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="53" xlink:href="015/01/072.jpg"/>
            <p type="main">
              <s id="id000959">Quintum, corpora dura magis læduntur à latis, quia ſcindun­</s>
            </p>
            <p type="main">
              <s id="id000960">
                <arrow.to.target n="marg173"/>
                <lb/>
              tur, mollia autem à tenuibus, quia diuiduntur: nam mollitie excipi­
                <lb/>
              unt aërem, & ita à latis non adeò patiuntur, & etiam, quoniam nec
                <lb/>
              franguntur, nec ſponte ſcinduntur.</s>
            </p>
            <p type="margin">
              <s id="id000961">
                <margin.target id="marg173"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000962">Sextum, etiam in duris penetrat aliquid aëris, aliter tota frange­
                <lb/>
                <arrow.to.target n="marg174"/>
                <lb/>
              rentur. </s>
              <s id="id000963">Conſtat etiam omnem lapidem marmoreum, aut ſiliceum
                <lb/>
              eſſe poroſum, ut dicunt. </s>
              <s id="id000964">Et etiam quia recipitur in mollioribus, er­
                <lb/>
              go etiam in durioribus & in duriſsimis: quod ſi non recipiant ut ui
                <lb/>
              trum, & gemmæ tota franguntur. </s>
              <s id="id000965">Hoc etiam uidetur ſenſiſſe Philo
                <lb/>
              ſophus, qui uult, quòd res franguntur ob poros.</s>
            </p>
            <p type="margin">
              <s id="id000966">
                <margin.target id="marg174"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000967">Propoſitio ſexageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id000968">Proportionem motoris in plano ad motorem, qui eleuat pon­
                <lb/>
              dus iuxta id, quod mouet inuenire.</s>
            </p>
            <p type="main">
              <s id="id000969">Conſtitutum eſt inuenire proportionem uirium, quæ eleuant
                <lb/>
                <arrow.to.target n="marg175"/>
                <lb/>
              pondus ad uires, quæ ipſum in plano leui trahere poſ­
                <lb/>
                <figure id="id.015.01.072.1.jpg" xlink:href="015/01/072/1.jpg" number="67"/>
                <lb/>
              ſunt. </s>
              <s id="id000970">Vires enim, quæ eleuant pondus a ſunt eædem
                <lb/>
              puta b, quæ uero trahunt c, ſed hæ poſſunt uariari, nam
                <lb/>
              quanto uinculum altius, aut decliuis locus magis, aut
                <lb/>
              aſpera ſuperficies ſeu ponderis ſeu plani, tanto difficilius trahitur,
                <lb/>
              & maiores expoſcit uires: hoc enim experimento deprehenditur.
                <lb/>
              </s>
              <s id="id000971">Duæ uerò poſtremæ cauſæ etiam per ſe perſpicuæ ſunt, nec demon
                <lb/>
              ſtratione indigent: niſi quod ſi planum ſit duriſsimum, ac leuiſsi­
                <lb/>
              mum, quod eſt aſperum facilius trahitur, quia minore ſui parte pla­
                <lb/>
              num tangit. </s>
              <s id="id000972">Nos præterea ſupponimus planum æquale undique
                <lb/>
              leue durum, & corpus undique ſibi ſimile, id eſt cubi formam refe­
                <lb/>
              rens, & uinculum in imo: Demonſtrare igitur expedit primum,
                <lb/>
              quòd in hoc caſu b eſt duplum ad c. </s>
              <s id="id000973">Quia enim cum a eleuatur b ui
                <lb/>
              res ſuperant motum obſcurum ſeu occultum, ſeu pondus a, & ſi
                <lb/>
              permitteretur ſine eo, quod ſuſtineret, deſcenderet iuxta pondus
                <lb/>
              ſuum, quod ſit d: nititur ergo per pondus d, at quia trahendo duci­
                <lb/>
              tur circa medium, nam plana ſuperficies parum differt à rotunda
                <lb/>
              terræ ob terræ magnitudinem, media erit repugnantia: in eo enim
                <lb/>
              quod mouetur, grauitatem habet d in eo, quod
                <expan abbr="nõ">non</expan>
              remouetur nul­
                <lb/>
              lam habet grauitatem, mediam ergo retinet grauitatem, quare ut b
                <lb/>
              ad d, ita c ad dimidium, grauitatis a, at b eſt primum, quod poteſt
                <lb/>
              mouere d, igitur c eſt primum, quod poteſt mouere dimidium a, ut
                <lb/>
              ergo dimidium a ad d, ita c ad b, eſt igitur c dimidium b.</s>
            </p>
            <p type="margin">
              <s id="id000974">
                <margin.target id="marg175"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000975">Propoſitio ſexageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id000976">Omne graue quanto proximius alligatum plano, tanto faci­
                <lb/>
              lius </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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