Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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            <pb pagenum="214" xlink:href="015/01/233.jpg"/>
            <p type="main">
              <s id="id003602">Propoſitio centeſima octuageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id003603">Si fuerit proportio primæ & ſecundæ quantitatis ad tertiam, ut
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              primæ & quartæ ad quintam, fueritqúe quarta ſecunda maior, erit
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              proportio quartę ad quintam maior quàm ſecundæ ad tertiam.
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              </s>
              <s id="id003604">Quod ſi fuerit maior quartę ad quintam, quàm ſecundę ad tertiam,
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              neceſſe eſt quartam ſecunda eſſe maiorem.</s>
            </p>
            <p type="main">
              <s id="id003605">Sit proportio a & b ad c, ut a & d ad e, ſitque d maior b, dico maio­
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                <arrow.to.target n="marg657"/>
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              rem eſſe
                <expan abbr="proportionẽ">proportionem</expan>
              d ad e quàm b ad e, quod
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                <figure id="id.015.01.233.1.jpg" xlink:href="015/01/233/1.jpg" number="224"/>
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              ſi maior ſit proportio d ad c quàm b ad c, dico d
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              eſſe maiorem b. </s>
              <s id="id003606">Quoniam enim eſt d eſt maior
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              b ad d eſt maior a b per
                <expan abbr="communẽ">communem</expan>
              animi ſenten­
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              tiam, igitur cum ſit proportio a d ad e ut a b ad c,
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              erit e maior c, igitur minor proportio a ad e quam a ad c, at propor­
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                <arrow.to.target n="marg658"/>
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              tio totius a d ad e eſt æqualis proportioni a b ad e, igitur ex com­
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                <arrow.to.target n="marg659"/>
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              muni animi ſententia maior proportio d ad e, quam b ad c. </s>
              <s id="id003607">Rurſus,
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              ſi maior eſt proportio d ad e quàm b ad c, igitur per communem
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              animi ſententiam maior eſt a ad e quàm a ad c, igitur e maior quàm
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                <arrow.to.target n="marg660"/>
                <lb/>
              c, ſed d maiorem habet proportionem ad e quàm b ad c, igitur d
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                <arrow.to.target n="marg661"/>
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              maiorem quàm b.</s>
            </p>
            <p type="margin">
              <s id="id003608">
                <margin.target id="marg657"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003609">
                <margin.target id="marg658"/>
              P
                <emph type="italics"/>
              er
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              14.
                <emph type="italics"/>
              quin
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              ti
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              E
                <emph type="italics"/>
              lem.
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              </s>
            </p>
            <p type="margin">
              <s id="id003610">
                <margin.target id="marg659"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              eiuſ­
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              dem.
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              </s>
            </p>
            <p type="margin">
              <s id="id003611">
                <margin.target id="marg660"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10.
                <lb/>
                <emph type="italics"/>
              quinti
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              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003612">
                <margin.target id="marg661"/>
              P
                <emph type="italics"/>
              er eadem
                <lb/>
              ſæpius repe­
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              titam.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003613">Propoſitio centeſima octuageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id003614">Si eiſdem uiribus & eadem proportione cum auxilio ponderis
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              tertij, quartum pondus moueatur quibus ſecundum auxilio primi,
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              neceſſe eſt quartum pondus tardiùs & maiore cum difficultate
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              moueri quàm ſecundum.
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                <arrow.to.target n="marg662"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003615">
                <margin.target id="marg662"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003616">Maneat prior figura, & ſint uires a quæ cum pondere b moue­
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              ant c pondus, et cum d pondere eadem uires ſub eadem proportio­
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              ne moueant e, ſit autem pondus d maius quàm b, dico e tardius &
                <lb/>
              difficilius moueri quàm c. </s>
              <s id="id003617">Nam ex præcedente e erit maius quàm
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              c, & proportio d ad e maior quàm b ad c, & proportio a ad e minor
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              quàm ad c, tum ergo propter uectem magis preſſum, tum quia d
                <lb/>
              non mouet e, niſi motum ab a, neceſſe eſt ut tardius & maiore cum
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              difficultate admoueat e quo a b mouet c. </s>
              <s id="id003618">Et ideo eo perueniri po­
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              terit abſque dubio, ut a b moueat uelociter e & a d, nullo mouente.
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              </s>
              <s id="id003619">Quia hoc accidit cùm d non mouet c niſi quia motum ab a.</s>
            </p>
            <p type="main">
              <s id="id003620">Propoſitio centeſima octuageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id003621">Si uires aliquæ moueant cum ponderibus aliqua pondera, ut
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              compoſita proportio ſit eadem proportioni uirium & duorum
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              ponderum mouentium aggregatum æquale duorum ponderum,
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              ubi maior fuerit partium inæqualitas, ibi erit maior difficultas.</s>
            </p>
            <p type="main">
              <s id="id003622">Sint uires a, & aggregatum ponderum b c & d e æqualia, & a </s>
            </p>
            <p type="main">
              <s id="id003623">
                <arrow.to.target n="marg663"/>
                <lb/>
              cum f & g moueat b & c ſub proportionibus componentibus </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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