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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 92r, page id 00068198:0183
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si Ex Hypothesi, quod in parabola sint arcae proportio
nales rectangulis circumscriptis, et situs centra gravitatis
idem semper invenil regulam clari grar schotentus hoc culdo
Nempe ponit d ecs ete arem ABC2 dari, et centrum ejus E
Hinc dabitur et area A(B) (C) A, et centrum ejus, calculo instituto.
Taudem posito coincivere B et (B) habetur quaesitum absoluse
idem valeb. et
ehsten. lit. 1, ad lib. 2. Cartesii
ea
qu pro aliis curvis simplicium aquationum stiinariarum
 Transeamus ad curvas in quivus area non sint propor
tionales rectangulis circumscriplis, sed habeant se alia ra
relatione sit s sydx: s(y) dx = Xy + ab,: X) (y) + ab
sumatur medium sydx: Cs(y )dx = Xy + ab, :, (X) (y)) + ab
et rurgus S_Y) ex: 5(V) dx = ((XV (yy + ab,:, (X) (V) + ab
fit S(CyBdx = S(y) dx, CX) (y) + ab, :, (X) (y) + ab
=sydx, (XD ((7) + ab,: xy + ab
felcus sed ita res furtur prima aequatio
Ex tali aequalionetient constanter β Sydri = xy + ab, et gerimaliter
y ((B- 1) yax = Xdy. adeo
d β- l, ax : x = dus: y Hoc ergo etiam reducitur ad aequationes
As (ydx: A) Sasex = X(1) + ab,: B ynt ab
et β ydx = Xdy + ydx, seu
lofint sed
dubitari potest an tale quid possibile, et quidem absolute quod libet curlibet
simplices
ddd
Sed socus erit si
conferendo res probabilior sperabilior, quod libet uni conferendo
quam
sit ergo unum LB ARes sila sumenda est ut etsi (X et (y) evanestant
tamen bealfiat aequatio, quod huc contingit. Assumumus st sydx = AB.CA
Assuunamus (yNax = A 3B3CA. fietu
syax + s(yDdx, :, sydx = X (y)) + ab,:, exDy + ab. Tollamus
1(7) ax = A _2B 2C A.
ydxe nempe 41 + SCyX: sydx = X (Y) + ab 1., x) yt ab, et fiet
(y) dx: X 4y)) + ab + 1
GXγy + ab
(ydx = 5(7) dx .
Ergo
y dx
3)ax
X (Y) + ab + 1 =
(X)y + ab
X. () 4 (xy + nabu
)+ ab
nam fiet sy
X) y +ab
+ l
X (Y) + ab +1
(Ny +a6
Xesry + ab
d
Ergo habemus legem
reductam ad
differentiales
((XD y Fab
Rdx = constanti, ubi considerandae X.
ut constantes, 
suidx:  ac
(X 9+ ab Hoc ricissim utie ad proprietatem duammmareara
f(y + ab +1=
exhat ducendam, si scilicat ad lansxpposito SCX, e g- Y
et fipt f et prodit curvae aequatio
Majo Itaque in ec est aliqua difficultas polius, si prima aquatione
ionis, nam unam
a
sunc hoc statim ex primo polebat
aponamus
ex hiic pres lo constantem et ulters 
aovia
tab
vaitur elatio
antrale reduncibilis
gax
e