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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 411r, page id 00068196:0817
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ses explicabit et hunc sngitu sempulum
et fiet cbcod0
(13)
opinor tollet. Si jam semel habemus arquationem ob XaV, 1+ C + ma =0.
148
ob vdco, - 1 + fa + hb = 02
6)
i differentiali carentem, vel ummabilem  ob Xdco, a 1+5 + mb = 0. al codv, -1 + eb+ (a =0d =
vel summabilem ea
seu
linan
in quasartum unt
 vel sactem differentialem poram
etemgatam
poterimus in ea tollere supermlnerariam literam
dae
ope aequationis assumtae  nempe
quod si aequatio differentialis non sit simplex sed in ea
ex du ascendant ad quadrati planum, sen ad secundus
gratum poterit multiplicatione per novas
Efferentialies alia conflari, in qua priori addita tollantur
hiterminui. Ut proinde sutem reductionem diferen-
tialjum caelerarum ad rationales evitari posse.
Quod iffinet ad differentio differentiales et
puius reducendae ad differentiales, et hae demum
(2
ad summabiles vel summatrices.
pro y scribatur y= v +c
1
Xdy + X dx = y dy vdco
fiet Xdv +Xax= vdv codx + codco
assumatur aequatio nova: aD + bc0 + X 0 cujus differentialis
xde
aeda 1 b deo + dx v0 mulsiplicunda per ex, fV, g0o, et fiet
multiplicanda per Cdv, fded, odx,, et fiet
0
(20
ea vdo + eb codv +CX du4
fa vdco + f b codeo + f X deo
ga vdx + 9bco dx + gX dx
sursus ipsius aequationis 4 differentialis a dv + bdco +
multiplicetur per h v, 100, mx, et fiet
0
ha v do + hb vaco + hv. dx
La C0dv + l b codco + l co dx0
M a X de + m b X deo + m X dx =0
Si jam ad aequationem 3 addantur aequatio nes 5, 6,79
es ex omnibus composita aequatio 12 p
G1
ob vaX, ga + h 2  o lo, gb + l = 0 X
ta
ea quae ut
ernt omnes.
reddatur ctablis sugmabilis tolci poterunt
non suam
fiet e - 1 - ma f = - 1 - mb h-
(22)
- gb
lde
quibus quatuor valoribus substitutis in.
aequationibus 1F et 16 fiet:
-1 - a -amb  - gab 20
(24)
= 1 - b - bma - gab =
(26)
et (e 1+ a + maa + gaa =0
ublatis jam in aequatione 12, terminis, in quibus differentatis
et posito m =  -g. fiet a= - 1
iemas non suae restutrit
po
em, (quia sedv= Lvd, et iti in caeteri
(27)
compinatur
-1 vV -1, coCd + 1 XX Z 0.
d
+ ea
+ha.:
+f
+la
ex
seu per aequationes 25, 27, 28, fiet
2)C
=1 VD - ∞AdC + KR 0
e. F.
+9
m
29..
unde per aequationes 19 20 21, 22, fiet:d
Th: - l
=1 vD (1 coco + XX2 sed haec explicatio non
+
+).
=M .. M
-
e
 procedit, destruuntur enim ut
tam V, quam co
Ergo non procedit pot setro assumta in aegus. 27. 28.
=g.
q.
Ergo ex aequ. 26 fiet m= 1 + a4 gaa,: aa
3
t valores ex aequationibus 19, 20, 21,22, 32. substitui
et ex ea fiet:
debent in aequatione 29
-1 vo L1 100o + 1 XX sed ita oritur idem alsurdm
quod in aeq. 31. nam
destruuntur v et co.
+g
.
+m.
non ergo licet destruere, hoc quidem calculo) terminos
ma..
maa.
gaa 
omnes, sed ut generalius procedamus praestabit aequa
1gaa
tionem 12 comparare cuma, quatione gneral
limabili ejusdem gradus. Quod si ne dolat
2
ax i
v qco +r xD+FXO+ Wvi=
  auisio aridd val vervinti taduo teia uid st
Ergo a