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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 331, page id 845634801:0337
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.81
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CFD selet
ux ericta
CcanSC
CC
CCHECHM
et
CFBC
rect
ICF
tendet
BD
exC
lt
E multB)
lioM
recire
sin et
Ct
c
1
similia
c
ver
115
IIC
c
1d
5. 
raBI
cent
F BOI
30
L L V 5
nonerir CB ad CD, sCuT CC ad CI, et ideo eo quoque casu dissimilia erune leGmenta
CB, CD. Ouod crac ostendendum.
lum AEF circulus secundus. IIII
isicur circuli sese muruo secabune
in A vel sele cangene, sed non sele
muruo secanE. ENenc enim AE
AB Scgmenca dilsimilia corum,
quorum sune subcentae, circulo-
rum. Sed Cune smilia. Similia c-
nim (unEerIANGULA ABD, AFF. II2
que es uE AB ad AE, ic2 semidia-
meter circuli criangulum ABL
circum scribenris ad semidiame.
puncto. Quoderat ostendendum.
culum, quem data linea recta _ datuS CIrCUIUS CONEIHSANE.
Sic dacum A punctum, dara quoque linea recta BC, ac datus detique CITCHIUSDEF.
Sporcec per A punctum circulum deleribere, quem recta linea BC, dc circulus DFF Con-
AMBINE. ExC cencro circuli DEF demirtarur in BC pespendicularis DC, secans ex dia-
MEEEO CIrCUIAI DEFin
punctis D F, de conne.
CtacurD A, quae ica le-
CetuTIn H, uc quod EE
subDA, DH aequale SIE
ei guod Ec (uD DC, DF.
de per puncta AH de-
leribatur circulus, quem
recta contingat in B,
ec agatur DB lecans cir-
CUIUIDEFINF, XCOn-
ReCtAEUEFF. R CCtUS eA
iBicur aneuluS DEF
leaque in quadiitaTerO
BEFC anguli oppolici
duobus rectis lUNE X
suales, rectus enim quoque est angulus BCF. Ouare quod tclub B. D aqe e et
uod sic sub DF. DC, id est ex constructione aequale ei quod Ec sub DA, DH. Sunc ixi
AEPUNCtA AHEB in circulo. Sed F. est in circulO DEF. Ounre circuluS DEF LecaLVel
rangie
Lemma TII.
Si per crura trianguliaxatur recta basi parallela, ilaque duo construuntur subio-
dem verrice similia triangula, qui circa rrianculum unum describetur circulus tan.
Setur in verrice communi à circulo qui circa trianculum alterum describetur.
SiE CrianOMIUMI ABD, ipSIUIS AULEM CrUTA AB, AD secerreCt 2 EF ip EI BD parallela, ir295
duo constiruuncur similia criansula ABD, A E. F sub eodem A VerCICC. Ajo circulum ett Cd
eriangulum ABD deleripei a circU.
lo circa criangulu AFF delcripro
rangi in iplo A puncto. Delcriba-
tur enim circa exian guIUM ABD
circulus primus, de circa criangu-
trum circuli rrianoulum AEF circum scribentis. Cum igirilt nO tete muruo secent circu-
AIABD, AEF, sele concingen in d. Ouare circulus ABD a circulO AEF canSeTUT IN A
PR OBL E N A VI.
Datis puncto, lincarecta, de circulo, per datum punctum describere cit-