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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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000522">
                <pb pagenum="27" xlink:href="015/01/046.jpg"/>
              & medij ad mobile, ac medium, quod reſiſtit. </s>
              <s id="id000523">Quarto ex motibus
                <lb/>
              imperfectis natura ſua, & non eſt uera miſtio, & hoc apparet in mo­
                <lb/>
              tibus uoluntarijs animalium, qui non ſunt neque æquales, neque perfe
                <lb/>
              ctè circa medium: ſed ſunt potius ſimiles uoluntarijs. </s>
              <s id="id000524">Et ideo de­
                <lb/>
              monſtrationes illæ Ariſtotelis quoad uſum nihil iuuant nos.</s>
            </p>
            <p type="margin">
              <s id="id000525">
                <margin.target id="marg86"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000526">Propoſitio trigeſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id000527">Omne mobile naturaliter motum, ſeu uiolenter uelocius moue­
                <lb/>
              tur in medio rariore, quàm denſiore. </s>
              <s id="id000528">Maior quoque eſt proportio fi­
                <lb/>
              nis motus in corpore rariore ad finem motus in corpore denſiore,
                <lb/>
              quàm principij. </s>
              <s id="id000529">In uiolento autem celeriùs perueniet ad finem mo
                <lb/>
              tus in corpore denſiore.</s>
            </p>
            <figure id="id.015.01.046.1.jpg" xlink:href="015/01/046/1.jpg" number="38"/>
            <p type="main">
              <s id="id000530">A mobile moueatur in b medio rariore, & in c denſio­
                <lb/>
                <arrow.to.target n="marg87"/>
                <lb/>
              re, igitur b minus reſiſtit, quàm c & magis adiuuat, quia
                <lb/>
              uelociùs mouetur: igitur duplici de cauſa a mouebitur
                <lb/>
              uelociùs in b quàm in c: & quia per corrolarium trigeſi­
                <lb/>
              mæ, & præcedentis proportio finis (ubi æqualiter moueantur) ad
                <lb/>
              ſua principia maior erit in d, quàm in e: ergo per
                <expan abbr="demõſtrata">demonſtrata</expan>
              à Cam
                <lb/>
              pano poſita d prima, b ſecunda, e tertia, c quarta, maior erit propor­
                <lb/>
              tio d ad e, quàm b ad c quod fuit propoſitum in naturali.</s>
            </p>
            <p type="margin">
              <s id="id000531">
                <margin.target id="marg87"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000532">Propoſitio trigeſima ertia.</s>
            </p>
            <p type="main">
              <s id="id000533">Omnia duo mobilia æqualis undique magnitudinis, quæ æquali
                <lb/>
              in tempore æqualia ſpatia pertranſeunt in diuerſis ſubſtantia me­
                <lb/>
              dijs, neceſſe eſt, ut ſit ponderis ad pondus, quemadmodum medij
                <lb/>
              ad medium, proportio duplicata.
                <lb/>
                <arrow.to.target n="marg88"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000534">
                <margin.target id="marg88"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000535">Sint duo mobilia a & b magnitudine, & forma omnino paria,
                <lb/>
              & ſint media c & d, exempli gratia: & pertranſeant æquale ſpatium
                <lb/>
              in utroque in eodem tempore, e dico proportionem ponderis b ad
                <lb/>
              pondus a eſſe duplicatam ei quæ eſt raritatis c ad raritatem d. </s>
              <s id="id000536">Quia
                <lb/>
              enim feruntur æqualiter, nam in æquali tem­
                <lb/>
                <figure id="id.015.01.046.2.jpg" xlink:href="015/01/046/2.jpg" number="39"/>
                <lb/>
              pore, ſeu eodem æqualia ſpatia pertranſe­
                <lb/>
              unt, erit proportio potentiæ a cum ſuo auxi­
                <lb/>
              lio ad id, quod reſiſtit ex c ut b cum ſuo au­
                <lb/>
              xilio ad id, quod reſiſtit ex d, permutando igi
                <lb/>
              tur d ad c, ut b ad a, ſed c ad d proportio rari­
                <lb/>
              tatis duplicat actionem, tum minus reſiſten­
                <lb/>
              do, tum adiuuando motum a, igitur proportio differentiæ motus
                <lb/>
              eſt duplicata proportioni raritatis: ſed proportio motus eſt æqua­
                <lb/>
              lis proportioni ponderis uiciſsim per uigeſimam ſextam ſexti Ele­
                <lb/>
              mentorum b ad a, igitur proportio b ad a ponderis eſt duplicata ei,
                <lb/>
              quæ eſt raritatis c ad raritatem d.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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