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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 84r, page id 00068049:0167
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NIB H
b yXX + byx + CcRy = exX + f x + g. seu 
seu y = exx + fX + g,: XX + bx + cC. Hjus figurae sic
expressae datur utique quadratura rationalis  sel jam
secundum Cydx. Datur ergo et (xdy, quadratura non-
efit quaerendo valorem, ipsius X, fiet:
e
rationalis
XX + by - f : g-e X + =(3 b2-5: y - C = = (2) by. F:, 9- C= Ccy+9
seu X + bg - f3: 2,9 C = YL by f -2ccyr9 y e: 2y-20
datur ergo (1. S,ay Y1y9+ my +n: 29- 2C)
jam sit  ed G  Cx + a D: X+B = Syy+ Cy1f.
st
datur (xdu per quadraturas rationales, ope reduction
praecedentis, quaeramus Cydx. sit exta = m Xtb
ex 1 fiet: m m:n = yy+ ey+f,: y+ 299+9
seu xtun yy +enegonnus e=bFfnn
= um
a
sg un
29 mmy
gy + hh. R y = 13: K seu y + hh: K 9 + G hH: 4HX = h + VK,: 4XC
seu per compend
seu v =hh + B+ BK: 2K se y. t2gmoc enn+ Y
∞)
seu y = + 29mm-enn + 14g9m = qcomman+ etn eGarf.: 2mn - Emm
D
o
4g
f.
Ancbidetia tia cdari ad +
Hinc videtur via dari ad dimensionem
ec
d so
Curvarum Ellipseos et Hysbolae et
superficiei, eoni scaleni. quae duo ad huc in Cunicis restant.
Nempe sit y= 2gmm-enuce: Enn-Erum +ZD habebitur X, (vax  rationali
habetur
quadrarura, quia habetur ea, ydx, E eequev Ergo summari debet V = 13gom et c: . 2n
aprae plerasque formas
aplectitur
ractenus desiteratas pro ut abitrarias a, b, C, e, f, 9 interpretamur.
B.Hujus carvae momentum ex condirectrice est
areae
fb∞ DR +C:X_
summa omnium x ab +Ct d. Ejusdem areae momentum ex condinectrice
ut
abetur pe
ecetet
(XXdus est autem ex 1, yyx = x +b ,c, et sit X Al XX 1 + b+7. robgus = rl: py Eblysus _C,: 9
X = n - b Ergo m = Cn- cb sit cb = a fiet m= n. seo hoc non licet, quia etanescit 
goum fsnn
un. mi
e 
e