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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 114v, page id 00068200:0230
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Z aeqpu. X
dZ aequ 1 V d.
Q aequ y.
Raegu.
dx ae qu 1 Z dy + 2y AZ per aequ. 3.
de agt
Zaequ vx. vaequ. yZ. per oqu. 
vaequ. 7
Xaqu. Zy
per aaequ. 1.
y aego vr
per aequ. 2
dy aequ. 2 vdx + 4X do per aequ. 4
+ Jay
aip. = FXdy
=4) y
ubi notandum numeros 1.2. 3. 4. in aequationibus differentialibus 5 et 6 significare nn numeros, sed signa
variantia, seu unitatem signo affectam.
Ex aequ. 4 et 5 erit: dx aequ. 1Z dy + 1  2V X dZ
Ergo X aequ. dX - 1Z d7 per aequ. 7.
DX aequ. dy - 30dx per aequ. 6
Aequando valores 8 et g. fiet: 4 dx dv + 2. 3. V dxdZ
20 dZ + 1. 4Zd
aequi dy.
Hunc valorem ipsius dus substituendo in aequ. 9. fiet: X aequ. 4 dxt 2. 3. V pA q- 2. 3 vdpar 34BE 
2. 4v +odZ + 1. +4 Z dudo
seu sublatis tollendis. XC et quia vZ aqu. 1. fiet X aequ. dx - 1. 3. de
am v pequ. . et se
quicquam. E Dubito
2V 1Z + 1. 4Z d0
vZ aqu. 1. et  Zd0 + Ddque aequ.o EEgo tolluntur omnia, nec proinde habetur
uit
Nac lirefsetiam sic procedere: dZ dx. + dZ 48) aequ dy 1
ut inde fiat datum
du aegr. a +bx + cyelry e
5+grahyt kxus erc Namoypun t dx _ii d7 
Nam ge aequ. X et 96
aequ. X
. Ergo Z aequ. X (6) X
61
et fiet: Ax L + X dy -ydx ) yes
V6)
+(5)(3)
et de aequ Xdy -ydx
216+  B) aequ dus y. et reducendo fier:
rgy X () (10)
y (4) 10) 6) (6)
Hac methods ob multitudi nem arbitrariarum putem prottema
quo explicata quantitas
pro arbitrio conferenda
esset cum data. Sed hon minuis
(2)
semper rebuai posse adi quadratures dx at dX N + dy Y + dx L.
a dxax
Ax X + dy y + dr Y + dy X , dxX
soelsus)
et du aequ X dy + y dx sit jam formau : X
degu X 7
20417
cujus differentialis gentratus
d24. 25
ey + X
dx + y dy fula
+ y34 935 qu0
24 25
136537
xle q
C (eot () + ad
ponendo Zaego XY. hoc formula generatis supra (t e 2.H
X + y
Xau ax
du ()
+ d ib - 17 dx + ∞ 269 du7qu 4 y 36t 217 49 16 dt cqu0
videndum, an tali formula ad date  adbita vel et tas
Is posse fieri, niti jamtum
u
(14) 9 (5) 4 dy X
(613 (17)
aqu. cujus differentialis generalis
ius.
∞diz
10t (1)
X significat
X aliquam
seu utcunque quo
sitam ex
abfracta vriatur semilis ipsi 4. sed hoc video non
merrimu et plan admirabilis compendium aequa–
tiones aequationibus conferendi, si quia hoc modo etiam maxima for–
mala ad paucissimos terminos reducitur; et si aequatio aequationi et
comparabilis, etiam in hujus modi terminis sibi comparabiles erurit. Ita
in aqu. 4. explicetur dz. per aequo 2. quod gueniet comparetur cum au
fiat. X
iqtqsx + Sed hoc ut fieri possit reti video omnia sic
x instituenda ut formulae generalis ex X com-
posita non scribatur hoc modo X, sed  +X X ubi notandum X22
esse formulam aliquam generalem ex X compositum et per X divisibilem.
vel etiam scribendo
X. intelligatu dX  Z aequ. X
22 verum in calculo differentiati pluliaris oritur difficultas
Nam da5
E explicando dque per aequ. 2. in et comparar possint qu.
X du + 5ydx. ubi posito x esse multiplicatilem
per X divisibilem idem crit Xq det y dx quod X dus xyex seu  qarique dx nam si x
non est divisibilis per X tunc Xay E5 habet partem referendam ad .
a + 2 + 3 + 4 + 24. 42 + 34. 34 aequ.o. he diffentialis de ax + de du + 42 dra de, + 24 d a2 ady + 43d 34 ly 1 frgo in aequ. 5. explicando differentias et subintelligendo eos quibus exc ascriptm est sub eorum primo fiet 
L13d34.  +34d43XC d. +22d42y + 42d24 634d43y
no- drodu vy 6+67.76458.85 5+57.75468. 86. fet
1ago 0+