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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 53r, page id 00068198:0105
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si sint duae quationes datae in quibus v, y, dv, du, per H affectiones
ipsius X, simplici modo, seu ut nullus sit invicem ductus affectionum ab y et v.
videnmus  quomodo  re dutantur ad aequationes, in quarum una
absit v, in altera y. sit 1d 10 a 10 dx + 1 dv + 12 dis = o
et 20dx + 2) do +22 dy = 0, ubi in 10 et 20 pono latere v et futcunque
omanus e sit 10 A1C V ex + 121ydx +, 1120 + 127 dy 20
et
Egdx + 2U1 vdx F221 ydx F 212 dv + 222 dy =0. Fingantur duae aequa-
tiones quvde + ar 910 dx + guvex + 912d0=0 et groadx + 921) a quadus
Addantur in unum Aeqq. 1 et 2, multiplicatae illa per 901, haec per 902, et tertia
100. qu1 adx + 111. 901 vdx + 121. gol ydx + 112. 90l adv = 122901 a dyg
multiplicata per 000, et fiet
200. 902 adx + 211. 9orBax + 247. 902y dx + 212. goradv + 22.902 ady 2 =0
900. 910 a dx F000. G1I VdX
coincidens cum
+ g0. g21 ydx
a
8000. 912 adv
Si
+gogrradus
000911 =. 111. 901 +211.902 000. 912 = 112.901 + 212.902. u
die
fint C iE 1II. 112, 801 4 = 000. 112. 911 = 112. 21.902. Ergo 802 = 000. 11. 9 1 -000.112. 91
 920 adx
11I. 112.901 = 000. 111. 912 = 11I. 212.802
11I. 212 = p1Z.~2 211
000. 2 A. 917 - 000. 211. 91
Et pari sure 801 = Z11. 112 = 212. 111
Restat 900 = 100. 901 4 200902 - 000. 910, : 9 0 = 121. 901 +ru 901 3 . 921
 une 921=
8IC
qualoor 100a ax + 110 vdx + 10c a do == 0
20 y dt es an quibus
dotae
desiderantur u qu
siut D=  
20d alx + 2t0vdX + Ediais =0
i + cZ r ea,: d
eritu ep ( +10ga d X +uObW dx + 110 CZ ax
noeaex
220yax
202
y- lid X mZ + na: a
101 ab du + 101 aC d.
+nonadx +holu de L 120mZ
+10r aa de + 1oial db + 10l a 7 de
o2 aadu + ior addal + 102 aZ am  + 102 a ldu +102 am dz
en 101 b +1928 = d
eritus l= - 101: 1 + 1obly = 4101 6.
tgota de
potest poni in = 0 et e = 0 fiat du= ol b + claoz L. Et 
i
alor.
Loi-node sed  video ita fore et 101 db + 102 dl =  adeoque et 110b t120 l olatoletur lo et alo
OetD, seu exalitationis eatum lvare
ex 1012 = 10C. 162 quod non licet
 video cadditionem in unum diarum aequationum juvare
de
e non licet
arum ( et D per
a n
120y dx
dC
tum diversimod
aequationum quatuor ope
00 a 
2
 H bita explicationibus
9, tollatur duo habebitur aequatio in qua solumt
C
ell
quid
a
qua
a
colle
ldca
dopaeter
du. Itaque
et W
et
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tuo