# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/21601/text
# Catalogue record: 21601 — Tentamen ad providendum, qvosqve ad summum assurgere possit curvae differentialiter datae aeqvatio ordinaria si qvam hab
# Incipit: xydx+aady+x²dy=0
# Date: 1700
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=21601&katnr=39694
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 188r (from the shelfmark LH 35, 12, 2 Bl. 188r°oben (=39695)): 1 page, canvas 375, page ids 00068195:0375 to 00068195:0375
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=375
# Lines: 31 recognised on 1 of 1 pages, mean confidence 0.87
# 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 188r — 00068195:0375
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000375.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
Tentamen ad praevidendum quousque ad summum
asurgere possit curvae differentraliter dato aequad
ordinaria si quam habet
Xydx + aa dy + X dy =0 sit aequatio differentialis ad curvam
quaesitam. dif Hoec differentietur, fret Ny dix + xdady +ydx + N pto s
posito ddy 2o. Hunc ope aequs. 1 et 2. tollendo dy set
dy = (ex oy. 1.) = - Xyax:  aatex (ex 2) y vex egxd
rydes
seu 3X x = Xdax + +X aat ubisingular est quod simmil
E
evanescunt dy et y, posita dus constante.
sed si fuisset Xyax + aady + X dx =o fiet
 differenlundo Ny ddx + X. IXdy + ydx f 2dy X 2X dx F XX ddlx = 0
et sit, d ex 1, du = - xydx - x dx, : aa = (ex 1  Fix
et fiet: Xydx + xax  py aa dux +y aac inde habetur
+Ex
alor ipsius y, et hinc videtur sequi in aequatione relaione
ex
exprimente inter Xet y non posse y assurgere ultra a
gradum simplice sed nesclo an fidi huic ratiocimo possit, quia
potest aliquando plane evanescere y, ut paulo ante
signa res inquisitione quid siat cali modo: datur verbi gratia
CP ex AB. Assuntur punctum C pro arbitrio in recta BK
et sumta recta alia quacunque e) cui ex C angulo
pc V recto eduta CV occurgat in V. et ex
quaeratur s, ut P ex AB et ipsarum VH
concursus sit F, est similiter (V) det (F)
usque ad altimum puncta escum () icidit in C linea euius FF.
Quod si aliud prectum sumas C func linea
(C)P) ducta cie concurref priai Cp in puncto  credo f.
est ipsa C