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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 251, page id 1815201908:0308
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EL L IPSIS.
Constructio es demonstratt.
XI BD per E centrum ducatux = coniusaruS A C, RanEq; continux B D, A C, acorol. 9.
BF: dico FB ese lacus rectum. aequidister enim B F ipE A C: ducaneur que huins.
Ordinacim linea OII guxe iuncta F D occurrane in I: ip (a vero F D secec AC li-
ream in R. Ononiam P. C, C FI ordinacim polcx sune ad axem BD, CrIE VE B qu2- B +. Buius.
dracum C HI ad quadracum F. C, sic B H D rectangulum ad rectangulum BF D:
(cdveB FID rectangulum ad rectansulum BFD, SiC TH B rectangulum c est ad c23. sexti.
rectangulum R E B (guia ex iisdem rationem habene compolicam scilicee ex BII
ad BB, _ CX HTD ad P D, hoc CA HI ad F K. )igicur ve quadratum O HI ad qua-
deatum CB, Sic TFIB rectangulum est ad rectangulum RR B, ee permucando in-
verrendo ve RE B rectangulum ad quadracum C F, sic PFTB rectangulum est ad
quadrarum GFI: sed cum d A C quadratum sic aequale rectangulo luper FBBD d 17. fexio.
(cum exconstruct. BD, AC, B F SINEETCS CONTINUX) crie F. C quadratum, (nimi
rum quarta parS quadrati A C cst enim F, CA C bilecta in P.) aequale rectansulO c 4. huius.
R EB quarea parri rectanguli super FB BD. igirur ec quadracum LIC aquale est
rectansulo IIIB: ergo TIC: porest spacium quod adiacecipsiLi B lacirudinem ha-
bens FB, desciens ab F B Frectangulo, similis fgurx rectangulo, BL D: quare
FBElacus rectum eAt. exhibuimus ergo, ec. Ouod cracFaciendum.
Corollarium.
E detnit. 0.
Inc lequicur primo quaruor lincas, nimirum lacus rectum aAIS LIHOFIS, AXem
maiorem, axem minorem, ex lacus rectum axis maioris in continua esse ana-
losia.
Sequitur lccundo qui datislareribus rectis axium, ellipsin extribuerie, quodin-
er Binasdaras, duas mediasinuenerie.
LKorsicie all
Seo ABC Mipae Ga SFC.
Slum exhibeto.
n