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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 376v, page id 00068196:0748
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aady + xy dy + xy dx  cidy = a Xdx. fist
aadus aaddus + Xydoys L. Xcts L X y ddx + yix +
C
aaddy + Xydduys + X a + H cx dis + Xy ddx Hydx + X dyda 
+ aydax + a dydx = a xdax + a dx. Ex 1 est
dus ~) axdx = xydx - aydx 3:, a a = Xy
  aex ax-raX ydx- 2a Xy x + X y ex  rex 1 cajisx
a- 2aa xy + 47
Ergo ex aeq. 2 per 3 et Y
2
Aaddy + Xyddy + Xyddx Ly dx F ayddx- axdax  acx  
multipl. per at- 2aaXy + XXyyEF
ydX + Xdx F adx multiper axtx -xydyx - aysx per aa- Xy
s E
X Ml( per a X  raxydx-2a xyda + Xs dx + raxy ax ra it L
aeq. O. ubi jam abest du
n
Ex aequ. 2 suffecerat ex cerpsisse terulinos
ubi dlx et ddus, fiet aa + Xy ddu + X y- ayraxddx
sod si effecissemus prae explicando ut coincidisseat ista coessici
es
8= rZ+5 B+ + et fiet:
dexdax = mdaque +nddo et ddu = rddZ + Sddv.
X= me flio 4
ex Xy= mr ZZ + RSivV + msfuroZ + ntrpZ ant spept
aa F mrqe YddZ + aa +mrZ te Sddv
et fet
=arZ+ s0+F madque =a rzesvet n ddo
=a M Ztnvip madque = a in ZLNVip n ddv
+ pYZ7 F es madu + mr g2 et nddo
deverent aequari coefficiens ipsius daque, et ipsius deo
sed non pulo rem ette possibilem. Tantum hoc posui in exeuiplum
illud ergo videtur videndum an non ope aeg. 1 et 2. talis
nova haberi possit aequatio disferentio differentialis in qua
deus et ddx per easdem quantitates multiplicentur
quod videm sic eleganter obtineri, si duplici differentiatione quaera
hibita Hucti simus duas aequationes, quam spet ex
en
1d + dax t= ddeo, habebunue valorem ipsius adeo
asi aais rad pott eprecti
si hinc ddus Eidax haberentur rationaliter fiereo e 1 Lh 10 + 1 ax + 12 adlX + 13 adxdax, 4 psa 
ubi vunta summari possim et dividipotest in aates ut
ddus = 10 dex + 1d  ddx + 12 a cdx erc +   de
20a
isque valor est finitus omnesque termini sunt summabiles praeter si in
Hinc video si liceret aequadem sic transorcuare ut saltem evanesceret
addx: de.  smna fore rem reductam fire ad quadraturas, sed bx puto
hoc licene
21dx
20+214 +2. a0 + 23a e lax erc
21 du de
quibus est  dax
daq
x etc