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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 481, page id 1815201908:0538
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E A R A B O L. A.
PROPOSITIO CCLXXIIL.
Ine denuo proportionales AE, AF, AD, _ AF aequalis latexI FectO
diamerri AD, ee iuagantur AB, AC.
Dicolesmencum AB ese ad segmentum AC ve quadrarum AB ad
quadracum AC.
Demonstratio.
Fomeneum AB est ad Termeneum A C a in eriplica-
caracione EB ad D C, id est serruplicata F B ad F C
cum F B, F G, D C proportionales sint: Ced AB, qua-
dratum ad quadrarum A C racionem habecb sexcuplica-
tam linea E, B ad F G igicur re quadracum AB ad qua-
deacum AC, AC AB segmentum ad serMEnEUM AC.
Duod erat demonstrandum.
PROPOSITIO CCLXXIV.
Arabolam ABC cuius diamerer AD, contingat in A linca A F;
deinper A describatur parabola F A G cuinS A F SEdiamerer & con-
tingens AD, dueacurque in ABC parabola ordinarim linea GC, Oc-
currens F A C ParabOla in G, IUINganCUTG AC, AC.
Dicoleemoncum AC esse ad lesmenrum ABC, re BD linea ad li-
nEaM DC.
Demonstratio
Rigatur ex O linea G F parallela contingenri AD. cric igitur legmentum L
ad esegmentum AB C, ve F A C criangulum id est criangulum C: D A, da Ca
gulum DAC; sed GD est ad D C, ve CD A criangulum ad criangulum D A C o
legmencum igitur RC est ad segmenrum AC, v  Ve Au MIICaI C. 104250. Mns
erax demonttrandum.
F
40
Scholion.
rbet hoc loco propositionem ducentesimam sexacesimam seprimam huius, secundum pro-
porriones quasdam arichmeticas contemplari, nimirum quae linearum.  srum
tam convexorum quam concauorum arithmetica sol progre (sio, siue incrementum.
Sit AB C parabolae diameter AD, ex contingens AF: quà divisâ inquorcunque parles
aequales punctis F, C. TI demirtantur diamerri FB, C I, TIK, F. C occurrentes paraodla in
B, B X, C: ex quibus ordinatem p onantur BL, IN K N, C. D. an L327  
+
iun.