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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 406, page id 1815201908:0463
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106
PROPOSTTIO CI
ducaturq: diaineres qua Occurrens parabola in I, de A F recta
Demonstratio.
DRoductadiameter B D, SCCCE F F, A E lineas
in L e M. Duoniam AC linca xquidictac
F. F eidemque est aqualis, erie AD, dimidia
rectae AC, aequalis L Fi, dimidix ipsus R Fi qua-
re _ L M aequalis cAt MD, adeoque L D in M
bifariam diuila: unde cum de L D in B, divisa siC
non bitariam, rectangulum LMD, id est qua-
dracum MD aequalc est rectangulo L BD, vna
cum quadraro MB, id esta quadraco BD, id est
aegnale erit rectangulo FDB. Rursum cumrE
BD adTC, sicL D B rectangulum sic ad rectan-
Bulum TICI, icem AD Cb rectangulum ad re-
ctangulum AC C, id est rectangulum cA M F ad
rectangulum AR B, igicur veL DB rectangulu
ad rectangulu FT OF, SIC AMT F rectanollum est ad rectangulum A R F; Cs AUICE vE
AM P. rectansulum ad rectangulit AR Rs siC L. MD rectarigulum ad rectangulum
HIK C(quia exiiidem racionent Habene compolicam) igitur veL D B rectangulum
ad rectangulum FTCT, (ic T. MB rectangulum est ad rectangulum FIR C+. e per-
mucando ve F. DB rectangulum cu ad rectangulum LMD, sic ITCL rectangu.
lum ad rectangulum FTR C:. scd L. DB. F. M D rectangula ostensa sunc xqualia,
ixicur ee rectangutum HCt aquale cAt rectansulo H K C. Quod erac demon
Darabolam A BC cuius diameter BD, ec ordinarim ad illam polira
LAC, contingar in A linCa AF, crectaque ex C diameEO C F qua
in IE.
DicoHOTrectangulum xquari rectansulo HKC.
buius
17
B + 7. hioins
Atrandum.
d+L.htonto
soleprb
DAR ABOL
contingenti A F. OcCurraL in P, perticiatur parallelogrammum AC F.
pressionibus.
T+O CIV.
CO contingane in A d C MICa HL, C E convenientes in F. ducta
que AC, ponacur ordinarim B e que P. C, A C lincis occurrat in F, X HI.
Dico HB quadrari dimillio aeguale esserectansulum FB, L16.
Demonstratio.
PR OP O S.
DArabolam ABC cujus diameter A D ee ordinatim ad illam pOTIFA
1. L
nales sunt, _ B HIdiffererie ponieur equalis
L R. Eccta G FL, TTB CBL quoq; provortio.
nalessune, adcoque B FT quadraco aequale
rectangulum I B, TIC. Rursum scum AI
in FACPrOPerea FTK in E divisa sic bita-
SaTUT ex C diameter CF; occurrens
228. hloius.
BClince in K. Aacgue e B a quals AI
Duomamiduut . Bd CrBlopo
re L B, HC rectangulum dimidium cltella a LB, HI C, adeotue e xquale
 suadrari HB. Sub ta .
riam, ex FT B linexe xequalis ponatur RL, crir de L B reliqua in F divisa Bitariam; qua
 o
RC