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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 93v, page id 00068199:0186
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siom dx +, dua t att n dx + 13 an
10m + un + 12 diffeentiando 10dm + mdio + 11dn + n du. + d12
Esto aegus. 20dm + 21 mdx + 23 dn + 24 n dx + 25 dx = 8
e3 (tom + Hn) dx F sit g = rom + un
Solvi potest (ex rgyax + dy. sit y - tom + un
qux + P y dx + + dy
solvi potest fdx + gydx +hdy = 0 sit y = 10m + un, et fiil aequatiosruble e et fiet
Squalio solubilis fax +g.0m ax + ∞ un dx + iolam + utan = 0. haec comporretur dalae O
fiet 10 = 20:h et 1 = 23: h et f = 25
120 -2odh = l20- 20dh. et g = 2h = hdro = 20d 4 24h - hd 23 +23 dh
+Em dio n du1
21 = g. 10 + hd1o C seu g = 21 - hd10; 10
24 = g. 11 + hdu seu g - 24 - hdu: 1
du
et grodx + h lo = 21 b
Unde si calculus probus sequeretur rem succedere, seu haberi summabilitatem aequationis cqualis 
dio = hdro 2odh hd10 = h
tch 20:h
in quibus m et n nunquam habeat
Resumamus Dectasit aequatio differentialis trium literarum, m, n) solbi potest ( dx + qydx + hdy =0 sit y-   +60n
erit dy = 4in d40 + d
affectionem replicalam, ut 20 dm + 21 m dx +33 dx=0 dato
dn
31 n dx
31, 1ondbo +fix = 3.
g = 21dx - hd40, 31 dx - h d60
40 dx
om ax g6onx
60dx
 40h = 20 60h = 30
h d4o = sid (20: h) = ( hd20 - 20 dh = hd 2o  20dh, et g = 2 1hdX -hd 20 + 20dh  uh dx - hd2o + 20 d h
c
b
a 60 du
Exprodibit
q4n fiet f = 23
sed pari jure h dbo = hd(3o. h) = hd - 3odh et g = 31hdx = hdzo +3odh seu g = 31hdx hd3o+ 30dh, quos duos
t, (20: h) dx
e
d: h) dx
20dx
30dF sed ita evanescit h
BCha∞ +20. 31 hdx - B20h d30 ( 2030 dh =0:
quod non mirum. putem tamen succuri posse per arbitrias fiat  2odp + 2 pdx + E3 dx et fiat
30. 2
1. 30)
319dx
30hd20
o= c0m et dp = sodm + m d5o g = yon et aq = 7odn + n d70. Ergo in 1eq. C pro m et n, pe fudo p et 9, est
dq
explicando pper Som, et 4 per 70n, fint exaeg. C. 20. sodm + 20 mdgo + 30. 7odn + 30mdzo F 23 d
=O
on x no 50 et 30 substituantur
40h = 20. 50 60h = 30. 70 9= 20d50 + 2150dx - hdgo Y 21 3 
valores ∞ = goh   20dso = 20, 20godh p 20h d40 - 4oh dro - 40dh + hdg6 - 4 teda) goh d2o: 20) et 30 d 7 0 - bodla thd6o eh as
Ergo ex ducbus mabbilbus ipsus gnfiet aodAM 4. esu d 40 ) h duo + 21 L ex C m. 14) = ut A n 190). h ago + 31  ( hac
10
66
Licebitne in data aequatiane O poro m ponere  p+9 et pro B ponere +p f9
essi lergo ne sit quidem nam quaesita evanescunt
piastar
o= 4oh20dm +40h 3odn + 40 h rimdx + 4ot. 31 ndx =F 40t. 23 dx
h = 20. 40gdx :, 40. 21 _d X - 20d 40 - 20. 69 glx:, 40. 31 dx - 20460
0= 20. goh dm + 2obohan + 2olmdto + 2ohndbo F 20fdx
+ 20940m dX + 20gbonax
40. 40.31 dx - 40. 20 d60 600. 21 dx - 60. 20d40 60= 684. 30, 20 unde
40. 30 = 20.60 seu 30: 20 =60:40
a 60 = 20. 40d30 +20.30d40 = 40. 30d20, : 20. 20 20460 = 40 d30 +30d40-40. 30 d20
et fit 40. 40. 31dx = 40. 40 d30 - 40. 30d40. + 40. 40. 30 d29 = 4 V 40. 40. 30. 21 dx 40. 30d40
Unde omnibus divises per 40, fit 40 sc3idx
20
ille
corax
 sed tollendo utrobus - +0. 3od40, connescit 40
et fa 21 dx = d30  L30d 30 = 30riap