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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 429, page id 1815201908:0486
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d
ARS C
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Proprietates contemplatur parabolarum sese intot
vel circulos intersecantium.
PROeOSITIO CLILI
ABCaNE ABC, AD F. parabolae communem axem AF, d VetII
Lcem A: ex quo demissâ linea AG qua parabolis occurrac in B
_ C, ponancurper B ec C7 ordinarim ad axem linea DFI, Gl: 8
CI quidem parabola AB C OccurrAT in KE puncto, per quod ex A secanS
Ponacur AL ex ex L ordinatim recta LM, OcCurreNS A BC parabolae
in N: dein per N PONaTuT AF, _ ex F. ordinatim linea R C F.
Dico DH KIlineas, irem L. MI, C F
incer se aequales este.
Demonstratio.
 Acio AHF ad AF, hoc eA HB ad LC.
duplicata eAt rationis IIB ad TK, hoc est
FTD ad TC. igicur FIB, TK, TC proporcio-
nalestunE. _C VE LR ad PC, SCHIB adLR, (C0
HTB cs ad ITD, ve est TR ad TC; igieur
HB est ad TTD, ve HL P ad TK. Xqualesigi-
TUFTUNE HID _x IK. eadem rarione oMtende-
cur lincaS LM, C F aequales cAC.
PROPOSITIO CLIV.
IIdempositis, rectxe AL, A F. SeCCNE
LDE lincam in O _ P.
Dicorectas FF, L. MI, GI, DHI, BFI,
OFI, PHI in concinua ese proportione.
Demonstratio.
s
Vomam NNT aequalis CAORCNIa OT, _E EF, 2L M, NM proportionales sime, a +2. huitis.
eeronca L F. LM. Cl linex in concinua analooia: et quia lM, C+ l, R L P1O
Porrionaleslune, _ Kllinex aequalis linea D FI, ConcinuabHIE quoq: L MI, GB DFI,
racionem cum P F, LM, GI: Clt aucem pexecerea ve GT ad DHI: SCDII ad BTI,
proporcionales igitAETUNE E F, LMI, CI, DFT, B IT. vicorius cum ACvE GI ad KI.
Ac BTTad OFI, lic aucem ve CF IadK I; sCCFTadDFI, e WTTadBH, recte (+l.
DTE BF. OHconcinux proporcionales lun ele e alId L
2dNMI, id cA ex demonstraris P M ad CT. id est CFTadD H. hocclt DH2aBL
hoc est BFT ad OHI; cruncOL, DTT, BFT, OFI; PET linex, adeoque omines LLs
LM, CL DFE, B F O H, P A in conrinum analosia. Duod exac demonctrandum.
AThh 3
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