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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 386, page id 845634801:0392
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386
V A R FORVM DE REBRS NIA FHE M A FTCFE
inaqualirer secti a recta BC, _ est DBC minus segmentum, C. BF. majus. Acque huicma
jori legmenco cum auferrur exiangulum mistilincum CCF, cemaner dimidium corius (p2
cii, sicur cum illiminori adjicirur criangulum CFD, criansulo GCF. xquale. Cum au
tem secacur magnicudo quaepiam, dimidia differentia segmentorum, adjuncta dimidia
magnicudini, Facie majus segmentum, ablata mivus. Dimidia igicur differentia incer (pa
cium DBC _e spacium CBE, est criangulum mistilineum CCF. (Cu CFD. Ouod primc
locoFuir ostendendum.
Secundo cadar in BE perpendiculariter CH, de Cubrendarur CF. Dicorectilincum ac
rectangulum eriangulum CHE, aequari mistilineo CCF. Ouoniam enim circuluSF C
est duplus circuli DC F, ideo cum secabuncur similirer circuli illi: Segmenca illius eruit
Seomentorum hujus dupla. Traque rorum segmentum C F, quod delcribitur in minol
duorum illorum circulorum, xquale est dimidio simili segmenro delcripro in majore
nempe spacio HIC. C, cum dupla circum ferentia C. C similis lic circumterentiae C F. Ouar
cum igicur rriangulo mixcilineo CCE decrahiie sesmentum C F, rantundem resticuie c
midium simile scgmencum HI CC. arque adeo rectilineum eriansulum CHF, aequale 
mixcilineo GCF. Ouod sccundo loco tuic ostendendum.
Siciguur dimidia difterentia inter (pacium DBC dt spacium C BF, ad a quara est euH
Fpurae mixrilineXRCMBCDC P seu C C F, cum re Cilinex H C F, uc erat faciendum.
Llulus corhiuatis.
Oepit agitari quaestio à lagacibus quibusdam Geometris, an diverricu
Ium quod facie circulus a linea recta vel circulari, quae ipsum tansit, 
angulus nec. nC. Circulus enim censetur figura plana, intinicorum lace
rum ec ansulorum; linea aurem recta rectam contingens quantulx cunqu
sic longicudinis, coincidit in candem lincam rectam, nec angulum tacll
Trague cum proposuit Euclides inter lineam rectam quae circulum tane
 iplam circumterentiam, non cadere alteram lineam rectam cis t uerat
ronov ris a dcias noi ris coet Depeias, s inquic E lepa d dela a d ep  Crat, NOM Cttala
rcoviar TELEXCINErV LOT SdeiaS nCI NVKN X  Et Depetas 3 reurd Ex épo. L deie. 
Apollonius Perexus cum idiplum quod in circulo Puclides inc(C in con
sectione demonstravie, ulus est voce rorsnon rcutas, nec inde elicuit la
rilma quale in propolitione Fuclidis legitur de angulo semicirculihis re
Bis:nqn uer a uoxoxnis rcorta axdons oEcas rorias ps  (cor est;
nornéx ae tcor. IEa vEnOn cemerC quis suspicetur ea esc adulterina, ne 
non latis conster Puclides, et alioqui Ceomerrica mulca corruane tunca
IMEHCa.
1. Anguli ex ipsa Fuclidis partirione, recti sunt aut obliqui. Obliqu
vero aucluncacuri rel obtuli. Cum itague angulus semicirculi non ut Ou
culus neque acutus, videtur esse rectus; is vero qui existimatur religuus
rectoneparoddis Colet rocari, angulus imaginarius, qcovia cinovinn.
2. Angulos circumferentia definic. Nulla circumterentia definit a
verticulum neparosdés. Diverticulum igitur illudnon est angulus.
3. Secto dissimilicer circulo, anguli sectionum dissimilium difterunepe
circumferentiam; quae aurem magnitudo metitur toram e ablatam, cadet
metitur e reliquam. Propolitisigitur sectionibus distimulibus, metiala
magnicudo quaepiam angulum majoris, metietur ex angulum minoris. 
Ferenciamigitur majoris e minorismetietur, id est circumterentiam.L
30ansuli sectionum circumferenta lune, e cum iidem non line majola
nequeminores dimidio circumterentix, sub qua se balc comprehendu
cur sectiones, ei dimidio censendi suneae qualES.
 aeVL ACL.