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>
            <pb pagenum="65" xlink:href="015/01/084.jpg"/>
            <p type="main">
              <s id="id001244">Cauſæ igitur quæ alleuiant ictum, ne diſſoluatur, ſunt ſeptem le­</s>
            </p>
            <p type="main">
              <s id="id001245">
                <arrow.to.target n="marg265"/>
                <lb/>
              uitas ictus, ponderis, fractura, mollities eius, quod icitur, mollities
                <lb/>
              eius, quod excipit ictum, motus eiuſdem, & figura lata, & inæqua­
                <lb/>
              lis. </s>
              <s id="id001246">Durities ergo, quatenus fracturæ opponitur, aliud eſt, quam ut
                <lb/>
              mollitiei: & utra que eſt cauſa, quæ auget ictum, ut reliquæ
                <lb/>
              oppoſitæ minuunt, dicemus autem de his inferius.</s>
            </p>
            <p type="margin">
              <s id="id001247">
                <margin.target id="marg265"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 9.</s>
            </p>
            <p type="main">
              <s id="id001248">Propoſitio ſeptuageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id001249">Proportionem immoti in aqua ad immotum in terra in excipien
                <lb/>
              do ictum inuenire.</s>
            </p>
            <p type="main">
              <s id="id001250">Sit pondus a in terra æquale b eiuſdem naturæ magnitudinis fi­
                <lb/>
                <arrow.to.target n="marg266"/>
                <lb/>
              guræ, & eodem in ſitu, quod ſit in aqua porrò a, ſi eſſet affixum ter­
                <lb/>
              ræ oportet, ut conuellatur, aut diſſoluatur aut frangatur. </s>
              <s id="id001251">Et clarum
                <lb/>
                <figure id="id.015.01.084.1.jpg" xlink:href="015/01/084/1.jpg" number="81"/>
                <lb/>
              eſt, quod totum ictum excipit. </s>
              <s id="id001252">Si uerò
                <lb/>
              affixum non ſit, euertitur, & tanto mino­
                <lb/>
              rem partem excipit ictus, quanto faci­
                <lb/>
              lior eſt ad euerſionem. </s>
              <s id="id001253">Vnde nata fabu­
                <lb/>
              la de quercu, quæ cum immobilis eſſet,
                <lb/>
              & ſtaret uento euerſa eſt, arundo flecten­
                <lb/>
              do ſe, cecidit quidem, ſed non eſt eradi­
                <lb/>
              cata. </s>
              <s id="id001254">Sermo igitur eſt de b inſidenti aquę
                <lb/>
              in comparatione ad a, quando excipit
                <lb/>
              plenum ictum. </s>
              <s id="id001255">Cum ergo b tangitur, ex­
                <lb/>
              cipit plenum ictum illo inſtanti, ſed quia
                <lb/>
              non excipitur ictus cedente materia, &
                <lb/>
              antequam materia cedat b mouetur loco, quia inſidet aquæ, ergo
                <lb/>
              non excipit ictum. </s>
              <s id="id001256">Proponatur ergo, quod moueatur b per c ſpa­
                <lb/>
              tium in d tempore, & ſit, ut idem b ab e ui trahatur per idem ſpa­
                <lb/>
              tium in eodem tempore ex loco directo ad eandem partem: qua­
                <lb/>
              lis ergo proportio e ad b, & aërem, qui cum eo reſiſtit, talis propor­
                <lb/>
              tio ictus f grauis puta in a ad ictum Y in b. </s>
              <s id="id001257">Quia per demonſtra­
                <lb/>
                <arrow.to.target n="marg267"/>
                <lb/>
              ta ſuperius proportio f ad a producitur ex proportionibus e ad b,
                <lb/>
                <arrow.to.target n="marg268"/>
                <lb/>
              & a ad e, ergo diuiſa proportione f ad a per proportionem c ad b
                <lb/>
              exibit proportio ictus Y in a ad ictum Y in b quod erat demon­
                <lb/>
              ſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id001258">
                <margin.target id="marg266"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001259">
                <margin.target id="marg267"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              2.</s>
            </p>
            <p type="margin">
              <s id="id001260">
                <margin.target id="marg268"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              42. & 43. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001261">Ex hoc patet, quod b quanto mollius, leuius, & ſtrictius in imo,
                <lb/>
                <arrow.to.target n="marg269"/>
                <lb/>
              & in tenuiore aqua, eo minus lædetur. </s>
              <s id="id001262">Et quanto ictus lentior fue­
                <lb/>
              rit etiam quod ſit grauius Y.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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