DE QUADRATURA

35 6

Prof. VII.

Prop. VI.

P R O P. VII. TUEOR. V.

Si pro e+fz'+gz 2ri + &c. fcribatur r ut fupra, Sc in Curvae ali'cujus Ordinata, z i±w K x±r 9 maneant quantitates datae 9, Y), X, e, /» f 1 'Scc. et pro o- ac t fcribantur fucceffive numeri quicunque integi'& Ii detur Area unius ex curvis, quae per ordinatas innumeras bprodeuntes defignantur, fi Ordinatae funt duorum nominum 111vinculo radicis ; vel Ii dentur Areae duarum ex curvis, Ii Ordin a 'tae funt trium nominum in vinculo radicis ; vel Areae triumcurvis, Ii Ordinatae funt quatuor nominum in vinculo radicis >8 l lic deinceps in infinitum : dico quod dabuntur Areae curvarentomnium.

Pro nominibus hic habeo terminos omnes in vinculodicis, tam deficientes quam plenos, quorum indices digm^ftum funt in progreflione arithmetica. Sic Ordinata s/cP-ax ***'ob terminos duos inter Sc - ax^ deficientes, pro quinquinom 10

haberi debet. At Va^+x* binomium eft ; Bl yja 4 +x 4 — ^ trin°

mium ^

ct fiet a — Qtk a.

I — 0 -+■ Xri x fk A + 0 X elA + 0 + n X eis

c ~ 0 + 2 An X gkA + 0 4- An -f p* X /Ia + 0 -f 2 /j.ri x «A + 0 + n + A” X/£ B + 0 + n + f*» *O + 2 i, X ekc.

d~

els +

: 6 + X b^A + 0 + + prt X^/a + 0 + An -f- ipn xfmA + 6 + 1M X enA -f 0 + n +

4-® + ’> + ^n + f t, ’X/’/B + 04-n4- 2 /xn X em E + 0 4- 2*1 +*»! Xfk c + 0 2 „ -f-/un X

0 + 3»i XekD.

Ex quibus venient

^ __ c 3—0 An X fk A — 0 -4* /*n X cIa

6ek ’ ~ f+^Xek

c 0 + 2 ?nV^A — 0 -(- An + — 0 -f- 2ur) cm A — 0 -f- n + AjiI/Xb — 0 + n

eis

0 + 2 n X

/3 — 0 + 3^*1'33A — 0-f 2 An +f*n]^A — 0 -|-An + 2 fj.r\fm A — 0 + 3^niMA — 6 + » +

fi • :-» 7 T“ : i " * 1 •

* wa — y-f 2-^ -f ^ 1 ^/a — y + 2/x))i/;«A — y-i- 3 ^u//a — y + u -r® +/*Tj//B — 6 + n + 2 fir,\emv — 0-)- 2n + A n [/~Ic — 0 -f 2n + pr,lclc

6+ 3n|