefinitam ab, qua a dato pun<3° ^tium fumat, -x vero defignante bd. In ed capiatur be:^ j pe fJunftaque ae producatur. Refta ae (qux pofitione data enaturam) curvx cdh afymptotos erit; id enim aequatio ,

ad

d— -f_ Scc. fatis indicat. Seriei autem infinit® 2

3-v

9 *

P