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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 199v, page id 00068200:0400
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quid s sic
(2)
Sit 104 11X +21 y + 12X + 22V + 112yX etc =0
et X = trationaliter ex Y, Z.
et y = rationatiter Ax V, Z. hoc enim semper
25
potest intelligi. Tollatur X per ex et y ex aeg. 1. per aeg. 3.
fiet aeq (4) ubi solum _ v et Z quaeratur dx per aeg. 2 fiet oqui
 sit jam X ydx = co
de rationaliter ex H, Z, dv, dZ
iv se
perco
a rationaliter V, Z, per ae9. 3 et 6.
habebitur
1x oq. 4 quaecatur
e. do. d9 _ rationaliter er y v, ex09.5. sitt
L
a
audem
et per aequ
I quae eq. 7 ita compo Ex 8g.
tollatur L peraegus deniu ex aeq4 quaeritur eju differen
tialiis v,Z d dec dz. dv= v rational. V, E Husope
s
ex x tollatur dZ cb quationum 8 et 4 opetollantur
 et ex 5g. 7. habebitur ag. in qua supererunt ed, V, di
s
 set rationalis, si co sit simplex habebitur quaesitim
revius resumamus; 10 + 11X + 21 y ere 20 seu gat. X, Y=D
in qua
=30+g1V etc posito _ 30, 4uetc. dari per Z. similiter Y = 50+ 5iv erc
50 60v
60+6cVen
40+41v et
du nt rationul B  v, de,  dZ (posito h sdx 0. Ergo
4)  20+71 ve
per 3 et 4, cd = ratioval per 5. dx =
16
sit Vde =co Ergo per 3 et 4))
uled
Au
ut
8o+divere de
ge 3 vL 90+gIB ora C
A0 HoVe
te tren
a
100+ 101 v  d + WoIBM
120+ 121 V CK
 subestituendo X et y valores in 0g. 1. sit ratumlx
c7
130 + 131V + ( et 122V etc. =0 posito 130, 131 ete
a
dari per 7. jam ope aeq. et ejus differcatralis erit
A
lx. du
190 +14 1V + 142 st ek
180 + 15IV + 152WV etC
jam
x 6y. (66 tollatur dv et v per 8y. 8bE
siet q in qua 4Z dn v, y Cd  de cot) 160 +161 veca
dz
actenus
=170+ (7Ivet
omnia acta sunt per meras aquationes simplices
Sed nunc tandem opus sabstituere sollere 
ope aequationum 9 et 7. et debet haberi
D: lz rationaliter ex y. Sed at hoc melias fiat
t
L
16
C
umatur potius aequatio arbitraria
 e
de
100+
iva
190 + c91V et
ibi 100 et 181 et 190, 191 et. sunt arbitraride per
E 2
aequando 18 et 9 habebertur aetque 200 + 201V + 20E v et
es
quae aqualio debet coincidere cum aeg. B 7, seu debent saltem habere
omuanem divisorem, adroque Talleudo v ope earum debet prodire
u
sesiditum evanescens.
e