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="id000976">
                <pb pagenum="54" xlink:href="015/01/073.jpg"/>
                <arrow.to.target n="marg176"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000977">
                <margin.target id="marg176"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000978">Sit graue a b c alligatum funibus in d ef, dico,
                <lb/>
                <figure id="id.015.01.073.1.jpg" xlink:href="015/01/073/1.jpg" number="68"/>
                <lb/>
              quòd facilius trahetur per fe quàm c b & e b, quàm
                <lb/>
              d a, quia ſi debet trahi ex a uel b, aut cadet, aut uis ex
                <lb/>
              a & b communicabitur c, igitur erit minor quàm in
                <lb/>
              c, & hoc naturaliter. </s>
              <s id="id000979">Mathematica autem ratione quoniam ex a tra­
                <lb/>
              hetur c, quaſi per lineam d c: at attractio recta eſt ualidior obliqua
                <lb/>
              igitur attractio c per d eſt debilior, quàm per f. </s>
              <s id="id000980">Rurſus ſi e trahitur
                <lb/>
              per d cùm a peruenerit in d, erit perinde ac, ſi attractum eſſet per li­
                <lb/>
              neam c d, ſed linea c d mouet duobus motibus, uno ad ſuperiora, al </s>
            </p>
            <p type="main">
              <s id="id000981">
                <arrow.to.target n="marg177"/>
                <lb/>
              tero ad latus, ergo lentius ad f per d c quàm f c, quod erat demon­
                <lb/>
              ſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id000982">
                <margin.target id="marg177"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              59.
                <emph type="italics"/>
              bu­ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000983">Propoſitio ſexageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id000984">Omne mobile quanto latius tanto tardius mouetur in plano.
                <lb/>
                <arrow.to.target n="marg178"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000985">
                <margin.target id="marg178"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000986">Demonſtratum eſt ſuperius quòd ſi mobile ſit ſphęricum, & tan</s>
            </p>
            <p type="main">
              <s id="id000987">
                <arrow.to.target n="marg179"/>
                <lb/>
              gat planum in puncto, quòd mouetur per quancunque uim aptam
                <lb/>
              diuidere medium. </s>
              <s id="id000988">Quia ergo ſi tangat in puncto facillime moue­
                <lb/>
              tur, ſi in linea paulò difficilius, ſi per ſuperficiem adhuc difficilius,
                <lb/>
              igitur cum fiat attritio in motu quanto latius eſt mobile eo diffici­
                <lb/>
              lius mouetur. </s>
              <s id="id000989">Sit ergo mobile a b, quod moueatur uerſus c, & quia
                <lb/>
              pars b ſeu dimidium mouetur iuxta rationem me­
                <lb/>
                <figure id="id.015.01.073.2.jpg" xlink:href="015/01/073/2.jpg" number="69"/>
                <lb/>
              dietatis, & pars a eodem modo, ergo conduplicata
                <lb/>
              difficultate, quia medietas b impedit medietatem, a
                <lb/>
              quanto latius eſt, & longius a b, tanto difficilius
                <lb/>
                <arrow.to.target n="marg180"/>
                <lb/>
              mouetur. </s>
              <s id="id000990">Et hoc intelligitur de corporibus ualde
                <lb/>
              latis propter dicta ſuperius.</s>
            </p>
            <p type="margin">
              <s id="id000991">
                <margin.target id="marg179"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              40.</s>
            </p>
            <p type="margin">
              <s id="id000992">
                <margin.target id="marg180"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              62</s>
            </p>
            <p type="main">
              <s id="id000993">Propoſitio ſexageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id000994">Proportionem duorum mobilium inter ſe cum auxilio medij
                <lb/>
              inuenire.
                <lb/>
                <arrow.to.target n="marg181"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000995">
                <margin.target id="marg181"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000996">Graue deſcendit naturaliter quatuor cauſis: prima eſt ponderis
                <lb/>
              magnitudo, unde quod grauius eſt celerius deſcendit. </s>
              <s id="id000997">Secundò ob
                <lb/>
              paruam medij repugnantiam, ideo quanto medium eſt rarius &
                <lb/>
              mobile tenuius, tanto celerius deſcendit: contrà uerò tardius. </s>
              <s id="id000998">Ter­
                <lb/>
              tiò ob impetum aëris ſub ſequentis: & ideo mobile quòd ex eadem </s>
            </p>
            <p type="main">
              <s id="id000999">
                <arrow.to.target n="marg182"/>
                <lb/>
              materia conſtat, ſemper deſcendit parte acutiore ſuprapoſita, ne aër
                <lb/>
              cogatur celerius ferri: & quanto diutius deſcendit, tanto magis in­
                <lb/>
              tenditur motus, at que augetur, ut ſuprà de claratum eſt. </s>
              <s id="id001000">Quarta cauſa
                <lb/>
              eſt, quod non impediatur ab aëre tranſuerſim moto, et à latere: ideo
                <lb/>
              leuia mobilia & magna non ſolum lentius deſcendunt, quoniam
                <lb/>
                <arrow.to.target n="marg183"/>
                <lb/>
              paruam uim habeant, & magnam repugnantiam, ſed quia tranſuer
                <lb/>
                <arrow.to.target n="marg184"/>
                <lb/>
              ſim impulſa minus mouentur motu recto, ut ſupra uiſum eſt. </s>
              <s id="id001001"/>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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