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# Piece: https://leibnizlegible.com/api/records/337/text
# Catalogue record: 337 — problemata quasi-Tangentium inversa
# Incipit: problema quasi-tangentium esset Dato puncto et linea ex puncto dato
# Date: 1689
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=337&katnr=57913
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 59r (from the shelfmark LH 35, 13, 2c Bl. 59r°): 1 page, canvas 117, page ids 00068199:0117 to 00068199:0117
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=117
# Lines: 34 recognised on 1 of 1 pages, mean confidence 0.95
# 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.
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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 59r — 00068199:0117
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000117.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
t opoblema est ex datu puncto lineam duc ere ad curvam,
problemnta quasi- Tangentium inversa
problema quasi langentium esset r Dato puncto et linea ex
puncto dato rectam ad lineamdicere, quae eam ita secet, ut ordinata
ex punctis intersectionum ad axem habeant intervallum datum. Poterit generalis
fieri aequatio duaum ceaduum intervallum datum habentium XX = 2 aX + aa =0
+ ab
eaque exaltari, si opus ut aequationi ex curva datae prodeunti conferatur, ut in methodo
radicum aequaldum. Sed si curva non detur, sed per lalia sit quaerenda oriuntur problemata
us agtum inversa. quaeritur linem C (C). ACD lalis ut ji DC sit aequalis datae F
sit AC = datae G, patet punctum tertium etiam cadere debere
in rectam C1C) quia H datur. Imo inserviunt omnia puncta rectae He
Eit ita uno puncto dato datur linca. Nidendum an et alias seu per
cum linca poit in per Cafinita puncta C. (C) (C) prodiens transiens est
anglutica; algebraica, tuno omnia puncta lineae serviant, vel ate ea vel unde
id sequitur omnia puncta interponenda inter C et (C) cadant in eandem lineam per
ala infinita puncta transcunter. Id videtur ex natura interpolationis. smper enim
eadem lex servatur, et ut transitus a C ad (C) et a C ad (()) et a C ad C) aderque
 semper mauet in eadem linea, adeoque interpolatio inter C et ACD, et inter
C et (CD, et te C Ergo et debebit interpolatio inter C et(C) manere
in eadem linea. Sed quando nulla talis linea Algebraica vel alia, determinatio
prodit, tunc quaeratur regula interpolandi eaque continuata in infinitum, seu usque ad
ebrum
terminationem, seu usue ad casum coincidentiae viea inter; quae est interpolandum
eo casa habe bitus regula absoluta
proponatur problema tale invenire linea in qua jungendo duo puncta C et (C)
et ex ipsis et puncto medio M ducendo normales ad axem, CB, (C) (B) et ML. sit
rectangulum sub BC et (B) (C) seuper aequale rectangulo sub ipsa AL, et constante F
tunc dico aut parabolam ic sutis facere quaestioni aut esse quaestionem impossibilem
Nam in casu quo C et C) coincidunt, qui casus semper casus pro quovis puncto curro quaesitae
locum habet, fit AB in F = BC. Ergo quod sieru. Hinc pates problema esse
postulare curvam quae habeat pot pryprietatem paratoxam, et fortasse impossibilem.
Artis foret ex cogitare propretates paradoxas possibiles seu praevidere
problematum para doxorum possibilitates. Ex cunis datis hoc fieri potest.