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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 298, page id 1815201908:0355
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Demonstratio.
Plamerro BD coningaca d
CaTUTNO, _ FHI diametre
PC. Tangancurque ND, PHI
Duoniam diametri P D, F FTeam
in lK quam L MI proportionali.
cer lunc dinila, erie rerectangulum
BID ad rectangulum BL D sic
FK HI, Tecangulum ad rectangu
lum IM FI: quarc requadratum
AI ad quadracum NL. lic qua-
dearum FK ad quadracum PMt.
e ii AI linca ad lincam NLsC
ad FMI id est M H NItur ve criangulum NE. D ad criangulum AIL, (IC PMH
criangulum ad criangulum P RM (quia ex iisdemillorum raclo componitur:) d pers
mutando ve DTT D criangulum ad criangulum PM II, Sc AIL criangulum ad erian.
SUlum ERM. ICdNT D, PMEI criangula Tunc aequalia, isIEUIE AIL, PR Mcrian-
suta, adeojuCEOTa AC L, F: CM equancur. Quod erac demonstrandum.
F CC A B C ellipsim aUa MIaIHCEEorum coniusariones AB, CD, EP,
LOHI, domnes quatuor dlamerri proporrionalicer (int diurilx in l, I,
M, L panictis, per qua ordinatim ducaneur linca NO, PO, RS, TV.
Dicoquadraca LVO, PO simul Cumpea aequari quadraris R S, TV
Cimul Cunpels.
Demonstratio.
Voniam eam AB, L. F, Idam CD, FTO proporciona
licer sunc divisx, etA ve A B quadratum ad rectangu-
lum ATB, SiC FF quadrarum ad rectangulum E L F.
e quadrarum CD antectangulum CRD, _ IICqua-
dracum ad rectangusum FIM C. Ex ijsdem enim racioni-
buslingulae quadratorum ad rectangula proportiones co
ponuncur. Pgicurve AB, C. D quadraca simul sumpea ad
rectangula ATB, C RD Simul CumPCA, SIC guadEAFA F F
CFT Cimul sumpea, Cum ad rectangula R I. F, IIMC P
mulsumpra: ex periturando ve AB, CD quadraca ad qua-
aald LF, G TT, AC ALB; CKD rectangula, Cunc ad re-
etangula R L P, AIM C. hoc eA a Quadraca PR, NI ad
quadrata 5L, L A. LCd AB, CD quadraris cmul Cumpris
74. huiris.
FR ad PN: Sed eriam est per constructionem ve TF ad B L, id est L. D, sICRM
PROPOSITTO CV.
b77. hujus. B Xquali2 TUnE quadrAEL F F. CFF Snul sumpea; igicur de quadracis NY, P F X9V2-
lia lune quadrata S L, TMI: ergO NO, P O quadraca simul sumpea xqualia sunE
quactacto dRitV. uda latcema.
   i  u e  e e e e e e e ete e e e   t e a   te tete ae e t te    ut ete     e  e e      es  s e e t te   e t. e pe  1  e1