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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 174r, page id 00068199:0347
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s
equatio
ut an = (3 X
Ergo 
Rulos
e
+
V
y
fie
sit sata
aallus
x aa
e
AXdD yyda. X
=BβXx +2 (Xy+ +VVyy oadZ = Bdx+) dis
Baagyax
ad a dis
Jaayus dy
ubi ut destruatur yudiu oportet facere Vγ+aa =0, quae quid
fiet V= a1) et habebimus aequationem.
Xxdx + 2aββ =1 ydx-
dut
v
a
k
fay + yd++ adque
+
y + a9
BBXXY. 1 dy  X ydy =0
C
a
cis
y +RI
ip
o
fD.X
a
taq
V
a
utique
at tad pxaa ladeoque explicando L
ipev L.
sed praestat darant pert
seu f: g est data. x
1
_
er clac
etax hac ab bFdx, =a)fd (B. 1) Fa D ct. laf
use ss
(C: A) dx -)
de
adf- fdx +afdf
quam ipsa resolvenda. Itaque
ubi urm asumsissevi
lygamq+ aan =0
nihil
uesen
Cnmus admunssem
cetrmastpli per murtplicatam adjungissamt sua dissi
 m ui poem
sulanam comparissemlum deti
substituendo vallorem ex termino yax, qui est 
nun haec aequatio paule adruc diffiitior es
ne atm sa
ut
qua
afAdu +Afydy =0
aga dy
fiet
C
f(C: A) ax = adf, fiet bf ax = a A fd B: H) + abat - a Adf-L
7+
C
ux tadsdu +dFydu = . coincidentianda
aactde
Ldk + aq
s
FdK. sed ibi pro Atdk
iodem mopo
CDonamu B=a
leva
fydK Tagdk
ad has sd ubi prius data fuerit multiplicata
l
si placet,
= 6 et ficta5+ adg +f dy + fydus = 0
ota coincident quar.
efyq tabfdx
leus
cum producta per At maltiplicata a Ny d+ + 3
ad 38+g Ex dus est
fDdk
ut
si colincidentianda qua ex data est formata f
e
valorem autem ipsius 9 substituendoa in Terminoly dx
antu
d
c
quidem aequatio est imaginaria. et praeterea simul evanescet ax.
multiplicatam et quae producta per - 2X.
1
C
XXdx + 2ββ)) Xydx + BVByyax + BB) XXdy +2β)) xydy + Vhyydy
ade
2
3
ex primi generaliter hoc modo ux
irgo a
a
1
extrationi
per Rmulh alico
gale+ CAy+ f qydx + oy ax+ hde L0 adqua ec
neralem ad quam modo hic Aro posito redalitur ipsa des +dx = pX Fyg): aa ex ciendi= BX +), y
ue
deprehendi quaerendo ad
1+
x in, plped
du dyde, rdu eoanesit
quae sibas