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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 392, page id 1815201908:0449
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aCoroll. 25.
ains
1bid.
D. huins:
59. huttos.
e Corocl. 35.
AR ADC
Demonstratio.
CIn vero: Ponancur continue proportionales CL.
CD, CHI a ex HI ordinarim ducaeur EIC7, 0c
curtens LB linex in C: critisicur punctum C, ad
patabolam ABC: adcoque linca AB a Parabola
ibus punctis occurrie. Ouod heribnon pocest
vnde CF, CD, CF concinux lune proxorcionales.
PRODOSITIO LXIIL
Sro parabola ABC diameter guxcum-
Lsque BD aequalis laceri recto, aetaque
per D ordinatim AC, que parabolX occur.
racin A_ C, iungantur AB, BC.
Dicoaneulum AB C eserectum.
Demonstratio.
Voniam BD diameter laceri recto aqualis elt,
Le A C ordinacim posica lincae DB, cD A,
C aquales sunc. adeoque e puncta ABC, ad
circulum cuius AC dismeter eAt: angulus igieur
ABC rectus est. Ouoderar demonstrandum.
AOPOSITIO LXIV.
Demonstratio
p
suis AC, quxe parabola OcCUTFAC In A _ C, IUnGANEUEAB, BC:
Dicoangulum ABC esse rectum.
Sco A B C parabolx aris BD aequalis laceri recto, act à que per D qua
DOnancur ex a d C ocaac a A Ls C Ct.
cruncigicur BF, sBD, BC linca proporrionales;
quia vero BD media aequalis laceri recto cA, crune
EBL, CLBC criangula similia; e angulus BAF
aqualis angulo EBC, id est CB C: led angulus
B A F. una cum angulo ABF, recto est xqualis, quid
angulus AR B ad axem rectus est: isicur ec ansulus
CBD onacum angulo ABF. enirecto sunCXqua
les. rectusixicur abis clus B C. Duod erac demonstrandum.
ROPOSITIO LX
IIdem politis.
DC duplicata est.
Dico AB adBC, eracu HabetC TatOneM etuS, CHIUS AV ad
Demooratio
Voniam in criangulis GBF, CBC anguli ad G recti sunE, linCXqUC RC, OC
Laquales exhypochesi, crianoula FB C, C B C incer le aequalia (unc, d PB, C B
F3d. um. CX quoque aequales: Vnde Cum EatIOA B ad LiB, EiplCaCA AC eIuS, cuius dupi.
Cacam
M BI  A et  . 1    u e. 1  1 . .  t  e u  .    ue     . 1  l  1   1  . . 1  1e. 1. p. .  . 1 . . 1