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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 15r, page id 00068072:0029
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068072&page=29
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X y. a = Sdz.
J.a = V:
l
d(v. Z)= dz
:2
X: a = (dZ: Z
L: a = dv: d2
(av: d2z)- (V
ed
a (dv: dZ) = ddze: de 3 (ddv: ddz) (dv: dz
via = V: Z
fint dy: dX =
Xia = W.Z. sint
de - 
1Z
aL
H: a = sddv: dv.
fit dyidx =
: du - W = dv- vd
dZ
y:a = dx: dv
e
d(v: Z
du
etZdu WdZ do:)
fiet duidue = d3d: duar
s si dz constans fit dy= dZ ddv: dudo, et dx= dd
av
ara
Aliter y: a = dv: d2 X: a = sdav: dv fiet dy: dx (ddv do: a vil Z
et pretdy: dx = - dz: du.
posita de constante, sit jam data aequatio Tancentialis quae.
Cunque du: dx = yy+XX, iaa fiet dv: dz = (dvdv: dZdZ) + qu sadv:v
seu fadgis= sed nita dare fieret y: a = dyidx quod absaru
Cetiam absu
x: a = sdd v: dZ, fiet aeux = quod 
ituum absurdum. An sic Xia= sadvive 5+) + et
1
e
aliter ya = dv: d2
 y: a = dz. dv  et dy: dx = 6 (dd b dZ: dvde ): (dz: 
seu y ddv: dede = = dy:dx  sed nit hinc
L y. a = 9 ViZ
p
X: a = dZ. d, jec Ergo per sriora
do. dx = y:a = d dv:dco et x:a = dZ: deo
fiet dy: dx = ddvi adz  
sit jam aequatio data
dy: dx = ∞ yy+ xx siaa fint ddv  Ed vdv +i dZ dZ
fit jam
a au
codc _Z ddZ C et U sddco: Z sit
da
sit aedno. dodoidcocco= da: adv, fie
seu Hruc datur na dav idd ex exia
e
advi dcodio  ex duidco, et res reducta
ads - adZ= dZ dZ
.
est ad quadraturas sed hinc binetur oriri absurdum
nam e ata dabitur bis adzue ado et nempe ex dodideri
naz
et ex dz. ded, ergo haec duo, dabuntur invicem sine qua–
c trs sed si quod non licet. quid sic siC
odo: dcdded ddu. dd v) t co rnecdicet facere do ex av etd)
s
da deo ddo = daz dodb + dazdzdz. sitdd
C
∞adA adque dudv. 2diod dv Ret du = 2d codu
esit ea ddz= dodco fint, addv= dedv +d2dZ. , do
et adq codco Lbdco et ay + ac = Lcoco + b bco frustra
qet fit aB dando
at
sit dd
Aliteri cbcodeo = (dDa D +d3dZ)  dd d.
D
 aazue. e
seu ado iaaque se sdV: Sanda
G aZ davaz
, daz. Naco 4Z
sed hoc non prto licere
de
laxdio
du du