34 6 D E Q U ADRATURA

Prop.v. cz^+dz 3 * + Scc, in 'r a ~ j , fumma arearum in a + B£ w + c ^ M+ &Z&+ 8cc. aequalis erit areae curvae cujus ifta eft ordinata.quentur igitur ordinatarum termini correfpondentes,et fiet a —de a,

£-Q+a n x/A+d+rj xeB,c-d+27,n x gA + O+n+M x/b+ d+zri x ec r& c 0,

et inde A — %-

_ a-e+Ai) x/ab-b-iXe

C — f— s+2An x^a — s+ B +*„ x/b8 + 23j X e

Et fic deinceps in infinitum ( m ).

Pone jam \-r> r+x=s, s+x=t, & c . et in area z 6 r x in a +cjs^ + d^ 3 ” + &c. fcribe ipsorum a, b, c, & c . valores inventos, &prodibit feries propofita. Q. E- D.

i. Et notandum eft, quod Ordinata omnis duobus modis inriem refolvitur. Nam index Y) vel affirmativus efte poteft vel n e 'gativus.

Proponat^

SXd+S xd

+ S Xrm

+ S Xen

+ 9 xfk

-j- 6 x fl

+ S Xfm

+ hr,X,X

4- s xgk

+ S X 'l

xle

+ xi» x fl

4j>»X,^

+

+ a Xine

Z 2 H S Xhk+ **X/>* -z>,

•\-2\-nXgl

+ 3^ xbk

+ p^xte

-\-2priXrnf+ 3l*riXne

= « = bc x ».

+ 0 Xep *

+ S Xft+ 8

+ '? ■'

+ 8 Xik+ Xfit

+ 2\*Xgm ---4" 4-, X »8— 1 . R>— J , 8^-' x *+ 3*»X/>1+

+ x lh+ 2 rnX”>g

+3 («X»/

+ 4 (ud x

Unde omnibus ab illa a divifis, et rite ordinatis, veniet fymbolum redae bc, quod initiopofuim 135Qi E. D.

(’) + jX>i\ X h A + S + n + 2>^. X£B + 0 + 2’i+*sl X/c + 0 + 3^ X eu.

~ d —s + jj/c — 7+7\g* — uhh

("•) Nimirum d —

r+ y*

V-