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# Piece: https://leibnizlegible.com/api/records/577/text
# Catalogue record: 577 — problema Beaunii Ep. 79. Cartes. Tom. 3
# Incipit: Angulus CID semirectus BC : CL :: N : BI et vel DC, x CB, y BI =
# Date: 1692-09
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=577&katnr=58154
# Work: https://leibnizlegible.com/work/00068116
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 22
# Folios: Bl. 1 (from the shelfmark LH 35, 8, 22 Bl. 1): 2 pages, canvases 1–2, page ids 00068116:0001 to 00068116:0002
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068116&page=1
# Lines: 42 recognised on 2 of 2 pages, mean confidence 0.88
# 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.
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# 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 1r — 00068116:0001
# Source image: https://digitale-sammlungen.gwlb.de/content/00068116/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 40 lines, status machine
problema Beannii Ep. 29. Cartes. Tom. 3
Angulus CiD jemirectus BC: CL:  N: BI
ei vel DC X CB, y BI = y - X et fiet
dy: dx:: n :, y -X. seu dy y = dyx = n dx
foc problema solutem est a Bernonlliovet Hospitatio
vid diar. parisiu 24 anni 1692.
Ego aliam
Constructionem Hugenio, misi, quam ait consentire qua cum posteriore
ab Hosprtatio sibi transmissa constructione. Vide Hagenii ad me Epistotam
septembur 1692. datam. soge des constautem et differentia fiet
dut du  dydx = nddx. seu dus = nddxc: dy- dx. seu fet
v = n log. dx Fb. Ergo y +b, :n est progressionis Gemetit Arithmetriae
dum dx sunt progressionis Geometricae. Adeoque et dum X +C sunt p rogressionis
Geometrico. conf. Cartes Ep. 72. ejusdem Tomi, an sit eadem
urva utrobique quaeramus BE et  DE, sit DE,Z et BE,V
DI = XV2 BE = BI: 12 F y-X,: 12 =( V = 1E DI + IE= 2
fiet, xV2 + v = g. seu x = v: Y2 + Z: Y2 et ∞ per 3 et la
y=v12 +x et de v. tr 1A. 12 et dy- vf2. d
seu y = +02 - v: 12 +Z. (2 seu y = v: d2 +g: 1. eu ergo
ag. l per 4 et 5 fiet  d2 + dv:, du = dv = n:  v
seu  viidque + vAdv = nag- ando
Aliter si DI sit Y et  BI sit co angulo ad
DIB semper
existente semirecto, fiet 2 = XVZ et C = y - X. Eoge
X = 1: f2 et y2 c +p. 12. Ergo ex Cqu. 1. fret
deor +dip: di
L
n: c0. seu e da 12: di = n - W,:co
seu dip  codco2.: n-cd
ita res rursus est
Atque  hinc apparet
reducta cta ad quadraturas
vaniari posse, et aequationem differentialem, mutato
angulo fra ordinatim applicatarum. Conjungi denique potest
suricere
nir hoc
coneraliter videatuus quid efficiat mutatio anguti
e
uideo
mertaxtio anguli et  epexis.

## Folio 1v — 00068116:0002
# Source image: https://digitale-sammlungen.gwlb.de/content/00068116/jpgs/default/00000002.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 2 lines, status machine
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