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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 290r, page id 00068196:0575
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Va.
e
e e
Co dy sd dus
0 ge
re
ad
cd
+B
c
sit
Aequatio incrementalis
eu CaxG. 2XXy = aaX: 3aa y - 2Xyy = dx: dy
quid si faciamus dy5 = bco. seu y= acvidu
Inde ex aeq. _1 per 3 fiet Ep aeq. 1. fit
sublatis fractionibus 2XXydu -aaxdy = 3aa yd Exyyd
Undo px aeg. 3. sit 2XX aC. du =aaxdus = haa dx qud 27a c. dx
seu subtatis tructionibus fit.
2XX a co edyus
 aaxe dus
e+ ponamus e+ 1= 0 fiet dy
et
+
(6)
8.
e
ayre
haa dxaco dy- 2Xa dxco.
o et exegue scet
et in aeq.6 supererit tantum  seu du seu tidy
a
e
3 et proindi exaeq. 6 fiet fiet dy et 1) = 1 et
A
co
a 2xxaco- et ex ag. 6 divisa per co fiet
2XXa
a
ed - aaX = 3a dx - 2Xaadx. q et
ay
sublatis fractionibus fat
codu
leV
v
2XKa cody -aaXedco = 3a dx deo - 2X da dx dys
seu dy = 3a dx aed + aa Xcoco
ZXX a C + 2Xa4dX (11)
Et quidem ex aequ. 3.
ob aeg. 7. fit y = dy a: ed
 adeoque du ddus a: cd. vided autem aequationem
 nihil nobis prodesse. sed potius ex aeq. a descendendum
esse ad differentio differentialem; di et deinde epe nova
aequaddn lodendam X ut solum restet dx inde habebimus
ade caeterum
ia = dx: dy de dX: dus = Adx dy = dx deus; dus = dZ: a
Ergo tdx idu - dx ddyidu
(4
dz: a
si esset  ydZ = constanti aco ter e =Z7 - 5c
assumatur relatio talis inter exidus et dy: a aF
denique daz: a (sea houm valores ut ea supposita
aquatio reddaturtractabilis, et uuc absolute talis erit
verte.
conu