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="51" xlink:href="015/01/070.jpg"/>
            <p type="main">
              <s id="id000908">Sit a mobile, quod moueatur per a b c impulſu uenti aut uiolen­</s>
            </p>
            <p type="main">
              <s id="id000909">
                <arrow.to.target n="marg157"/>
                <lb/>
                <figure id="id.015.01.070.1.jpg" xlink:href="015/01/070/1.jpg" number="64"/>
                <lb/>
              to cum naturali coniuncto: & ſit terminus naturalis e,
                <lb/>
                <arrow.to.target n="marg158"/>
                <lb/>
              & uiolenti d: uter que in directo c, dico, quod tardius per­
                <lb/>
              ueniet ad c quam d, uel e. </s>
              <s id="id000910">De e manifeſtum eſt, quoniam
                <lb/>
              motus aëris, qui intendit motum a, diuíditur in partem,
                <lb/>
              quæ iuuat motum ad d, & partem, quæ mouetur ad e,
                <lb/>
              igitur fit minor adiectio. </s>
              <s id="id000911">Et etiam quia a c eſt longior
                <lb/>
              a e ex diffinitione rectæ: quare tardius perueniet ad c quàm ad e du
                <lb/>
              plici ratione. </s>
              <s id="id000912">Dico etiam, quod tardius ad c quàm d. </s>
              <s id="id000913">Quia enim
                <lb/>
              uis, quæ fert ad d repugnat ei, quæ fert ad e, & uis, quæ fert ad e, re­
                <lb/>
              pugnat ei quæ fert ad d, igitur tardius perueniet ad c, quàm d. </s>
              <s id="id000914">Nec
                <lb/>
              potes dicere, quòd uis, quæ fert ad c adiuuet ad motum è regione
                <lb/>
              d, nam cum unus motus non poſsit perfici ſine altero, igitur quan­
                <lb/>
              tum motus ad e retardabit motum ad d, tanto motus a c erit tardí­
                <lb/>
              or abſolutè motu ad d. </s>
              <s id="id000915">Verum etiam eſt, quod c e breuior erit a d,
                <lb/>
              quia motus ad e ſemper contrahit motum ad d naturalis uiolen­
                <lb/>
              tum ob cauſam dictam. </s>
              <s id="id000916">Vtrùm uerò motus ad c abſolutè ſit tardi­
                <lb/>
              or, quàm ad d, non ſuppoſito, quod c e ſit æqualis a d, ſed minor,
                <lb/>
              nunc non eſt locus determinandi.</s>
            </p>
            <p type="margin">
              <s id="id000917">
                <margin.target id="marg157"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000918">
                <margin.target id="marg158"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              20.
                <emph type="italics"/>
              bu­ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000919">Ex hoc patet, quod motus æquidiſtantis mobilis, finis eſt mini­
                <lb/>
                <arrow.to.target n="marg159"/>
                <lb/>
              mus omnium: quoniam mobile quaſi quieſcit in illo. </s>
              <s id="id000920">Velut ſi a mo
                <lb/>
              ueatur ad b, inde deflectat ad c minimus motus erit in b, ubi incipit
                <lb/>
              naturalis: nam cum incipiat, erit debiliſsimus, quia non
                <lb/>
                <figure id="id.015.01.070.2.jpg" xlink:href="015/01/070/2.jpg" number="65"/>
                <lb/>
              eſt motus actu: uiolentus autem æqualis eſt naturali,
                <lb/>
              dum minimus eſt: ergo cum ex diſtantia medij palmi
                <lb/>
              duplicetur, naturalis erit motus in b minimus, niſi b c
                <lb/>
                <arrow.to.target n="marg160"/>
                <lb/>
              eſſet minor dimidio palmi. </s>
              <s id="id000921">Et etiam quòd eſſet minor, quia ut di­
                <lb/>
              ctum eſt, uter que ſimul iunctus eſt æqualis uni eorum non impedito
                <lb/>
              uel minor.</s>
            </p>
            <p type="margin">
              <s id="id000922">
                <margin.target id="marg159"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000923">
                <margin.target id="marg160"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              57.
                <emph type="italics"/>
              bu­ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000924">Propoſitio ſexageſima.</s>
            </p>
            <p type="main">
              <s id="id000925">Omne mobile motu naturali deſcendens parte, deſcendit gra­
                <lb/>
              uiore ſecundum grauitatis centrum.</s>
            </p>
            <p type="main">
              <s id="id000926">Sit a mobile, grauitatis centrum b, cuius pars ei pro­
                <lb/>
                <arrow.to.target n="marg161"/>
                <lb/>
                <figure id="id.015.01.070.3.jpg" xlink:href="015/01/070/3.jpg" number="66"/>
                <lb/>
              ximior ſit c a, dico quod deſcendat motu naturali c a,
                <lb/>
              parte tangendo terram, quia enim totum a non poteſt
                <lb/>
              deſcendere ad centrum deſcendit b, quia eadem eſt na­
                <lb/>
              tura partis, & totius: totius autem terræ natura eſt ut
                <lb/>
              centrum, totius ſit centrum grauitatis, quare b breuiore uia fertur
                <lb/>
                <arrow.to.target n="marg162"/>
                <lb/>
              ad centrum, ergo per c d proximiorem partem ipſi b. </s>
              <s id="id000927">Sed pars pro­
                <lb/>
              ximior neceſſariò eſt grauior, quia centrum eſt in medio </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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