# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/11725/text
# Catalogue record: 11725 — [Mathemat. Aufz.]
# Incipit: Cum plures sunt radices ejusdem aeqvationis,
# Date: 1693
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=11725&katnr=45402
# Work: https://leibnizlegible.com/work/DE-611-HS-855907
# Title: LBr. 560 · L'Hospital
# Folios: Bl. 13 (from the shelfmark LBr 560 Bl. 13): 2 pages, canvases 25–26, page ids DE-611-HS-855907:0025 to DE-611-HS-855907:0026
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-855907&page=25
# Lines: 31 recognised on 2 of 2 pages, mean confidence 0.91
# 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 — DE-611-HS-855907:0025
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-855907/jpgs/default/00000025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
per l.n fiet M = ac

## Folio 13v — DE-611-HS-855907:0026
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-855907/jpgs/default/00000026.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 30 lines, status machine
cum plures sunt radices
jusdem aequationis
ut si tam quam n ipsi
aequationi XX+ bx + ac 
satisfacit, poterit seribr
l+ bl+ ac =0 et
mm+bt ac 20
Hinc p fieri possunt variae
aequationes ad duas incognit
4)
ut Urmm + b(ltm) +AC~
quae est adocrculum
et U= mm + b(l. m.) =0
unde fit L +  l + m + b = 1
quae est ad rectam.
Unde e
Il+ mm = bb + ac =0
habemus ergo duas aequationes
6 et 7. illam ad rectam
lunc ad circulum quarum
inter sectione salvetur habetur
quaesitum
oportet
 autem esse ac  non
ac H  bb major quam ac
si per aegu. 2 et 3 tollamus b,
fint b= -l - ac: l = mmac.
sit Hm m t ac m lrum- ael
se mam acL-M) = o et dividem
ac