# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 261, page id 845634801:0267
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=267
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000267.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.83
# 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: the recognised lines in reading order, one per line.

isa
c
coMP
Tet
PSEY DO-ME SOL A BVM.
proporrio inxqualitatis non equalicaris, de proinde CF, F D suneinaequales, non eric F.
cenerum circuli. Teague recta FG circulum non canoet, sed secabir. Secel IBtt in G, 8
compleacur parallelogrammum circulo inscriprum C C D L iplam que C l ablcindat A L
in K, L aUCatHFR SIpH C C parallela, abscindens C D in S. Estigirur GR sCH CS HI
E. D aqualis, _E E B ipA A K. Ee quoniam sune in continua proportione AF, LC, LD
E. B exhypochesi, ideo crie F C ad F. D, SICUE COPOSITA ex A F, C D ad Compolitam et
EB, CD. EF IADAACCNdO CFIEHE SE dIHCTCHCIA IBCCI L S, L DHACSAdL D, II2 IEF
262
ear Breual. Lgo LA a GlaoPCB. uoca.
difterentia inrer A L, L B lCu A R 2d COmPOHLAI CA LB, C D SCdCH GuOgne VES F ac
ED, 1Id R F 4aF K. O_ALCF R CaDCHICH qua COMPMMTa exEB, C D. Verinque dema-
P ROPOSFFIO V.
Circulo dato e inscripea: per centrum circuli ita secare inscriptam, ut
eomenta in (eripex line in continua proportione inter legmenta diametri.
enero recta AF compola ex AC, CB xequalis, lecans circulum in 6, Fl, iplat Ve10
Sit datus circulus, cujus A centrum, dara quoque ir scripra BC. Oportet Facere quod
Popolirum est. Agarur diameret CHL, e  uC DL C COAHIAI, CWIHALEE ex A
BC in I. Ouoniam ioitur angulus C B F. est in lemicirculo, ideo est rectus. Lit aurem
AG Fi ex ByoOthe ipSI A C B aequalis, eaque secat circulum in G, H; BC vero in l.
Caare ex iis quae demonstrara lune, est ux C T ad IB, ita B T ad IC, e ita C Tad LH. Cir-
culo iraque dato cujus Acenrrum, data quoque in scripra BC, ita lecta eAt B C in LPCF A
cenerum, ucin (cripra BC segmenta B L, LC sine in continua proportione inter mutua
diamerri C LL segmenca C l, IFI. Ouod erartaciendum.
Si secetur lnea recta inxquanet. meeea et emem sella ce
eomentum, erit aequalis dimidix differenFIX (CGMENEOTUIM.
Secetur A B recta inxqualirer in C, aequalirer vero in D. Fs igitur D C differentia
inter AD semissem sectae. d A C majus segmentum, vel incer DB id est AD, e C B mi-
hus scementum. Dicoiplam D C esse dimidiam differenciam segmentorum AC, C B.
Duplecur enim C. D in F. Cum isirur ab aequalibus
D, DB anFerentUE aequalESD C, DF., HC A F.
aequalis CB minori legmenro. difterentia aurem in- A L
ex AE, id es C B, e A C est F. C, qua constructa eAt dupta ipusD C. Elt isicur DC
ditterencia dimidia segmentorum ina qualium AC, C B, in guxe secta cA AB. Duod exat
octendendum.
P R O P OS F FF0 VI.
P RO.