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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 361, page id 845634801:0367
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13
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11
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COrI
RESPONSORVM. LTBER VIII.
6
ExFcors. Sub A cencro, interrallo quocunque AB, de seribatur circuluS, IM GHO MIIa
recta FB quancum. MSInIL, adrc-
Ctam FI de ad sionum ejus Langu-
culus constirmatur FIHI angulo;
FBA aequalis (per 23 primi,) Per
cignum Lrecta ia Parallela tiarre. 3
etx FB, per signum vero Bparal-,
lela HaL reCtX FL recta BC, jun Ct2,,
BI, e demissa in IH perpendicu-3,
lari BN
AnodAEIS T. Ouoniam igituE.
iToCcetium ABF, HIIF anguli sUNE,
requales _ AFFI urrique COmmU-,
vis, aequiangula e similia erune,
ABE_HIIE iloscelia. Onia verO,
trianguli AB C perpendicularis,
CE secat basin AB bitariam in F. 13
_ ad rectos AFI, BE l ansuIOS, Ca,
larera AI, IB _ anguloSEAI, FBI,
Facie adinvicem aequales (per 4 3
exci) cum proportionalia sine Cin-3
Sula Singulis laFera. CXFerUM CUIM3
TrIaNDUIOTUM ABF _E FIIF ErapC- 3
ZIABEIK CC IFBG SnE xequiangu-3
la. (Acque haecapodictica hacte-3
nus vera lune, sedjam lequiturp2-,
ralosismus) _ in Cimilia criangula,
dividancur, (cilicer BIOR IFB. A-3
liud in IBK X IFB sectis angulis,
Oppositis ex 20 sexti. EFErIaHBI- 3
lum IBF Cc commune, sequetur (ex ejuldem Monito) ba Cn BF unius esle ad dimerien
dem BI, ur alia balis F. L ad eaudem dimerientem BL, dt idcirco aquales BF _C F L (PernO-,
nam quinci.
Anod sEis LI. Rursus et secundo cum ilo sectium ABF _ HFLBales ac reliqua laterA SINE,.
proportionalia, si aliqua balis BF sic major EI balireliqua, lacus FL majus erie latere BF,
(cum sinc similia eriangula BFL _ IBF,) Sed ec minus nempe aequale ba(i IF minore (up. 3
Polica, quod ticrinon porest. IEaque eruneBF e lF recia aequales.
Arod AEIS LLI. Rurlus ec cerrio in criangulis BFI, IFB aequalibus e habentibus unum.
angulum BFLuni LEB aequalem, uitaque rectarum FI, FB est communis ba huniusac la.
erialceriusreciproce (per 15 sexri) ex proinde aqualia erunrilo (celis IF B laceca IF ip(I FB,.
de anguli qui ad balin IB aequales.
divessuos dolireo O. Secundo dico angulorum ABF, AF B unumquemque esle criplum,
reliqui.
ArodEs. Trianguli enim AIB exterior angulus FIB rel FBF illi aequalis, binis LAB, 
BA incerioribus est aequalis, cui ad datur 1B A aequalis ei qui ad A. Forus AFB e proin-
de religuus ABFCplus ctic anguli BAF reliqui.
Euuxceaoua. Ulolceles iraque criangulum ABF habens unumquem que eorum ABE,
t B qui ad balin sunc ansulorum criplum reliqui qui ad A, conslicuimus.
Llen-
tur circumterencia hexagoni BC, _ cadar in semidiamerrum AB perpendicularis C F.
agacur aurem altera semidiamerer AP, Secans C B in quocunque F puncto, perpendicu
larem vero CF in I. (Fcquid enim acriner ad constructionem secare C F. bitariam in D.
X per D agere parallelam ips AD, ad indicandum F. punctum cum in quibulcunque le-
ctionibus eadem omnino viscat argumentario:) Denique jungatur FB.
AIoesSpOS nECOTO. Dico rectasIL
E. B esse aequales
Kaeraoxan. Producatur enim.