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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 377v, page id 00068196:0750
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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
i  ax ax - 2aX ydx- 2a Xy x + X y ex + rax 1  taiis
Ergo ex aeq. 2 per 3 et Y
a- 2aa xy + 47
2
Aaddy + Xyddy + Xyddx Ly dx F ayddx- axdax  acx  
multipl. per at- 2aaxG + XXyy5
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. 10. ubi jam abest du
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 spep
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
+ pY23Fese madz + mY ge et nddo
deberent aequari coespficiens ipsius duzue, et ipsius deu
sed non pulo rem ette possibilem Tautum hoc posni in excuplum
illud ergo videtur videndum an non ope aeg. 1 et 2. tatus
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. onia fore rm reductam fore ad quadraturas, sed bix pulo
hoc licene
21dx
20+214 +7. a0 + 23a e lax erc
21 du de
quibus est  dax
X
daq
x ell