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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 214, page id 1815201908:0271
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bPerta
EIR CV LVS.
PRODOSITIO LXZEVIII
VIrculo ABC, quodliber pors sonum inscribatur regulare; ductaque
SCx G CenErO, GFI quae laceti B C normalicer insiltat; ex H pona-
Dicororum polygonu ad BC quadrarum cories lumprum, quoc la-
celu e pers Bim Camrationem obcinere quam HIL recta, ad B6.
Demonstratio.
VcaltuE ex C centro ad angulos polygoni
tCca AC, BC, C C, ec. Guoniam poly
coniregularis lacera aequalia lunc, crune singula
criansula AGB, BCC, COD, Xc. incer le X-
qualia: ac promde duplicia crianguli BFI G, cum
BC in FI dinila sc bitariam: sed _ BFI Ccrian-
suli, duplum est rectangulum BFTC, hoc cA
aBOFI, isitur BCC criangulo aequale cA
BOTII rectangulum, eA aucem BOHII, re-
ctangulum, ad quadracum BC, VE. EIB, adBC;
isicur eriam BCC criangulum, est ad B C+ qua-
deacum, re TTT ad B C: quia vero idem de lin-
Sulis polygoni criangulis eodem modo demon-
Aracur, Paceerorum polrsonum ad quadeacum
BC cociessumprum, quor lacerum cst polyso-
num eam proporcionem habere quam Elllincar
adreccam BCi. Uoau onAtrandum.
Tur FII, ad rectos aHe OS ip(IBC.
PR OPOSI
IC
 t 
IIdem polits,
Dico duplum polygont al Guacacu ca, qua porsconi peri-
merro suxqualis, cam rarionem habere, quam HC linea ad hlCa
Polysoni perimetro aequalem.
Demonstratio.
Scenim cocum poissonum, aguale triangulo balim habenci xequalem b linex
Locoriperimereo agnalis alcicudinem vero FTG; isirur duplum polygoni aequacur
rimetro e HIC alcicudinem; led rectanoulum hioc ad quadracum lineae aqualis
cociperimerro polrsoni, cam obciner proportionem, quam YIC lincaad lincam
xqualem coripecimetro; ergo polysonum bis sumpeum ad quadracum lince, quae
Perimerro sic xequalis, cam haber racionem, quam FTC linca, ad rectam coci peri.
meeropolyroni xequalem: quoderac demonstrandum.
Corollarium.
triansulo illi, bis sumpro, hoc est rectansulo balim habenci aequalem polysonipe.
Oc loco non videtur omicrendum sequi ex hac propolitione per ex quae in li-
beo de progrectionibus Creomerricis diximus, circulum bis sumpeum, ad qua-
dracum sux peripheria, eam seruare racionem, quam lemidiameter ad perimerrum.
eleculum alcea Cemeitam peata ad Guac ac pelnechenculalis. Calui picboi
eoee Glati quarca pars aammceri ad circuli perimeet acsce alleo
elPblicio.
t tu  ui.  1  e  s .   e  e   . 1 1.  a  . 1 1. 1 t t e        p   t  i. i e e            t  i