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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 381, page id 845634801:0387
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=387
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.88
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daneuli
iut
eMVE.
L
R ESPONSORYM. LFBER VIII.
id est AC, aequat solidum sub duplo quadrato Cx BC _ COmpOSITA ex FF, FG, id est tri-
Pla AC. Ouare POad PT est, licuE cubus ex AC ad Colidum sub duplo quadrato ex
AC _ AC: et pottremis binis analogix terminIS ad AC adplicaris, eAPQ ad PY
liCuE AC quadratum ad sexruplum quadFaCIMI ex BC, id est, ad duplum ex AC quadra.
duae circumferentix P C. P T quarum haec a d illam est quadcupla, Sicur eriam quadea-
cum subcenla P T ad quadrarum subrena PO. Duod cractaciendum.
PROPOSTETO YI.
Ex circumterentiis duorum circulorum exiltentium in Fattone quausu
Plalunulam describere, cui rectilineum extibeatur x qualc.
Exponarur circulus quiliber sub
Ocenero descripeus, in quo luma-
aur circumfereneia P P cui quae
subrendicur ad subrenlam ejuldem
circumferenrix quadranci sIc qua-
drarica pocectare, ut quatuor ad
unum. Deinde per puncta PY
incerrallo V P vel VF aequan-
re diametrum circuli jam de-
Ccripri, delcribatur circulus aITer
Lub V CenFrO. ScceTuT aucem cir
cumferencia D T quadcitariam in
DunCtis O R, S, _e LuBTendAnEME
Quadranres illi PO. OR, RS, SI
ac denigue PT. Dicotactum ese
Quod oporruir. Descripram enim
esse lunulam OPTSR consaram
ex circumterentiis P OR. SF, PL
ad quos circulos in rarione qua-
dcupla existentes perriventibus, ic2
Ut ei rectilineum exhibeatur aqua-
le. ips nanque lunulx R P F X
quale esse rectilineum quinque. la-
TCTUM PORSI.
Ouoniam enim circulo P R I
inscripea P T ad inscripeam PO cs
quadrarica porestare, aequatuor ad unum, de conlequencer longirudine ur duo ad u-
num. Oua ipratione consticura est lemidiamerer circuli P T ad lemidiamereum cireu-
i PR T. Ioicur circulus P T ad circulum PR T quadruplam haberrationem. FF (egmen-
cum P F Cmile Ac lesmenco P 9. valerque quadruplum segmenti PQ. atque adeo
iP(a Seomenta quaruorinter se xqualia PO, OR, RS, ST. A lunula igitur O P TSR du
CCTANEUE (EBMENEA PO OR, RS, ST. Addatur vero leementum P F. Fanrundem ergO
unula  P FSR supplet Scementum PT, quancum eidem lunulae adimune sesmenta
Rectilineum iraque quinque larerum P OR S FlunuIa OP FS R àcircumtereniis
duorum circulorum existenrium in carione qua dcupla deseripex, effectum estaequale, -
cur oporrebat.
C A P Y F XTI.
De Mistilineis sive anculis sive ficuris.
era  MistilinetS lire angulis sire figuris HACtENUS OCCUVFeTUNE rxvI
uncoreatere lunctal.
tum, acque adeo ucunum ad duo. In circulo ixicur subO centro delcripco, sumprae lun
A d d 2
O. OR RS, ST.