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# Piece: https://leibnizlegible.com/api/records/894/text
# Catalogue record: 894 — [Aufz. zu Differentialgleichungen]
# Incipit: xdy + adx + ydy = 0 (1) cuius differentialis
# Date: 1690
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=894&katnr=58475
# Work: https://leibnizlegible.com/work/00068047
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 2
# Folios: Bl. 6r (from the shelfmark LH 35, 6, 2 Bl. 6r°): 1 page, canvas 11, page ids 00068047:0011 to 00068047:0011
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068047&page=11
# Lines: 61 recognised on 1 of 1 pages, mean confidence 0.78
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 6r — 00068047:0011
# Source image: https://digitale-sammlungen.gwlb.de/content/00068047/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 61 lines, status machine
exdy adx + Aydy =0
cujus differentialissH
lonamus d
BO aa
B
2
sint sx dy- acd
X ddye + Paxdy +sa ddx + Ayddus +aydu
 mx dy +nydx + pxex + gudus +ratx+ tal
Et differntianto ipsam 3. filt: M Xdd + maxdy + ny dax + n dydx + 
Pxddx. + paxax + quddue +geudus + raddx + taddy =0
sequationes 2 et 5 (mulliplicata pliua per h) addantur in unum
fiet: +MX daus + maxdy + Laddx + q yddys +q aydys + 
6)
si
+ ny ddx e
+La ddy
+ pX ddx + p dxdx
formulam arbintu
praeterea aeq. 1. multiplicetur per arlitardam fax + gdy- talem
ut fict homogenea ipsi 2 vel E vel 6 et productum multiplicationo
enit tr fxaxay + afdxax + fy dxdys + 9xdy dy + ga Klyrgy dy
addantur in anum aequationes b et 7.
+in Xddys +r a dex +quydy +q dydus
h
es
t
emaxay
+n yddx + ta ddus +pXddy pdx Ax d
fiet:
Exaraus +gxaya
axdy
al
e
a
potuissemus quidem promibiliaria fdX+ odue sumere fdx+gagik B
Afum itemque for tam ag. 3 multidicare per similem arbitrariam, sed
videamus quid 3fut, abstinendo a s in differentio differentialibs.
sumotur jam alia formula differentulis nedulus 10f
 dictn (adxuli +  n fay. G+b ai seK. XrC
+ Ca (1a ag +15M: 19y+ISXFb + 16 X: a + 17 y: a =0 quae differentiata
lio ddu +nddx: 10dy+naX 
+
det homogeneam ips E
nam ex ipsa differentiata sublacis fractionibus siet :36
a 14 dy +152X 10dy + 11 x + 10 ddy 4 nalx. 14y 415X + b 6, 2
X1bdx. 10dy + ndx. 149+15K +b + 17 dy. 10dy + udx. 149+ 15XrI.
quae aequatio 10 Eomogenea est aequationi B. Sed quia video
et quidem plena, sed quia in eq. e deest yddx et Xdda: poco ad sup
plendo aliquid aequationem diuisam prius perteax differen
tamus, fiet: Xdy: dx 4 a 4 ydy: dx 20 seu Xdydx: X + Xdly. dx+ dy
sed non sul cedit. Num istud. itaque si volumus ira retinere plena
e1
potusset initro fieri: X = 20∞+ 127C et y 220+23Z+a
quae sobstituenda in aeq. 1.2 ita tamem ut in a9. 3. meet tantum puo xseriba
tur x et pro escubitur  ilemque in aec 9 et 10. tiac melhod u
replebimus oes terinos, si jam hac arte resdamus vet e comparabiles. et e
ipsam et surmabilem mac summaeissius ad axB Gaem
imgemus se Bhd est vai
10
2