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# Piece: https://leibnizlegible.com/api/records/1157/text
# Catalogue record: 1157 — [Aufz. zur Sekanskurve]
# Incipit: Invenire secantem, qui minimam rationem habeat ad suum arcum
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1157&katnr=58695
# Work: https://leibnizlegible.com/work/00068073
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folios: Bl. 13 (from the shelfmark LH 35, 7, 1 Bl. 13): 2 pages, canvases 25–26, page ids 00068073:0025 to 00068073:0026
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068073&page=25
# Lines: 53 recognised on 2 of 2 pages, mean confidence 0.83
# 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 13r — 00068073:0025
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 52 lines, status machine
minimam
jurcure mximam rutionem cecantis ad
Javenire secantem, qui minimam rutionem habiat
ad suum arcum. Manifestum est quo propius punctum 1n
minima.
Sit radius Y
Sumitur verss A, vel vertus C eo
majorem esse rationem secantus BY
ad suum arcum AD, quaeritur medium
punctum E ita ut ratio secantis BF ad
arcum BE sit omnium Cep possibilium
Est autrur Cx meis demonstratis
arcus sit arcy a, tangens T, secans, v,
erit a = bY
C dc. Est autem H= VV-rr
mttu
 a = et a tdt = vdv.
b
s
seu dt = vav: dvn-rr. Ergo fiet
a =
rodo
. Et  =
vrovir
CraV C
dvrovir
debet esse e omnium possibilium minimum, fiet
r d0) = ao)
rovir
Seu ta = rr.
e
Seculcrus eatis seu radius est media proportio-
nalis inter arcum quaesitum, et sum ejus
tangentem et arcum, qui ni cujus secans
 qui maximam habet rationem ad suam
secantem.
Felicitalis erit tate problema Maximae
t minimae invenire, in quo t simul et
maxima seu minima et quantitas transcendens
est  t videami
tolli possit. ut
fu inter
 quid s fiat, siquaeratur differentiac arcum
ut secantem minima:
v.
Crr= W. fitt du- rrdv
vervar
vivir
seu vevver = rr. seu vt- vurr-
= O
quaentur an ratio sit minima quando differentia
est minima. Non segutur

## Folio 13v — 00068073:0026
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000026.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 1 line, status machine
Oi