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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 58v, page id 00068198:0116
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6
1
K 3I a
P. 10.
R. I1. 31
1. 12. 31 +2
1. 13. 31 +2. 12. 32 +3
37
quid si si sic: retineamus
22. 430 Y21. d31 + 20d32
=24. d30 +23, d31 + e2 d32t y Bg lx, da + ydb + yydc + ye etc a 0+ 1bG k29) + 3Cyy + 4f Y+ et =3 -0
23d30 +22. d31+ 21 d32420d33
10, et sit aequatio
-du: dx = XX + gy, ∞XF yy, : da erit 10 = XX et 11 =0
 et 12 = 1. et 13 14 etc 20 et 20 = a4, et 21, 22, et C =C
et fiet 1 10.31 = 20 d30. Haec aequatio sep onatur quia in caeteras non
m
influnt, aeque enim redit 30. Porm
3. 10.334 1 12. 3 sa 1O. 31
20 d31 = (1. 1F 3B+ 2. 10.32
2.1032 + = 119 3 = = 20 d31
20 d 32 E 1. 12 31 A X +3. 10. 33
20d33 2)  X, 2. 12. 32 + _ AV
A+6. 34
H p 3, 12,33 + X . 5. 19.35
Ergo simo potius ordinemus
20d30 1. 10. 31 .eHaec ae quatio primaseponatur
20 d31 27 2. 10. 3
e
1
20 dur Z, 3 10. 33 + 1. 12. 31
20 d33  4. 10. 34 2. 12 32
20 d39 3 5. 10. 35
3. 12. 33
+d +1
aa d31 = 2 X X. 32. aa d, 2 = 31
si omna ponamus3
34, 35ek
esse 0, possumus facere
d32
d31
1. 12. 31
2.10. 32
seu dlng ()d(37) -
Imo video si conserves (2A (31
12
1 2. 10
32, non posse evilari
fini a ddg = 22 asqu dationem, q et eundum ad 33, vel 34, et
ita semper iri altius
e
do F L5. 81
Fsuiamus alicubi, ut in aeq. uto
. 13. 33 Btato d32 + 22d30- IE. 11. a +. p- -, 1. 1
22 d31 . 3
G. 13. 35, 5) 20 d34. 522d34
c6. 13a 36 (61 20 d 3f   a33 a 
13. 372 20. d3 6t 3. ter. d34. L
+
5E.
tel dc13, 24522, caetera absint fit
1.13.31 = 20438+ 
2. 13. 32 C] 20a311
f. 15.34 81 20 d33
2et. Aate
3X. .
k
c
3 et d34 +8  sed ita fiet ob _S
F
aa
etiam d32 = d ila per aeq. 3 et 4
habebuntur 30 et 3, 1, sed eadem
da adhuc semel per aeq. 1. et 2.
d Ergo non succedete. Ergo
36) et 35 a sit 0
obum
10. y +1 =0 yd10 + du x + 10dy 20 sit . aequatu  ryd et dudx + u   yx  ride
sit aeqratio data pydx + qu Ady. fintu qparando fiet B+ dio seu d’Esd  logi0 = spdx et u = siogax
b. 
x10
rdio tgdus dio + dd H. + 10 dl  = 0 _ ey 20y + Eidu  =0) differentiando fiet
+, 20 dgit 15. 70+ da  et ddy + d2y =0 sit aequatiodata pese lvenda ptet dus
421 sx
1. 15. 31 72. 142 +3,13, 33+ . 12. 34+5. 11. 35136 = 25. d30 424. d31 + 23 c3era 3 3 a t u dx 2 + dyti = 0 seu- dy: dx = 4: t = + = C: D. seu 2 D = (C. seu fiet
1 14.31 +2. 13. 32 43.12, 35+g. 11. 39+5
20: d30 = 1. 10. 31
20d34 =
X se
x
Pydxedxu Rgdydxi+ Y ddus +tdxax Multiplicandus hanc per 215rC fiet
Pf2: H) ydxdx et 9(2t. Y) dy dx  2ddus 14 A(El: Y) dxdx HiceB potest, reservari infinem
Hic d22 = E(2.Y) dx potest C rese duari infinem
Aosunt aequationes duae una d2o = (9 p: Y) 2)
aiere  42∞C  20 = (9.1321 - d2Ys quas duc erdo invicem fiet, 20 d20 = (Gp rr) 2i = 21 d 21 (p. 1)
= 2odro
Esto 10=11 = 12-
et extet 13
et sit 211410
ut eplet 20 et 22
d30 +20. d31