# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 280, page id 845634801:0286
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=286
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 96 lines, status machine
# Lines: 96 recognised, mean confidence 0.78
# 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.

280
2
C 7
Ouod aurem sir sub diagoniis quadrilareri circulo in(CripH, quale est ei quod Eic sul
duobus laceribus oppoluis, una cum eo quod sic sub duobus reliquts. Quare quod Helua
AC, DBid cA quadratum AC vel DB, aequabitur ei guoeoB, id est quadia
co AB vel CD una cum eo quod Ec sub CB, D. Sum aurem datxe ex hypocheli rectae AL
CB, CD, DA. Ouare dahitur ipsa AC.
Sed lunro AB, CD lacera inaequalia. Rurus SI lacus BC laceri DA est aequale, 2C
cidene ut anre aequales diagonia, a
dabuneur exposica methodo.
Sed scundique inequalicas, uE pO.
te sIc BC lacus majuslatere DA, 8
AB majuslatere CD. Ononiam rC.
Atx AB, CD Cune inequales, crune
circumferentix quoque AB, CD in-
aequales. Ouare non cruneparallela
AD, CB, sed exrra circulum produ
Atx scle commitrenc. Conveniane
in F. Rene igicur duo eriangula FAB.
F. CD tiabentia angulum verricis
communem ad C. EF quoniam 21
gulus DCB una cum angulo oppo
siro DAB est equalis duobus recti
_ idem angulus DC B una cum AM
sulo(UO exrerioreE CD EguorurduO.
bus rectis, urrinque ablaco angule
DCB, AcanguluS E CD anculODA.
equalis. Ouare Similia (uve crian
SuIa EAB, LCD, _ est ED adFC.
SICUEEB ad EA. ABC FB autem aB
Scindatur EF ip GE.D equalis; _CON
era ab5 F A ab (CindaEUEFC ip C EC
aqualis, _E jungatuEFO. FrianguI.
IGITUTEFO, FDC aqualium Guncl
cerum ec angulorum. Angulus enin
ad verricem urrique est communis
quem aequalia comprehendunc lace
ra siru permutaro. Leaque data el
CF darx DC aequalis. FF quia estu
FD id eAEFad EC id CAFO, icaL.
ad E. A. ideo erunr parallele CF, A.
AbscindatuE quoque abS FB rect.
FH aequalis ipEI FA, dC juBSRNCU
GC, AFI. EA iBITUEVE FC ad L6
aeque adeocriansula CGF, HAB Similia. Er quia C A, CFI sune aequales, verinque det
pris aequalibusE.D, EF, FcDA aequalis ipsi FFI. Dara estigiTE COmPOSITA Cx CF, HB
quoniam compolita illa es differentia datarum CB, DA. Caererum sccacur difEerenit
illa secundum dacam racionem. Nam proprer limilicudinem eriansulorum L AB, C6
CAt ABadHB, (ICUEFC sCu CD ad CF. Ouare dabuntur (CGMCNEA CF, IIB, 4que 2d
dabunrur FB, GA. Illa auterendo a daca C B iplam CF, haec addendo ipsam C F lel 6
ipED A. Icaque ip( C A agatur FL aequalis de parallela. FirigituE AL ip SI OF X GV2 NS, Cu
Einc parallela GF, AB. aeque adco lB disterencia cst incer daras AB e C F id est C D. Frial
bulum isitur FIB est datorum lacerum. Fi aucem simile eAtE AB, cujus basis datac
AB. VUATE CTUTA quOquC AABHMEALLA, L. B, ulquC AdCOFF, FG, SCNED, FC. DaChu
igicur laceribus craperii ABC D circulo in seripri datx sunc diasonia C A, DB. Ouod etab
ostendendum.
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