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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 431, page id 1815201908:0488
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et.
c
P A R A BOL A
PR OPOSITIO CLMII.
Ontingane se CaCMS In vertico, PatabOIX dux ABC, AVL, pOH
sc et  Ccaltibus AE, AC, e concingenre Afl, ducaneur
quocque IH parallela axi communi F AC
Vico LHDrectanguliim, ese ad rectansalum LFTD, veKE. HIBrectan-
sulum ad rectangulum HEHI B.
L 1 Demonstratio.
2 Ectangulum IEI D ad rectangulur
TFTD, criplicaram habet racioner
eius quam habec IFT ad TH, id est AIY
ad AFI. scd _ B FTK rectangulum ad
rectangulum BHK, criplicacam habee
cacionem ejus quam habee FIK ad IIK,
id est A FL ad A FI: IGIEUF VE BHIK ee-
ctangulum est ad rectangulum B FTK, siC
IHID rectangulum est adrectansulum THID. Ouod’érac der
PROPOSTTTO CEVIII
ontingane le rursum exterius in vercice patabolx dux ABC, A F F
ad eundem axem G II constiruea, Cumpioque in ABC perimerro
puncto quovis C ducancur ex C linex C G, C I secantes AB C parZ
bolam in B _ Is, ec axem GHI in C dc l. dein ordinarim ponantur BHI,
RNI, TE, GF.
Dico HI Blineam ad lineam MIE; duplicaram habere rarionem eius
quam habet C F linca ad lineam lF..
Demonscrata.
Veatur ex Cordinatim linea C Ii.
OuOnIaML EAM N A, AL, AM Ii-
nea quamN A, AC, AII bCOnrinuX
proporcionales lunc ex N A prima v
Erique seriei communis; rario AFT 2d
AM. cercia nd ecorriam, duplicaca
eC eius quam Habet A C+ ad AL, SC-
cunda ad secundam: (ed A FT ad A N.
duplicat a quoquerationem habet BFI
ad KM; igicur BFTeIt adK HI; VE A C
est ait AI: X TTBadMK duplicacam
habec racionem eius quam haber (7P
ad IF. Ouoderacdemonstrandum.
PROPOSTTIO CLIZ.
ScoABC parabola axis AV
aequalis lareri recto; et pet D
parabola descrivea D F. F aequalis
hin
it
ioton
Patabeta