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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          <chap>
            <p type="main">
              <s id="id000869">
                <pb pagenum="49" xlink:href="015/01/068.jpg"/>
              dum ordinem in duas tantum partes non ratione latitudinis, quæ
                <lb/>
              eſt æqualis, uel etiam forſan maior, ſed ratione uarietatis operatio­
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              nis quæ minus ſentitur, & maximè in primo ordine.</s>
            </p>
            <p type="main">
              <s id="id000870">Propoſitio quinquageſimaſexta.</s>
            </p>
            <p type="main">
              <s id="id000871">Proportio cuiuſuis binomij ad ſuum reciſum, uel ei commen­
                <lb/>
              ſum eſt duplicata ei, quæ ad numeri latus.
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                <arrow.to.target n="marg150"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000872">
                <margin.target id="marg150"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id000873">Cum enim proportionis medium ſit latus numeri eo quod ex bi
                <lb/>
              nomio in reciſum ſuum fit numerus ex his, quæ demonſtrata ſunt
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              generaliter in tertio Arithmeticæ de omnibus binomijs cum ſuis </s>
            </p>
            <p type="main">
              <s id="id000874">
                <arrow.to.target n="marg151"/>
                <lb/>
              reciſis, uel in quadratis lateribus erit <02> numeri media proportione
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              inter binomium, & ſuum reciſum, igitur cum proportio producto­
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              rum ex binomio in commenſa reciſo ſit, ut commenſorum ad reci­
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                <arrow.to.target n="marg152"/>
                <lb/>
              ſa erunt omnia producta ex binomio in commenſa reciſo ſuo <02> nu
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                <arrow.to.target n="marg153"/>
                <lb/>
              meri, igitur proportio binomij ad reciſum ſuum, & omnia com­
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              menſa illi, eſt duplicata ei quæ ad <02> numeri.
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                <arrow.to.target n="marg154"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000875">
                <margin.target id="marg151"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              6. P
                <emph type="italics"/>
              ro­
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              poſ. </s>
              <s id="id000876">lib. de
                <emph.end type="italics"/>
                <lb/>
              A
                <emph type="italics"/>
              liza.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000877">
                <margin.target id="marg152"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <emph type="italics"/>
              ſex
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              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000878">
                <margin.target id="marg153"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <lb/>
                <emph type="italics"/>
              ſeptimi
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              eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000879">
                <margin.target id="marg154"/>
              P
                <emph type="italics"/>
              er
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              6.
                <emph type="italics"/>
              deci­
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              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement:
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000880">Propoſitio quinquageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id000881">Motus rationem ad pondus inuenire.</s>
            </p>
            <p type="main">
              <s id="id000882">
                <arrow.to.target n="marg155"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000883">
                <margin.target id="marg155"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000884">Oſtenſum eſt antea, quod motus naturalis uelocior fit in fine, ac
                <lb/>
              magis augetur ob aëris motum, ubi uerò hæret eſt ac ſi quieſcat.
                <lb/>
              </s>
              <s id="id000885">Eadem autem eſt ratio in motis uiolenter, & naturaliter dum ęqua­
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              li impetu feruntur. </s>
              <s id="id000886">Sed ſubitò poſt etiam, quod motus æqualiter
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              augerentur minus tamen creſcit proportio uiolenti ſcilicet ob im­
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                <figure id="id.015.01.068.1.jpg" xlink:href="015/01/068/1.jpg" number="62"/>
                <lb/>
              pedimentum naturale. </s>
              <s id="id000887">Sed ſi uis mouens fuerit
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              adeò ualida ut proportio incrementi ex aëre ſit
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              maior, quàm impedimentum, & in crementum al
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              terius mobilis naturaliter moti, motus ille uelo­
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              cior fiet naturali, ut in ſphæris ferreis ex machina
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              igne excuſsis, quod ergo attinet ad præſentem
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              motum ratio eſt eadem. </s>
              <s id="id000888">Quicunque ergo motus
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              minoris grauis cogit deſcendere lancem ex ad­
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              uerſo proportionem habet eandem ad ſuum mo
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              bile quam habet graue æquiponderans. </s>
              <s id="id000889">Sit ergo
                <lb/>
              ut a ex b, c, d, e, eleuet eodem ordine pondera e, f,
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              g, h, erit ergo ponderum h, g, f, e, ad ſe inuicem, & ad a qualis mo­
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              tuum ob diſtantiam intentorum. </s>
              <s id="id000890">Experimentum ergo docet, quòd
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              dimidium ponderis æquilibrium facit ex palmo minoris dimidio
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              motum manifeſtum, & ex palmo quarta pars ponderis, ergo ſe ha­
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              bent prope portionem.</s>
            </p>
            <p type="main">
              <s id="id000891">Propoſitio quinquageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id000892">Quę ex alto deſcendunt cur non eandem pro diſtantia motus ra
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              tionem in libero aëre ſeruent conſiderare.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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