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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 357, page id 845634801:0363
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.88
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cacis ab.
cujua
ea aB
900
dia
circulo
Et
Dc
nE
riis.
RE SPO ASDRVM. LFBER VIII
P ROPOSTFFO
Dacam circumterentium lecare in impelala Lactore.
Sir circulus sab A cenro descripeus, in quo AEIAT QUA WDCLCHCMIMKCLCMELa De quam
oporreat ica secare, ur rora BC ad parcem ejuldem se habear in rarione imperata L da L.
Sumacur iph circumterentix BC recta BFI equalis, de scribendo helicem BFTIG, ac in an-
cecedence constructione, _ HaF BHI ad BM, ScuFZ adZ. Fc a puncto B incidacin he-
licem BIO recta BN, eequalis BM abscindens circum ferenriam circuli in O. FRigiMmE
circumterentia BC ad circumterentiam BO, Sicur recta BHL ad rectam BN sCu BM, id est
SiCuEZ adZ.
Duare tactum est quod oporuic.
PR OPOSTF+0 VI.
mi-diamerro ex differentia inter duplum circumterentix qua lesmentum
comprehenditur, et in scripram ejuldem duplo, aequale est quadruplo iplius
scomienri.
Sub a cemrro describatur circulus BXC D sectus a quacum que BZ C. EF sic segmen.
cum BXCZ minus semicirculo. Iphaurem C. XB circum ferencix lumatur circum teren.
tia BD aequalis, e jungaturDC,
PEoduCaFUTO; In E, ITa UED E SIC
aequalis circumterentiae DBZC.
Dico id quod Acplanum sub AB,
CE aequari quadruplo sectionis
BXCZ
Agacur enim diameter BAC,
secans C D in HI, _ jungantur
CA, CC. Secacurigitur CD bi-
Cariam et perpendicularirer in
EI. Ec criangulum B C C aequalc
eA ei quod Ar sub alrirudine CHI
e AB, quae dimidia est baHSBC
Ejusdem vero erianguli BCC di-
midium est criangulum C BA.
Constac aurem sector C AB tum
scomenro BZCZ rum criangulo
a AB. Idem sector est aequalis
dimidio ejus quod AE Cub AB
e circumferentia BC. Oua-
Ee seomentum BXCZ una cum criangulo C. AB, id est dimidio ejus quod sc sub CF.
AB, aequatur dimidio ejus quod Ec sub AB ec circum ferenria BC. Omnia quadruplicen-
ur. Scemencum igitur BXCZ quater una cum eo quod scsub CD, AB, xquarur ei quod
ac Cub AB _E circum Ferencia DBXC, hoc est sub AB _ reCtA DF. Ilringue auteracur id
quod scsubCD, AB. Ouadruploigitur sesmenti BX C. Z. Xquacur id quod sic planum
ub AB, C F. Ouod crat ostendendum.
PR ODOSFFTOVII.
Dato circuli segmento inrenire quadratum aequale.
Sudarum eircum lehmentum BL. CN. OpOrtetscemento BL C Ninvenice quadeacum
Equale. Describatur circulus, cujus spacium BL. CN porrio est. Aucisitur seementum
L.CNminus est lemicirculo, aut majus. Sic primum minus. In descripcoixitur circulo
X 2
suma-
Si legmentum circuli sit minus semicirculo, id quod sic planum sub se-