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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 425, page id 1815201908:0482
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P AR ABO L A.
PROPOSITIO CXLVII
Ine dux parabola AB C, DC E ad cundem aremCOnILIEuCE, et ABC
Dparabola lacusrectum; minus (ic latere recto parabola DC L, nec
Sicb parabolas AlaS CONCUITTEFC. Op Ortet durem punctum concurlus
allignare.
Constructio es demonstratio.
TE A C latus rectum parabolx ABC, et DFT 12 -
cus rectum parabole DCB, linea AD adiiciacur
quedam DF, VE A E sE ad F D, SCUFET D est ad A C.
_ ex F ordinacim POnAEUE F C occurrens parabolX
DCF in C: dico illud esse punctum incerlectionis.
Duoniam est ve FID ad AC, sIC AF ad FD crie
FID F rectangulo, aequale rectargulum G AF. sed
HIDF rectangulo aequale est aquadeatum FC; situr
ee C AF rectangulo aequale quoque est quadracum
FC. unde punctum C est 2d parab0la5 ABC, DC F.
exhibuimus erzo punctum concurtus.
AP ROEOSITIOACXEVIII
AbeanEparaBOla AB C, D B F communem aXeM AL, a MlLICeS
Opolcent aurem carum incerlectionum puncta exhibere.
Construc es demonstratio.
IE ABC parabole racus rectum A HI, _ DBP2-
rabolxe latrectu P D; SececurquC AD in F,
veHIAFrectarigulo aequale sic rectansulum FDFo
_ PEF F OrdinatIm PONAEUE F B, OCCUErenS Para
bola AB C in B. dico B punctum esse incerlectio-
nis. cum enim EB in ABC parabola ordinarim
ducta sic ad axem A D, F A HI rectangulum xqua-
le cAquadrato FB. sed F AHIroctangulum equa-
leponitur rectangulo FD F; quadracum igieur F B
aequale quoque est rectangulo FD F, quare FB
ordinarim applicaca est a F D axem; in parabola DB: adeoque pustetum B veti:
que parabole est commune. exhibuimus igitur; ecc. Ouod cractaciendumo
PROPOSITIO CXLIZ.
Vine dux parabole ABC, BDC inxquates, tavences commune
actam AF, qua udemaxis sic parabola ABC, dlameter vero
parabole BDC: lecenique se in B e C punctis, oporcet illa extribere.
in
VerEex A communis TIE.
LBATOS A,.