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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 1v, page id 00068051:0002
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timeo ne semper _ X et y siviul sublata secum tollant dax, ddus, 
quod ita videbimus qt hi quia abest a non possunt esse aliae quam hae quantitates
y: XI, dy: dx, ddy: ddx, x ddu: x, patet autem tolli posse
has duas quantitates yix, et xdax: d. residuis manentibus
duabus dyidx, et ddy: ddx. Itaque spes adhuc manet
sit exemplum: a )f1 X ax + uXdus : x quam differenta
s
ilo
y ax
bis 
fet: (+ 10 X dx ddx + 10 dx3 + 10 X dy adx Fro dy dx + 11 Xdx dai  dxdeuxirdlus B
y dys ady)
- 10 X dx ddx
Y dys ddy)
dyd
y axadys axa ydydax dis dx) exd
11 X dy dex
= 11 Xdy ddx
ydx day
= 10 Xdx ddys
ydya
=UXdy idu
ydxalx)
Ubi tamen rursus tallu et  sin video et mivor non posse tolli xe 
quia simul tellatur et dax, dayue. Videamus an non possit formula obtineni
in qua sublatis ordinariis manere possint differentio. differentiales
g. sit 1axd+ soq 10 dx, et vibio rem non posse obtineri, nisi assur
gatur ad dax. verb. 10 Xddx + 10yddus + i 1 daus +  1 adx
de
dax
day
ax
ayt
et 12 dy + 12 F 20 haec reducta dabit: 10 X Ay adx ady + X dy au  x apd exdbus.
y) du  dex  ils ux d axady x
Ax
Sed simplicirem scribere possiumus. 
12X dx dAx + 13 Xaxclus + 14 Xdy dex +15 y dx Ade +16 de ddx +17 de dly  
y ay day ydy dux yaxd xdy s di sar di alx
+18 dx dydix + 19 dx dy ddus = 0
tus axadus
dy axdax
V
Geideaur ex quanam
differentiata talis oriatur:
X ex dux Xddx, dx et horum aequalibus
sit scil.   20 dx + 21 X dx dux + 22 Xdi ddy +23 Xay dldx +24 X dy ddus + 25 Xali, b 
2
y du ddy ydi dex Yax adu yax ddx
Scil. ex
dyt
linus difalis: D: x H 21 Suffecerit ad hic simplicur: X
+
P
uus diferihalis: 2ode x + 2Xd a +2IX dx x erc. seo hic illud vitiem, quod Prodit dudx
62
tu dau
dvadus
yay dd es y dis attus
ideo ascuntitiam aequaveno 3 esse debere talem, in qua sit relatio
inter . Co, deo, ddco. posito c dari utcunque ex X et y; ut
COdda +30 deo = 0 vel codd Cddo do 430do
vel dao + 30 Cd deo dded + 31 co ddo = 0
vel deo + 30C dio ddo + 31 co do adco + Zt co ddco
Et ata porro, et ut verbo dicam
Et
 ponatur co ddeo -g fiet aeq. vel 9+ 30 vel ( + 309 +31, ve l9 430 131913
Etc p.
et ita porro, nec apparet quibus aliis modis assumi possit progressio
deo
Verum cd esse potest utcunque format. ex x et y. formemus rationaliter, integre
homoeoptote sit Cd =  +41X _ lfiet cd do hod= dco = 41 dx adgo - 41a 
ay
a abcu deet hopsu
Cd ddco 430 de = 41X ddx +a1. Xadus +, AY  + 2. 30. 41 axau 20 Hoc si
arrax multipliitur hoc per a dx + dy, et fint a Xdxdix  etc. sed ita non assurmitur ad 
ydas
y cdq
unde tollendo xerus tollitur semulilila duus oportet ergo trasire ad ao, et t
y dy ddy
Verum Video jam quod omnes istae Hrypotheset ut 2 =40 codlo 2o
vel ded + 30 codio Eldio  31 Cd aco, 20 et An porro hur non profunt, quia non pe tolli
Ergo
X et g, s quin simul tollatur daco Xdax +X
disco redeundum ese ad pripum, motum maginae praecedentis,  sublato pruum y, dende X et du
in non ibsevari pommeontosis
 ady