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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 20, page id 834940469:0104
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=104
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
# Lines: 28 recognised, mean confidence 0.89
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

HE naTUEX VE duCFA IN quaCunque AO recrae perpendicu
laris aequiraleat pocencia verique Ll LM; crie receangulum
MIK aequale mixcilineo IA F L: Snon ACitas dueatur curra
AVY calis naturae uc rectangulum MIV hac aequale mixciliz
neO IA FL, e demonttrabitur secundum renorem huius
propolitionis rectas (quae CurraS AY, AG, tangune in pun
Cis V _K) ese inter se parallelas, quod es ab surdum con
era propolirionem praecedenrem.
Fluius eciam proxolirionis rarii sunt casus, Ped hocinteb)
lecto, in reliquis nulla rectat difficuleas.
PROP. 7. DROBLEMA.
Rectam ducere datam curvam tangentem in ejus puncto dato
simodo curva sit ex earum numero, quas C arte sivts
appellat Ceometricas.
TECurrA BEI C hyperbola, cuius diamerer recta A H e
ordinacim applicacae EFL, KC, calis nacurae, uc Colidum
ex quadroco a B P in AE (IC ad lolidum ex quadraco a BK im
A K DE CubUS ab F: II ad CubUM A RC. Sit AB dAFA a3 BF B, eC
raeio Colidi ex quadrato a BF in AF ad cubum ab FMT UC a3 2d
c3: oporcet invenire punctum F, ve ducca recta FHhyperbe-
lam eangE in pucto FL. ex daEIS AB, BE, dAEUE AL aL B_E LFS
YC (ab 2c3 nfa b3c3). Sit F FZ ee D F rihil leu CCrUMO; dE
proinde eric BDb --0 _ A D a , b -- 0, FL Z- 0 icem DC VC
(53 a b2 = 253 a b0 a c3 a02 rC3 b5 3C3b20 a 3C3b02 (303)
quonium supponimus ordinacim applicaeam DC incidere
in curram in eodem puncto C rbirecta FHeidem (E modo
Dosibile HE) CUErR OcCUErIE, CrIE UCFHL ad LFita DO ad DF;
e ideo rectansulum ex D F in E FLNEMPO YE (b 2C3aZ3-