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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 439, page id 845634801:0445
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à latete
CYOLOMETRTCA, SEV, ANTTMEAEETZ
AC, media est proporrionalis inter circumferentiam BC et A D. Sic A B parrium 7.
Circumterentia B C, quae quadrans est perimerri, crirminox Fr. Nam diamerro existen-
Ee r4 Perimeter minor est 44. Sit aurem AB 35. CircumFerentia B C minOr CrILG5.
Ouod vero hrsib A D, B C, aequale es quadrATO Ex AB. OIarC erir A D major 22 3
Oualium aurem AB, id es AC, valet 35, talium eAt A F 14; A F verOMINOF22 =Z. FrIE
isitur A D major quam AF. Ouod erarostendendum.
Traque si ex diamerro A B abscindarur recta A C ipsi A F aqualis, ex compleatur parallelogram-
mum C HID A, ipsum erit EFEPOunNES, non quadratum. Ficum complebitur quadratum B C, acta
diagonia B K non cransibis per LI, sed per aliquod L punctum remorius à D puncto. Ouod ad vitan-
dum eseudoeraphema prastabat adnocasse.
PR OPOSTFTO TII.
Ouadratum ab ambitu circuli, minus est decuplo quadraci a dia-
ICTTO.
Sic enim diameter 7. Diamerri quadearum exir 49. Iphus vero decuplum 490. AF
ambieus circuliminor erir 22, _ proinde quadrarum ab ambitu minus 484.
Fuic aurem hac arabum in quadrando circulo jamdiu explosa sentencia, Cuadearum ab ambi-
cu circuli esse decuplum quadrari à diamecro. Neque vero ferendus est, qui adversus demonstran-
eem Archimedem avn Palixcos Anapodicta proposuerit.
PRODOSFFTO IV.
Circulus ad hexagonum ei inccriptum rationem habet majorem, quam
(ex ad quinque.
Circulo, cajus A cerirrum, inscribatur heraconum B CDE F C. DDico circulum cujus
A Cenrum ad BCxASOnUM BCDEFCrarionem habere majorem, quam (ex ad quinque.
Punctis enim AB, A C, BC, cadac in B C perpendicularis AL.
Ouoniam igitur in erian-
Bulo ABC CTUITA AB, AC X-
qualia sune. balis secta cs bi-
Fariam in Z e lunc aequales
BZ. Z C. Frianculum aurem
aequilarerum cs ABC. CruTa
enim ambo sunt semidiame-
eri. Sed _ balIS, cum (IC la-
tus hexagoni, Cemidiaerro
est aequalis. Constituca isitur
Temidiamerro B A (Cu AC 30,
AEBZ (CUZ C 15, AZ VerOHC
minor 26, cujus quadratum est
676. Differencia vero quadra-
EOTUM AB, BZ eA dunCaZAE
675. Ouod Arporro lub B2.
AZ rectanigulum, criangulo
B A C est aequale. DUCAEUE
itaque r5 in 26, AUnE 390.
Oualium igitur quadearum
AB erir 900, calium eriangu-
lum A B C erie minus 390, vel
Aenre qusdrato AB;0, triangulum ABC eric minus13. Tungantur AD, AE, AF, AC
(omnibus divilIs per 30) exi-
Constatioirur hexrgonum BC D E. F. G criangulis Cex aequalibus ipli B A C. OuatC qua-
lium quadeacum A B eric 30, calium hexagonum exie minus 7 8. Vel qualium quadeacum
AB erie quinque, calium hexozonum erir minusparribuscredecim.
A2hH3