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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 85r, page id 00068201:0169
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dats
quaesita 8 =0 E = 30 + 31 y + 32y + 331 + 34y + 35 y +36y etc =0
d8 = d30 + yd31 + y d32 + y d33 + y= d34 etc. e B6 + 1. 31 + 2. 32y +3. 33y + 434y etc. dy
seu ede seu  dE+ dody = 0 seu dy = - d9: 49. jungantur aeq9. 1 et 8 fiet
Od + D d920 Quae debet esse identica saltem virtualis, cum ipsa aeq. 4. jam
aeq 4 est indivisibilis, ex hypothesi, nam talem assumere licet, ergo non si aequs. 4 et 9
non sunt formaliter coidenticae, oportet aeq. 4 posse diti esse divisorem aequationis 9
Explicetur aeg. 9. pet
20 d 30 + 20 d31 y + 20 d32 y. + 20 d35 17 + 20d34y . ...
+ 21. d30 y + d1 d3iy +a1 d32 y + 21 d33 )
+ de d30y + 32 d31 y + 2 d 32y ...
+83 d3017 23 d31 y
...
+14 d30...
FD. 1.51 F 63.G + f0. 3. 339 + 10. 4349 + 10. 5.351)...
+7. 1. 31y + 81. 2. 325 4+1. 3.339 + H. 4. 34y...
Fg2. 1. 31 y + P2. 232 9 + Y1. 3. 33y....
F13 1. 31 y+ 13,2. 32y....
+14. 1. 3, y.. . .
dividatur haec aequatio 10 per
aeq. f id est 5. ita ut  astendat
sitiavet a 3o+ 3IGy. vel 30+ 31y133G
vel  30 + 31y + 3279+33y
et ita porro
Sed quia divisio instituenda est per , e praestabit ita scribere
aequationem 10.
3ed301434212 d20yix
) vicquia est super
lineam  unam
quicquid eA superlineas tres
valet si  sit 30+ 319+32y
quicquid super tres quatua
valet si 8 sit 30+31yt3ry
et ita porro
sud
1e a319+V a3y +~d31y+ 23 d3, y
1
90d32 y + 2d32 y
valet si Gpoheth
l
H1. 232y F +22. 32G + (7. 2.32
itaque ordine rem traetemus unum gradum aequationis
quaesitae 4  vel 5, post alium adhibendo, ut appareat
quid in eo fieri possit  reductibnead  et atm
rationales
ad quaenam aequationes differentiales datae
possint reduci ad 30+31y.,  deinde videbimus etiam
quae rationales differentrales datae, possint reduci ad 30+317+ 32y,
et ita pergemus donec sese offerant aliquod treoremata 
vel saltem Tabulas condemus in oblatis usui faturas.