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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 2
# Folio 6r, page id 00068047:0011
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exdy adx + Aydy =0
cujus differentialissH
lonamus d
BO aa
B
2
sint sx dy- acd
X ddye + Paxdy +sa ddx + Ayddus +aydu
 mx dy +nydx + pxex + gudus +ratx+ tal
Et differntianto ipsam 3. filt: M Xdd + maxdy + ny dax + n dydx + 
Pxddx. + paxax + quddue +geudus + raddx + taddy =0
sequationes 2 et 5 (mulliplicata pliua per h) addantur in unum
fiet: +MX daus + maxdy + Laddx + q yddys +q aydys + 
6)
si
+ ny ddx e
+La ddy
+ pX ddx + p dxdx
formulam arbintu
praeterea aeq. 1. multiplicetur per arlitardam fax + gdy- talem
ut fict homogenea ipsi 2 vel E vel 6 et productum multiplicationo
enit tr fxaxay + afdxax + fy dxdys + 9xdy dy + ga Klyrgy dy
addantur in anum aequationes b et 7.
+in Xddys +r a dex +quydy +q dydus
h
es
t
emaxay
+n yddx + ta ddus +pXddy pdx Ax d
fiet:
Exaraus +gxaya
axdy
al
e
a
potuissemus quidem promibiliaria fdX+ odue sumere fdx+gagik B
Afum itemque for tam ag. 3 multidicare per similem arbitrariam, sed
videamus quid 3fut, abstinendo a s in differentio differentialibs.
sumotur jam alia formula differentulis nedulus 10f
 dictn (adxuli +  n fay. G+b ai seK. XrC
+ Ca (1a ag +15M: 19y+ISXFb + 16 X: a + 17 y: a =0 quae differentiata
lio ddu +nddx: 10dy+naX 
+
det homogeneam ips E
nam ex ipsa differentiata sublacis fractionibus siet :36
a 14 dy +152X 10dy + 11 x + 10 ddy 4 nalx. 14y 415X + b 6, 2
X1bdx. 10dy + ndx. 149+15K +b + 17 dy. 10dy + udx. 149+ 15XrI.
quae aequatio 10 Eomogenea est aequationi B. Sed quia video
et quidem plena, sed quia in eq. e deest yddx et Xdda: poco ad sup
plendo aliquid aequationem diuisam prius perteax differen
tamus, fiet: Xdy: dx 4 a 4 ydy: dx 20 seu Xdydx: X + Xdly. dx+ dy
sed non sul cedit. Num istud. itaque si volumus ira retinere plena
e1
potusset initro fieri: X = 20∞+ 127C et y 220+23Z+a
quae sobstituenda in aeq. 1.2 ita tamem ut in a9. 3. meet tantum puo xseriba
tur x et pro escubitur  ilemque in aec 9 et 10. tiac melhod u
replebimus oes terinos, si jam hac arte resdamus vet e comparabiles. et e
ipsam et surmabilem mac summaeissius ad axB Gaem
imgemus se Bhd est vai
10
2