# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 366, page id 845634801:0372
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=372
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000372.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.80
# 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.

AD, AE, quas ducta quadrataria B P principium habens in BEnem in Y. seceF INF, C
GI. Dico ese mrFFTadCL. ica anoulum FA
ad anculum GAI. Cadane enim in ABpCt
pendicutares FK, GL. Ouoniam iBItIEF, C
puncta sune parodica quadratariae, secta el
Temidiamerer BA in R. L Similiter aC cirCUM
Terenria BC in D, F. leaque es uE BA 2C
RA, ita circum ferentia BC ad circumferet
tiam DC, _E uEB A ad L. A, ira circum FCreHE
BCad circum Ferentiam FC. Ouare est R A 2
LA, uc circumferencia DC ad circumteren
tiam EC. EF VerO K A, L A sunE ip (SFL
G L aequaleS. Er circumferentia D C CA an
Eerentia E. C amplicudoanguli G AP. OVarCCSZUEFHL aC
20r0s+t1O L.IL.
cumterenca, d minimam incidentium ex centro in quadracariam.
Sit Acenrum circuli, BC quadrans corius circumferencia, AB, AC semidiametri o
thogonix. Er ducarur quadracaria cujusprincipium B, finis D. unde fic AD minima
cidentium ex cenero in guadrarariam. Dico A B mediam esse proporrionalem inter ct
cum ferentiam BC, ec rectam AD, id est, esse ur circum terenciam BC ad AB, ita AB ad 
Si enim nON IEa SE, CAOUE CirCuMFCFeNLIS
BC ad AB, ita AB ad AF, BE CCHETO A inCC.
vallo AE describatur circulus ab scindens A
in C. F.R igirur circum ferentia BC ad cit
cumterentiam GF, sicur semidiameter A
ad semidiamerrum AE. EX hypochesI auECA
et circumferentia B C. ad A C id est AB, L
CHFAC ad AF. OuarC CAt CIrCUMFCFCNEI
GF ad AE, SICUE AC ad AF. F. RIgItUEC.F ipL
A C. aequalis. E.st aUTeM A P. major ipla A .
velminor.
Sic primum major. Secabir igitr CF. qua
deacariam BD. (ECCFINF, _ cadarin A
perpendiculariter FH, e connectarur AP
ferenrix inscripra. Non est igitux AF majo
quam ipla AD.
SecundO SIE AE minOr quam AD. Circu
lum igitur GE tangac ad F. recta CccanS qua
drarariam in L. EFjungacur AP ec produc.
cur uc anre ad circumferentiam BC, qual
sccerinN; GE verOin MI. FR ixituIEBC aC
NC, (ICUEOF id est AC ad MF. BC aucen
adNC. CA, SICnEBA ad LF. F B igituE BA2
LE, SICUT AC adMF. Sed BA, AC CunEX qu
L
le5. A: quales igItE qUOquC CNenEL L.,
Hlocaurem est abCurdum. Dupla enim ipliu
L. F circum(cribicus duplo circumterencia
MF. PrX
V AR TOR DM DE REBVS MA YREMAFTCIS
360
plicud
EtI AL Oecaeu Serpendiculares F L
GI, ita angulus F A FI ad angulum C AI. Ouod erat octendendum.
Semidiameter circuli est media proportionalis inter quadranteim cit
e
av
circumterentiam BC, quam secet in K. E A igitur BC ad KC, GCuLC
Cad FF. BC aurem ad H C CH, SICUFBA ad FHI: erit igitEBA ad FFI, GICUEAC
EE. SedBA, AC sunc aequales, PFLixicur ec FF esten quoque aequales. Hocauren
abturdum. Dupta enim FFL duplo circum ferentix FE. in scribicur. Ce dir aurem ciecl
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