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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 55v, page id 00068198:0110
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Veut in mentem alia ratio
sit aequatio differentialis data, ut ante. sit
dy idx = 10 + 11y+ y +13y:, 20+ 2y+229y + etc
fial d=
( 51+ S2 gy Fel 30 + 31y +32 gy f eu
60+0 y +62y9r eu
Ad ita oportet 50r51y erc habere Ferationem ad 60 +61y etc. qualem 0 ad
ut sit C = dd vel 6D+ a) dD, ut summa ex datis C et D posset haberi
per quadraturas. Sed haec omnia rurus nimis a miscent
An sic- dy: dx = C: D  et rursus = 2 h
ubi O et)
ssunt datae, et 4:  quaesitae quantitates  fiet Ot = 2D, et differentiando
Odq + GdO =  d2 +4d3 sit ergua O= 10+ uy4 1yy + 13y, et
= 20 + 21y + 22yg 29yh r et et 14 = 30 + 39+ 34y + 33 9 + ek. et
t = 40 + 4y + 42y y + 4313 + ek
do =  dio F ydu F gy di2 + y d13 CtC F, 21 dg + 2. 129ly. + 13. 113yydy et c = d0 axr dotus
Et ita in caeteris
a Ie dit sr  l 1oaB  Aoy di4
hd02, d10. 40 + d10. 41y + d10. 42yy + di0. 43 y + d10. 449 
+odu 
+ d. H1. 40 dI1. 41.
dy,. 1. H1. 40
1. 11 4
2. 12 q0
d12. 40
1. 11 42
2.12 91
3. 1340
di. 42 d11. 43
d12. 4 1
dig. q0
1. 11 43
2. 12 42
z. 13 41
4. 1440
di2. 424
d1c. 40
1. 11 44
2. 12 43
3. 1342
414 4)
5. 15. 40
2o. 304 dro 319 Fdro 3yy e
1. 21. 30
d21. 90 d21. 31
du3a
l. 4.31 1. 21. 32
vro E
11. dgo
11. 1. 41.
10. 2. 42
12. 141
11. 2. 42
10.345
l 0a3e
20 d31
58. 1. 31
dque  1
Odt t, 10 d4
os
dy, 10. 1. 41
12 d40
I dai
10 d42
13d40
12d41
11 d41
10 d43 1 1 nd 43
10 d44
131. 412on 14. 11
12242
1312. 42
1. 3. 43 R12. 3.43
104. 44 1114.49
10.5.45
Ita habemus ompientem  numerum arbitrariarum. s
sed video si haec ubi quaesita non ducuntura in se invicem, 
sufficiens earum numerus adesse. Ponamus qu aequationem datam esse
dy: dx = Xxtgy:, da
erit 10= XX et 12=1, et 20 = -aa po-
caetera omnia aberunt, quare nec assuruamus ultra F. yy, si licet et fient
aequaliones doo. 40 rrodad + 10 41 = d 10. 30 + + 3o;  fi4 2ogg 420.1. 31
10. 41
+2.12.40  + 10d41  10. 2. 42 e) = d ro 3 20d 31
div. 42. + 11 2. 12. 4
Lia at
2. 12 43 Ad
12d40
1e  d 
n.rgr ) = 1d2 33
()= 
20d32 26. 333
20d35  20, 134
20d34
it st 36, ex, 20
alqta evanescat vel proegreu
ut sa evanescat ent dar =0 H 43, 44 et
sumtur a1 pro arbitrio et 42 constans arbitrara, et 41, 40 pro arbitiio prorsus, fiet
habetur 3d per a) h, et 3 ser ag. 3, sid 3i pr aer d iet ho per aegi. 1, et haec dumnta quiditu a plata
2 d31
20 d32
21d30 ndzo et
21. 282
20.33
20. 2.31