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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 379, page id 845634801:0385
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enim e
leototit
et
recta
D.
Aores,
IMC
SDC
Mt
OCto3)
RE SPONSORYM. LTBER VIII.
SICUE quadTatuM ex B C ad quAdTAEUI EEPIMI Ex BC, minus quadratO exBZ. Ex Cum
quadrarum ex BZ aequale sic ei quod sc sub BD, BC: est BZ ad FI, SicuEBC ad BC cri
plum, minus BD. Ip(a POrrO BD vAICEBC FEF, IINUS AC. COIMPOMLA CHMHCMDD CK
BC, CD. Iplaq; C. D constructa eAt xqualis excestui quo AB, id elt dupla BC, praeltac ipli
AC. Er∞O CsE BZ ad FL, SicuEBC ad AC. Sed quadratum ex BC ad quadracum ex A C est.
ur unum ad eria. In circuloigitur sub L centro descripro, sumprxe lunt duxe circumferen.
EIXFC, FL quarum haec ad illam estrripla, sicur etiam eriplum est quadrarum F L a d qua-
deatum FC. Ouod erar faciendum.
PROPOSTTIO II.
EX CIFCIIFETENEIIS ALIOFUM CIECUIOFHMI EHIIFCEIMIM I PAEIONC LLIPIa IUI-
nulam describere, cui rectilineum extribeatur aequale.
Exponarur circulus quilibee sub L cenrro descripeus in quo luIaEUT CITCUMFeTCHEIA
Fl, cui qua subrendicur ad subcenlam ejuldem circumferencix erienti sic quadrarica pore-
Itace, vecria ad unum. Deindeper puncta FI, incerrallo HLI vel FK sumpro aequalilatere
rrigoni eidem circulo P L inseripri describatur circulus alcer F L L SuB R ceNETO. SCCCTUE
aurem circum ferencia F. leritariam in punctis C, II, ee subcendancur rrienres illi F6, CF),
HII, ac denique F I. Dico factum
esse quod oporeuir. Delcripeam
enim esse lunulam GFLIEI conAa-
tam ex circum ferenciis FGHIL, FL. L
ad duos circulos in ratione cripla
existences, perrinencibus, ita ur ei
cectilineum extribeatur aequale
IpS namque lunulX CFL IEI aqua
le esse rectilineum quadrilacerum +
GTII.
Ouoniam enim circulo FCTII
inseripea F P ad in(cripram F C est
quadratica porestare, uc eria adu-
num, iraque longirudine estur la-
cus eriooni eidem circulo inseripri
ad semidiamerrum. Oua in ratione
constitura est semidrameter circuli
LI ad semidiametrum circuli
FOFII. Igitur circulus FLI ad cir-
culum FC FII eriplam habet rario-
DeM. EF Cegmencum L FL Simile HF
(ComentoFONT, valerque criplum
lcomenci FON. Acque adeo ipla
eemenea cria incer le aqualia FON, GFIO, TIIMI. NequE veTOTII recta, Dedum recta
E vel F C secabic circum terentiam F. L. L, propcer Smilicudinem circum terentiarum
NG, FLI, exjam demonstraris. A lunula IBITE GFLIFLAUFCTANEESCBMENTA FON
BHO, LLIM; addatur vero segmenrum L.PI. Fancundem ergo lunula CFLIFL suppleE
Remencum FIL, quanrum eidem lunula adimUnE LeGMEMEA FGN, GHO, HIM. Recti-
locum icaque quadcilacerum FCFL lunulae L. FC FL L circulorum à circumterenriis duo-
um circulorum existenrium in racione sripla descripra, eflectum est aequale, (icur opOr-
cebal.
PROFOSILLO Y
auelculo duas circumterentias lumere exittenres u laloe uaru.
ela, in qua etiam se habeant rectarum, quae iplis circumterentiis subren-
dunET, quadrata.
FixpO