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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 17r, page id 00068043:0033
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B B. pay. ullima pro ifferentialibus so evendis
et quod aequalio summatoria. determinatioo diffelentiali
at
sit aequatio differentialis generalis, differentiis non assurgencibus  ad potestatem
a 1bxacygexpxyeg.
a +bx+ cy ++CXX+GXy+gyy dx +lemxrny tpxxtqry tryy dy aequ. 0
rationalis
bic
10eo y assumatur ejus valor in teger, per x et novam assumtitiam v.
seu py aqu. heexin dicxillhorxnormm
Si
1 aequ H + 1X +2V + PXX +  12 xV + jo
et sipt  aeq. 3
substituatur is valor in aequ. 1. ascendet D ad stum gradum in aequ. 3.
ssumatur aqu. 4. et fiaut formulae tollenda numerus viginti
in gradu primo enim sunt mediae participantes de utraque: een
sunt numero  in est nulla, in secundo una xB, in certia duae,
el in quarto tres XB. X Yp. XV inquinto quatuor summa
X1B W
facit decem, quae bis sumenda tam in dx quam cu ax, facil 20.
At in aequ. 2. sunt solum C arbitiariae.
Aequation. 3. uddenda et forcunta arbitraria
differentialis generalis, summabilis. Seu diffednera
formula generalis: 6+ 3X + 4v + 3 XX + 341V + 4 v ec. usque adi
e
ubi erunt arbitario cirius differentia etiam eris  ascendet ad ro
ubi etiam erunt arbitrariae ubi plures nova habebuntur arbitrariae.
sed jam video prodesse solum nobis 34XV. 634Xv. 34Xp
etct usque ad 3C34 X BE quae sunt numero (1+2+3+4+5) Quindecim
unde addendo prioubus 6 fient 21.
videtur sufficere ut faciamus _ aqu h4 KX + V
y aequ h + fx +Z v. et substiluamus valorem in aequatione 1.
partfiat a +bx +.
(3)
Oaeqo
Bato pusx
+ CXX
ch +cfx cZV + fAxX +f7XD
+fhx
g
tnar
+otax tersa
Ztirtz iltb
qta trH
rh b)rhtx+(ta
H1Z XV +BvDZd + βX
O
0
l
I +mX tZB+ pXX + q22V +rZZBB
nh+nFx arzo + Px +97XD + rZV Fdx nh + nt X +
+BY
22+ r1Z7 + D ∞9
d.
Id
Ih Eghsa Xgliqv +gFx + Eg ZXV + 926
 4. M X
Hd, ei senso) r trhtxrs EV + r Hux
+B vodxAu Exvdo
4
7
10
C
aequationes A. B. C resolvendo evanestt
2. Exaequ. C fit qaequ. 29
exaquiA sit axtrea m. Est. 29. equ. h facita put est in cerso
u
+) ex 3B d
si
s
dutu eficere ut qil
a qu. 29.