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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 877, page id 1815201908:0934
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ATRTCARTM
S PR IALILL
Fundamentdus propositiones complectitur naturam deno-
minatorum concernentes.
EROPOSITIO PRIMA.
prumuisrarion possibile cA denominatores exhibere.
Demonstratio.
Ac est murua gux dam ancecedentis ad consequens habitodore cundum exces
LLsum, et defectu el aequalirarem. Cum isicur rnius racionis ancecedens magis
excedas consequens, vel ab eodem masis deticiar, quam alcerius racionis antecedens
suum excedar consequens, vel deficiarab eodem; manifectum est unam rarionem
maiorem minoremuo esse alcerL, plane verna quanciras alcera maior minorue est.
Ouare sicuri porest exprimi rectis lineis quanto vna quancicas alcera sic maior vel
minor, ica etiam rectae lines extiberi pollune, qux octendant quanto rna proporcio
maior lic vel minor quam alcera. Aequi racionum denominatores luncrales recte li-
RCx, vepacet ex 2. detinicione. Ouarumuisigicur racionum possibile est denomint.
coresexhibere. Ouod erac demonstrandum.
Pcoblemanice aurem exhibebimus denominacores propos. uy huius libri.
eR OPOSITIO II.
Varaciones habences cOmmuNE CON(eqUeNS, CAM LOTEIUNEuF FalO
nem que incer anrcCCdentes terminosreperitur.
Demonstratio.
GTeratio Aad B, _ C ad B: illarum
aucem denominatores HHC L, e F:
per gcastum principiuns duius libri, D
ductuh B, exhibet H, limilicer F du
ctum in B exhibec C. 1gitut veD, ducti
in B. ad F, ductum in B, Ia cA A adC:
sed D in Bad F. I B, cam habec ratio.
guens tabenTeS, _C. Quoderacdemotaa. 
nem quam Dad L. ISut A ad C, cam
obtinec racionem, quam D ad F: se d ve D ad E~ira ek ratio A. B ad rationem C B. a Pa
ex
gicur vees Aad C, ita clteacio L1B ad C Bi quare alla lacten  
TEEEE
Corolla-
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