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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 373, page id 1815201908:0430
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P AR ABOL A.
quoniam igitur est IIB ad BD, ve BD ad
B Cm erir componendo permucando FID 2d
DC, ve DB ad BC, est aurem re FTD ad
DO, AC AHI ad FC, ereo ve DB ad BG
id est per construccionem B H ad BD, SC AII
2d F, C. unde a FI A quadrarum ad quadra-
cum EF est ve HIB, quadracum ad quadra-
cum BD, id est (cum AIB, BD, BG, sinc conei.
DUx,) ve FT B linea eA ad lincam B G, aC pFO.
inde punctum a es ad parabolam, d AD li.
nea leccioni bis occurrie. Quod fuii demon-
Atrandum.
Corollarium.
Fincpulchra educitur proposicio: nimirum s B C, BD, B EL ponantur concinux
ex ex C ordinacim linea CF P; agaEUEqUC per pUnCTA F. eC D linea, OccurrenS
TCCEX ex HI ducta e iph C. P parallela in A: quod punccum A sic ad parabolam.
demonstracio habetur in priori propositione.
Sequitursecundo nullam lineam parabolx in pluribus quam duobus punceis oc-
currere. Cum enim parabola, secrio sic coni, ex ipsi cono nulla linea, in pluribus
quam duobus punetis occurrat, parec nec rilisectioni coniea, lineam in pluribus
QUaTA AUOBUS PUNCTISOCCUTTETO.
PROPOSITIO XZVI.
Darabolam ABC secent dux quaevis parallelx AD, B C quarum dia-
mecet ponarur L. l.
Dicoiunctas AB, DC diamerrum in eodem puncto C decustate. l
(IAC, AD aequidistenciunctx q. AB, C B conveniantin C. dico C pun-
ctum esse in diameero linearum BC, AD.
Demontio.
Voniam E P diameter est rectarum
LBC, AD, igitur diuilae sunebitariam lIM.
BC. AD inpunctis F_ F. vndeve AF
ad BF, ACH ACi ad B G: hoc eA F C
ae L V. ICAM AL ad B F, ica F. D 2d
FC; HMI BLD ad F C, ica cAt F C, 20
Fe, noeca De a CC. isicurpunctu
CConun Mcribus lincis AB, DC,
LL. uodtuit primum.
Idem quoque ostendieur si C punctum
cadu uabolam. si iam ponancur AD, B C parallela, d IUINCEX AB, CD cOn-
deahe in puncto quonis C, dico C punerum esse in dinmerro ad quam B Ci AI) Or-
Linacim. ponuneur: ouc
Divila enim B C bitariam in F demirratur ex C per F linea C P. quoniam igi
Cu AB, BC aGdictanE, erit AF, ad F D, ve BF ad F C; sed B C in F. bitariam
elincacum B C, , cc. Suoeateorandum.
ponirur diuilas isicur _ AD in F, 2 quoque divila est bitariam: vnde C P diameret, u.tmini.