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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 263, page id 845634801:0269
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=269
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.85
# 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: the recognised lines in reading order, one per line.

ento
et
p5d
6d
rCul
CPt
15
PSEVDO-ME SOL A BV V
PR OPOSFETO IZ.
Si diametrum circuli ita secet in (cripta ur segmentainscriptx sint in con-
Cmmaproporcione  a lca aelI. ansul, quitucin lectio.
ne, duplum completCCu
metri Circuli Cubrendeur
Circuli, cujus FE centrum, diametrum A B ita seCeEIn E in SCripTA C D, UE E C, E. L
Ccomenea in(cripta C D Ent in concinua proporrione inrer AF, F B Cexm
aametri AB. Seceruraurem C D bitariam in O ex FIcenero, unde angulus OFIF. et
Complementum OF FI, quoniam angulus ad O estrectus. Subcendatur deinde ad patlc.
Drecta BZ, Cumpra xqualiscrienti diamerri AB. Dico anguli O HI P duplam amplicu.
minus crit circumterentia, qua a triente dia
a uEuE
dinemminorem esse circumferentia Z B. Connectatur enim A Z, e per C acta iph
CD perpendicularis, occurrar diamerro B A in F. FritigituE F A ip (i C D aequalis. IFa
QUCTOL F E erir composicx ex rribus proportionalibus A E, E C, E. D equalis, quae ma.
jores sunc rriplo medixe F C. OUAre F F ad F. C majorem habet rarionem quam eria ac
unum. id est quam A Bad BZ. Hlabear eandem quam AB ad BX, de subrendatur BX.
eritioitur B X minor quam B Z, ex consequenter circumferentia B Z. major exir circum
Cerencia BX. Eadem aurem estratioFIE adOF, QuaI FF. ad F. C, similia enim sune
crianoula HI E O, PF C. Peaque erie AZ ipsiusFIO parallela, _ circumferentia BZ du-
Plâ amplicudo anguli OHE, CeuX AB, seu C F F. Duplaigicur amplicudo anguliOHF
minor est circumferenria Z. B. Ouoderar ostendendum.
PROPOSTTTO X.
Ad dacum angulum ei xqualem qui sic in sectione inscriprae circulo, ee
CIAICEFI, EXtIDETCMUEIIA CAFUM LEBICHEA II CONFIHUA PFOPORTONC. OPOF
cebic aurem in eotriangulo rectangulo, cujus balis subtendetur angulo
daco, perpendiculum esseminus trience hypotenulx; quoniam hypote
nula ad perpendiculum est licur diameter ad subrenlam duplo comple-
menti angulilectionis.
Oporteat exhibere circulum cui inscripeam ica lecet diamerer, utlefea MCOI
lnua proporrione, e praeterca angulus qui sier in sectione xqualis sic an gulo dato. De-
Lurangulus AB C, reliquus aurem c recto in quocumque triangulo rectanguloB A C.
ca ramen ut ejus eriangalihyporenula A B Ccmajor eriplo perpendiculi BC, ob ca qua
jam expolira et demonstrata lucie. Cumixicur ab AB abscinderur AD, aequalis dupla
CB, FUIF.