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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 129v, page id 00068199:0258
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0 = 10 + 11y, differentrando det o- d10 + y d11 + 11 dy seu ddy =- d10  y du, quod conferendo
dutae differentiali dum dya = 20dx + 21ydX fiet dnc: 11 = 21 dx et dio = - 11. 20 dx
0 = 10 + 11y + 129y differentietur fit d10 +y d 11 + vyd12 + 11 dy + 2. 129dy. + 9y 42
Do
quod si jam 2 sit constans fiet d10 + y d11 + 11 dus + 2. 12y dy = 0. Esto jam
data differentialis 102∞ 20 dx + 21 (B dx + 22 d + 23 dv. faciamus
V = y + 31 fit de = dy + d31. Ergo ex aequatione data fiet.
0 =
20 dx + 21. 3dx + 21ydx + 22 dy + 23ydy =0 ~ d10 + y du + 1 dy +2. 129 dy
a 20 dx
+ 22 d3) +7 la + gedus
+29y13 239431 2331d9
2
i d31
coincidentiando sit 23 = 2. 12
21 dx  da seu 1 = f21 dX
11 = 22 +31 Ergo 31 = 11 = 22
11= 22 +23,.3] d1 = 21+ 23.8
Ex hac ullima fit 11 + = 21 dx + 23. 31 sed hoc = 22 +23. 31. Ergo fiet
Coinciventando primum primum fit 2.12 = 23.
25
(21 dx = 22, quae est limitatio. sed ita 31 calculum non intrat
V = 32y, et do = 32 dy + y d32 ex Et ex data C
fiet 20dx + 21.32 ydX + 22. 32dy 47,32. 32 ydy +23yy d32
+ 22 Y d32
+ 2397 d32
faciamus
st 12 = 23. 32 + B
et 12 erit constans
sed ita  non est similis formula
25 2. 12 = 23. 32.32 = 2, 23.32 + β
20dx + 21 V dx F 23 dv + 24 vdo
fint ae = 3yee di4 + yd13 + 13dy
22. 14. 14dX + 22. 2. 13. 14yax + 22. 1313yy dx
d
sed ita 32 adeoque
Juo et 11 frat constars, contia quam oporbt
L22Vex
20 dx + 21 V dx +22 vV de + 30 d v + 31 v do = 0 =0 fiat V =
sit da la differenlialis
20dX + 21. 13ydX
21, 14dX
30d14 +30y d13
3I. 14d14 +31. 14y d13
+ 30. 13dy
+ 3l. 14. 13dy
+ 31. 131
+31. 139y d13
+ 2. 12 ydy=
12 = =. 31. 13. Ergo d12 = Z3Bd13 + L 13d31 = 22. 13. 13 + 31. 13d13. sed ila
+1. 13y d4
recidetur in quaesitum. Ergo multiplicetur per liucem una aequalio per 2. 12
+ yd1
a0
+ 11 dus
+ yy d12
alter a per 31. 3 et fiit 31. 13 d12 =
2. 22. 13. 13 12 + 2. 31. 13d13,12
2.30. 82.1 + 2. 31. 12. 14.6
d. 1 = 31. 13. 2 d30 n 13 + 31. 13 2.90. d1. 13431. 13. 2 30 12 d1z
e
adeoque
12 = 2. 22. 13 2. d13
31. 1
20 + 31. 14
2. 30+31. 14 d12 + 2. 12 d
2. 12. 2. 22. 13. 14 dx + 2. 12. 30 (13 4+2. 19. 31. 14. d13 + 2. 12. 31. 13d14
d11 = 283 2
A1
et frat
30 +31. 1, 12
de2 = 4. 22. 13, 14 dx + 2. 30 d13+ 2. 311 4 d13 + 2. 31. 13d14 -
2
2
20 + 31.
2
ad
13
d
30731. 14
1
si  ene affectiones a 14
Et
oErgo in aeq. 4 ponamus 13=
fit 3112 = 2. 22. 12 dx  seu dn. 12=
un
invicem
haberi ad 14, nec opus aat adhiberi a)
non ducum
imo polesfieri 13 =1
ipsiu 31 L aequando fit L1 = 4. 12 14 f 4. 31 a14) = 2d30 ( 2. 31 d ).. et duos ipsius d12: 12 vatores aequando, fiet
idenim in pelestata est fint 3c du
2. 30d12+2. 12d30 + 2. 31 12d. 4 72. 1 4112 (d A =
t2.
Bdi quos duos valore
Ruisus 31 du = 4. 22. 12. 14 dx
.22. 30 d + 2. 22. 14 dx = 2, 22. 51. 14 dx = 31 d30.
OF. 31. 14
R sumamus pagina versa, nam veceor ne
quis sit calculi error
Et ita 14 habetur ordinarie
13y + 14
Hoc coincicentiandam
hydy
4 psi C
20
+ 3
2. 22 134
31 12d