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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 443, page id 845634801:0449
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riet
CZCLOMEFRZCA, SEV, ANTTMEAEKXZ
L. E MLAL A F A DYO VEK A,
Primum.
Decem minora criangula aequalia sunt sex segmentis hexagoni et duo-
bus complementis lecuriclae.
Ouorum enim eriangulum hexagoni constat legmento de securicla; Securicla vero
duobus seomentis e complemento: ideo duo rriangula hexagoni constant lex leomen-
ris ee duobus complementis. Sed duo criangula hexagoni seu majora equalia sune
decem minoribus. Ergo decem minora eriangula aequalia erune sex legmentis _ duo-
bus complementis. Ouod erat ostendendum.
Secundum.
Ouadeaginta minora eriangula aequalia sune circulo et duobus comple.
mentis securicla.
Ouoniam enim circulus aequatur sex (calpris hexagoni, sex aurem scalpra aequalia sinE
ex triangulis hexagoni e sex segmenris, sex porro criangula hexagoni valeane crixinca
erianoula minora: ideo circulus aequarur eriginca eriangulis minoribus ee sex lexmenris.
Elcrobique addantur duo complementa securiclae. Circulus ioirur una cum duobus com-
plemeneis securiclae aequabitur eriginca criangulis minoribus de sex segmentis e duobus
complementis. Sed lex seomenta ex duo complementa valent decem minora criangula
per anrccedens Lemma: Ergo quadraginca minora criangula aequantur sex segmenris
hexagoni e duobus complementis securiclae. Ouod erar octendendum.
Y E Y A A P FO N.
Dico eriangulum minus aequari suo residuo.
2 5 A2od 1E15.
Ouoniam enim circulus cum duobus complementis securicle (quae quidem ralene
duo criangula minora, ex duo relidua minoris crianguli) aquancur crisinca lex minori-
bus crianoulis _ insuper quaruOT. TIrrinque auferantur duo criangula minora. IIIiC
cum auterentur de duobus complemenris, relinguene duo residua erianguli. Hic cum
auFerenEuE e quacuor rriangulis, relinquene duo eriangula. Ergo duo rehidua ae quaneur
duobus eriangulis.
Elenchus äooMozisias.
Ab equalibus eoris non ab equalium parte auterenda aequalia sune, ue quae relin-
quuneur maneane aequalia. duterre ex equalium parre est adlumere religuum e toro
reliquo esse aequale, ur hic circulum aequari eriginca sex minoribus criangulis. Illud vero
perucgatur, et cM Fallissimum. Sibi demonstranda concedere, est velle videri demon.
Arative errare.
AD FETAAPION ALEYD, LEMM AFA DYO YERH
Primum.
Viginci quatuor quarexe trianguli hexagOnI _E Lex LegMenTa sunE a qua-
lia visinei quaruor sermentis e (ex complementis securicla.
Ouoniam enim criangulum hexagoni constat eribus segmentis de complemento se-
curiclae, circulus aurem componatur ex sexcriangulis d (ex segmentis: ideo viginti qua-
ruor Ceomenta cum (ex complementis circulum adaequant. FF quia quaruor quarrae in-
EeOrUM ComPOBunE, aequabune quoque circulum vioinei quaruor quarexe crianouli he-
Xagoni una cum sex seomentis. Dua aurem uni aquaneur xqualia lune inter le. Ouare
vicinci quaruor quarrae crianguli hexagoni ex sex legmenta aequalia lune riginei quacuor
Ceomenris e sex complemenris securiela. Ouod etar octendendum.
SCCUM.