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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 375, page id 845634801:0381
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1s balla
upII.
suliqu
bis. 
10
RESPONSORVM. LEBER VIII.
E H E O R F M A 1II
Si Sccetur lemi- circumterentia circuli in parues dorcunque ae quales, dt
a termino diametri cducantur recta ad quae libet scctortum puncta: cIt uE
minima cducta ad diametrum, ita compolita ex aasecto, de minima, dt
ea insuper, cujus quadratum adjunctum minima quadrato etticit quadra-
cum diametri ad composicam ex omnibus eductis duplam.
Sic circulus lub A cenero, diame-
rio BC. delcripcus. SCcetUE aurem
circumferentia BC in parces quor-
cunque aguales, ur pore octo, et GInE
illa BD, DF, E F, FG, GFI, HIL, IK,
KC, d subrendaneur BD, BF, BF,
BG, BFI, BL. BK. Est igituT BK aequa-
lis subrentae DC, cujus quadeaium
adjunctum quadrato ex DB aequale
CA quadraro ex BC. Dico eseuEBD
ad B C, ica compOsITan ex BC, BD.
BKE CCuD C ad compolicam ex omni-.
bus duplam, videlicet compoliram
duplam ex BD, BC, BF, BO, BIL, BI.
BK, BC, ut haec abunde demonstrata sune dc expolica in Analyricis angularium sectio-
num.
Est condicus C anor: sinuum per singula sexagesima scrupula parcium quadrantis circuli, in parcibus
qualium sinus corus adsumieur 100, 000,000. Ouarit aliquis summam omnium sinuum singulis
Scrupulis coneruentium. Ouoniam igitur est ut sinus unius (crupuli ad sinum tocum, ita sinus unius seru
Puli sinus complemenii, es sinus corus ad sinum rocum. prosinum complemenei, ex cransinuosam com-
Plementi: addat Locista transsinuo sam complemenei unius scrupuli suo congruenei prosinui, e insuper
Sinui eoto, es constabicur duplum sumna quaesita. Transinuosas. videlicet, voco hyporenusas, quas sux-
pedicat Canon faecundissimus; Prosinus, latera circa rectum, quae Canon faecundus.
Transsinuosa isieur complementi unius scrupulinumeratur. 343, 774, 681,923
3433 774, 667, 379
100,000,000
6873. 643, 3493302
Est ixirur 343, 824, 674, 651 summa omnium sinuum scrupulorum quadrantis; ip so sini 1010
Cc parcium nunierato, cam accuraca quam parieur in ea hypochest linearum symmetria.
C A P Y Z 1X.
Arbeli, ex Lunularum quadrationes aliquae.
Cnulam unam quadravic LTippocrates Chius. Lunulas aurem post FLip-
Poctatem quadrarit nullus GCometra. Neque enim Analyticum qua
drandi lunulas tractenus propolicum fuic a quopiam arcificium. ErgOun
verlalia univerlaliter docenda sUME, _ quadrandae nOn una, Led infinit
Cadem ex generali metho do lunulX. Primum aurem proponam de atbelo.
PROPOSFFTO I.
Arbelum describere, cuirectilineum exhibeatur equale.
Tois de Cinois quinass na) ZSporS oi onvroruo reursor n Zest r déquara. Suncaucem
urbeli seu arbela sa nunnosceq sidnesa, uc aduocavie Scholiactes Nicandri. IEaquE Pro-
us appellavie arbelum spacium ctibus circum terenciis comprehentum. Vcecce, deleri-
bacuF
Prosmus vero.
His addatur sinus totus.
Summa fib