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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 184v, page id 00068199:0368
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4
hic jam magna dificultas
quomodi possibi liceal futo ex senebus
nfiuitis per regressum eruere finitam
X+
E relationem. Num ita fimitam enemis
sud determinati progressus quod non est
sates determinatum,
remedium
od ibi e videtur ades
sit exddy=y ard
etiam non solum adcibetur posilo ddx =0
sit y = 11X + 1X + 13X + etC
 X Ady = 1.11 4, 12X + 3. 13X + 4. 14X
deus =. 1. 2. 12 +2.3, X +3. 4. 14X et
et XX ddy = E2 112. 12X +2.8X3 + 3 4, 14X et
= 11X - 12 X - 13 X3 - (, 4X eu
Idque probe notandum. Cum
t alias ista impossibilia non videantur. impossi–
quod est impossibile
 bilitas a oritur cum id ipsum restituitur le ipse
 ed pelittum cum idem ubique grabus ut xxddus
y,. quo casu evanescit constan-
um evanescunt ipsae quaelitae, et oriuntur aequa
sed sed pari jure
+
xdy,
ts
absurda esset aequilio: Xaque L _ ydx
tiones impossibiles
lamfir sit y - 1X = 12X + 13X et
iy = 1.11 +212. X + 3. 13X tM
et fiet +1. HX + 2, 12X + 3. 13X + ecc 2 = 9
= 1. 12 - 1. 13X el
3
Qualio
est impossi
ali. Et tamen data possibilis videtur. Quid ergo:
a L 12
- 1. 11
fati an hoc indicat rebere fieri yL 1 + 12
X
a
3
1
3X
A it-
13
ila rumpitur
concursus incognitarum recum ipsis earum
etet du = utt=
et
1. X
2X
C+ adxar
sit ax dldu = y dXaxtiola +1. 2. 12X + 2. 3,13X +3. 4 14X e
2E sublatorius
C-10 = 11 X ~ 12 X 413X er
fit 10 = a et sed 12 = Z H et 1 = 1I XIC
et y= 10+ ux taxeu
et 14 = f. 2. 2.3. 3. 4H1 et fit y = a + = X +
2
2
1. 2
+
1.203
1.2. 2.3
1ZX F
M. sid mirum idem prodire
nisset aequatio t plena,
G alia.)
e aut ddx =0, prodiret idem, et tamen diversa
t
1. 2
4X
ed quid sic
aequationem differenlratem
c primi gradus ut suxu vdx, + adu + adu=
0 Led
sumamus
dydx +yddx +oddytgdus + addus-
curva
inde invenietur muntis ore nonc e per seriem pasito ydd q = 0.
rbret
disterentiando
e
ipuissut agax t adaxt yda + dy + ady. fed
lormus hanc posteripe non esse possivile. ec licer sic fingne
sed eadem serins prodibit
e 
quo a