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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 60r, page id 00068196:0119
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5May 1697
similiter
tio vice
es
oc dignum in qntitione
uotiescanus aequalio dalu
ut
V
differentialis, in qua una litera
absolute posita non assurgit ad potentias, licet
s
su
Xiget dy: ax assur
caut itcunque semper licebit aequationem Tiam differentralem
uxempli culusa
rausformare in rationalem
ib
e
 Xia
e
esL
t
+
ax labentur
si dascondati  cotanga
et gumatur
rationatite
elitur
dy dydy: dx dxdx =
sit
cava
hhoc prosit pro qbadraturit
Dax. v  vuar  v ov
vo seu dx:do = - 313~: 13 cum alias sic liceat procedere
Vytaia  sit summund ax= dy: Vyta: a sit
dx=
Z
ody:a sed habebitur Zdu s. habetur d
ve
et labebimus
cerdendum quater d ves enien prodes pro
ux ax. adenastendetunt
agede aydu
derd
ata,: a fiet y:a = (dx: v fietue doodef
ax. v = = a 3uodo:
na
 Zaado: v = (5to )2(Xdv: aa) + dx: V
a: V3 - Sdx: v +1 - seu (dx: V = a - V: V seu dxo
XX + ya,
desida dydy: dxax:
e sit y.a = ax: v fietqus du: dx (3) = a: V
aa. VV (4t0) = (XX: aa) 
seu ao
lyiax
23
na et sydque = a
+d
yta: a = a:Z, et firt
jam yta: a2 a:
1t -qdu
7
et fiet y = a4a:
Hoc igitur semper fit ermulatio. sit duiax = a  + aagus: a sit y: a = fax: v seu dy: dx = a: v
+pax: B dx: vres
et fiet a: v =1
4
Gax. Y
se et discentrando adv: vv=
tk 
ietad dudv: dxdx = a: v = 1. Aliter dy: dx = hy+ vy: aa 26 seu a: V- bsdx. vF P (
et fit a- a dv: vv) = b dx (.V) + 2 f.. axli V) et fit s..= adv = bAX V: a) ax, : vdx = s... et
aa du dv + bbvv: aa) dx dx = 2bvdoax,:qvvax ax = (5. et set denique
C
a = b aadv. bvax 4 at dodo + bb vrdrdx. 2a ab qu dx 2 sed posten ut habeatur
l
sine
vax
aa 6x x ax
 Caxivoni
verse nova pommatione