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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 378, page id 1815201908:0435
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P ARADOL A
PR OPOSTFIO XXZIV.
Sco ABC parabole aris AD aequalis lateri
recto, ductaque ordinarim linea quacunque
EB, iunganeut AB.
DicOAF, AB, C. D lincas esse proporcionales.
Demonstratio.
Vadeacum A B aequale est quadraris AF, F B: led
LF B quadratum aquatur rectangulo F A D; igicur
quadracum AB aquale est rectangulo F. AD vna cum
quadrdco AF; id est rectangulo A F D. qUATC A F, AB
ED lincae sunc proporcionales. Ouo derat demonstran
dum.
PROPOSITIO XXZV.
DArabolam AB C cuius diamerer. AD contingar in A linea AF, de
missilq; ex A lineis AB, AC guae parabOlX OECUTTANEIn B e C
reanguli E. AB, D A C xquales sine ductisque ordinacim BF, C. D, in
veniatur A G, media INEeF A F _ A D.
Dico AG aequarilareri recto; _ (i anguli P AB, D A C aquales fuc
rinc, ee AC linea aequalis laceri recto, dico AF, AC, AD ele pFOpOr.
tionales e sI AF, AC, AD Fuerinc continux, e A C media aqualis la-
ceri recto: dicoangulos E AB, D AC esse incer se xquales.
Demonstrati.
Sulus D AC exhypocrehiequalis elt ansuIOL. AV
addico vel dempeo communi angulo BA C, angulus
B AD, aequalis est angulo F, A C, id est angulo AC D,
(Ob A F, C D paraIIClaS) aequales aurem lnE ee an-
suli BF A, C D A, criangula iBICuE AB F, A CeDin
cer se similia sune ee ve BE 2d F A, sic AD ad DC.
inde FAD rectangulo, aequale rectangulum BF.
CD; est aucem F AD rectangulo ex hypoctiesi equa
le quadratum AC, _ quadrarum H C aquale re.
aansulo BF, C D, cum BF, AC, CD linCX prOpOE.
cionales sint per pennuleimamsigirue quadrarum AC.
aequale eAt quadraro HIC. e A C linea equalis linca
Ie adeoque d lacctrecto. Duod cric primum.
Siciam AC HCa a Qualis laceri recto, de dneull
L AB, D A C EGUaLLS, dico AF, A Cm AD in conci
raa esse anal0912. St cinur non sine proporcionales, in-
VCMHIAEAE INFEF AF _ A D media A T: cric igitur per
primam parcem huiuslinea AP, aequalis laceri recto.
oulos F. AB. DLC cere a saut queam enim AF, AC, AD concinua
sunc proporcionales, F. AD rectangulu X quale est quadraco A C id est quadracO HC:
sed 8
Veacur ex C ordinatim linea G FI. Ouoniam An.
2bid. B2deoque _ A G linCX. quarC AF, AC, AD in contitua sunc analogla, HOC quaeuis
alia media InEeE AF _E AD, pEXPeF A C. Ouod erac secundum.
Rurtum AC A C+ aequalis laceri recto, _E AF, A C+, A D proportionales, dico an
opta u pte sui sue it t el t i a pet ut ut pue ue u p te i i u   u e u s    e p t e  t    tee et et  t t       ee   a eta a st t s