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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 852, page id 1815201908:0909
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DYOTYS ELAA
Demonstratio.
FCII CB EqUalES PONAnEUE NMI, quas C A diameter bilecet in C, rectis au-
cem B F aequalesfIANE NY O, MI K, CTUINEIGICUE PET PEXCCdEMEEM NCM, OR
Etis BE, reCR GFI, NIK aequales sunC MMcer se; ablacis igieur vel addiris communi.
buS MFT, relique OM, ITK aeguateslunE. Sed M C dimidix ponuneur iplarum CB.
id est ex constr. plarum FTI; isieur d HIK dimidixe lunc TII: quare cum L RK li-
nea dinidens III rectas bifariam, vera sic parabola, e TTIETAHSLACX IM NM veram
quoque producane parabolam, pater II P. L vircualem eAle parabolam.
Abeane circuli duo conceniet Communem diameeralem DF: et
Lex D reCtX PONantuF D B L. Acurrences circulominori in B, ma-
iori in L Punctis, per que rectae ducancur F. C Nnormales ad DFdiame-
merrum, C occMtant in O: rectae aurem DE cransterantur in F, GR,
verx ac Formales parabolx. quoniam eam GFI quam MIK linca xquales lunE re-
PROPOSITIO CCXXIX.
DicoLL Parave
_ D, BE. transterantur in GHI, K I.
dene raldate.
P
Demonstratio.
ECEHEUE FFF Bilactam in L L. quoniam
Sicur D P. lineis a GHIaleS CUNE E R nOrIMA
les ad D F, punCTA DR K ad a veram fUINE p2
rabolam. quia vero tam OFL. KI, quam FI L.
ecta XqualEStME, EOLE G K in L. bile.
eta sunc; adeoque dc OK ad GK, HC O L
elC Ad GT: quare L. L puncta ad veram quo-
QuE lune parabOLAMI. VIceriuS POnanEuE Pel
Ferancur aurem amidix rectarum CK siuc
DL in GMN PatetbMIO veram es(C Pa
dimidiae iplarum a GuaLES TaNE. (Cd eEOP, L HI
quoque per constructionem aequancur; reli-
queigitur Ci bl. M l agtales lunt; unde
incelligantur ONheri aequales MOrecust
MPN rectansula agua lune rectangulis
OTTK, id est per hyporhesim DBF. quia
vero rectanrula DB F egualia sune quadea-
eoconringencis DM, rectangula DB,F 2
deoque _ MPN, aequalia sunc: unde cum
NMs ad veram sinc parabolam; puntela quoque PP veram c producune parabolam
lame la  aumas rera quoque octenla c parabola, constaE HL
puncta aee rablatet  Panautato
D e F Contingentes, DR, F T, quas in R
ec I lCCEEqUEHIS R L paraIlelA D F, ErANS.
rabolam. Simiticer dimidix lincarum FIL
cransferantur in PO. Quoniam igieur MO
aequales sune dimidiis CK, rectC NIO, GL
isicur eum dimidie linearur LLL Causta  LO Formalem constieunne parabo.