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="id001908">
                <pb pagenum="105" xlink:href="015/01/124.jpg"/>
              cum uerò uideatur in illa tanto celerius a deſcendere, quàm b,
                <lb/>
              quanto eſt ſemidiameter a longior ſemidiametro b, liquet ex hoc,
                <lb/>
              quod æquali uelo citate deſcendunt, ſed ob uelocitatem motus in
                <lb/>
              aëre latet diſcrimen anticipationis contactus ſoli a ante b, qui di­
                <lb/>
              gnoſcitur in aqua, ex quo patet exactam eſſe æqualitatem. </s>
              <s id="id001909">Sed reſi­
                <lb/>
              liunt ſemel in aqua ambæ, cum pluries in aëre a ſolo, quare etiam in
                <lb/>
              aqua perturbatur cognitio in parum accuratis, at que ſenſu præditis,
                <lb/>
              ſicut etiam in caſu, ne altera alteram perueniat, utra que comprehenſa
                <lb/>
              duobus digitis, altera alteram tangente, & uſque ad centrum in
                <lb/>
              aquam demiſsis ſimul digitis dilatatis dimittendæ ſunt.</s>
            </p>
            <p type="main">
              <s id="id001910">Propoſitio centeſima undecima.</s>
            </p>
            <p type="main">
              <s id="id001911">Cur ex medio tela ualidiorem ictum, & naues in ſcalmo à remo,
                <lb/>
              ac malo recipiant inde ex puppi explorare.</s>
            </p>
            <p type="main">
              <s id="id001912">Ariſtoteles uidetur in Mechanicis, & qui eum ſequuti ſunt, ui­</s>
            </p>
            <p type="main">
              <s id="id001913">
                <arrow.to.target n="marg392"/>
                <lb/>
              dentur rem nauticam quòd ad remos attinet, referre in longitu­
                <lb/>
              dinem partis, quæ ſcalmum tanquàm hypomochlium interiacet
                <lb/>
              & manum: ea enim circa medium nauis cum illa ibi ſit latior ma­
                <lb/>
              ior eſt. </s>
              <s id="id001914">Sed & qui lembos ducunt, & in puppe magis diſtant à
                <lb/>
              ſcalmo & in prora, quàm in medio nauis, nec tamen uelocius il­
                <lb/>
              lam agunt: non quòd ratio illa falſa ſit, ſed quia uelocius ferun­
                <lb/>
              tur etiam ob aliam cauſam, quàm ſit hæc, & magis uniuerſalem.
                <lb/>
              </s>
              <s id="id001915">Primum igitur ſumamus, quod ſuperiùs demonſtratum eſt ſcili­
                <lb/>
                <arrow.to.target n="marg393"/>
                <lb/>
              cet, quòd ubi pondus aliquod æquale undique tanquam in li­
                <lb/>
              bra ſuſpenſum fuerit, proportio ponderis partium inæqualium
                <lb/>
              ad duas partes æquales, eſt confuſa ex proportione longitudi­
                <lb/>
              nis earundem, & quadrato eiuſdem proportionis. </s>
              <s id="id001916">Sit ergo diui­
                <lb/>
              ſa a b in c, & fiat c e æqualis c a: proportio igitur ponderis b e ad
                <lb/>
              pondus e a eſt compoſita ex proportione b e ad e a, & quadrato
                <lb/>
                <figure id="id.015.01.124.1.jpg" xlink:href="015/01/124/1.jpg" number="119"/>
                <lb/>
              eius
                <expan abbr="ſecũdum">ſecundum</expan>
              longitudinem. </s>
              <s id="id001917">at poſita agi
                <lb/>
              na d g in medio a b, proportio ponderis b e
                <lb/>
              ad pondus ea eſt, ueluti longitudinis b e
                <lb/>
              ad e a, igitur proportio
                <expan abbr="põderis">ponderis</expan>
              b e ad e a,
                <lb/>
              cum agina eſt extra medium in c, eſt tanto
                <lb/>
              maior proportione b c ad ea, quantum eſt quadratum illius pro­
                <lb/>
                <arrow.to.target n="marg394"/>
                <lb/>
              portionis, ergo b e pondus maius eſt, cum agina eſt in c, quàm in d.
                <lb/>
              </s>
              <s id="id001918">igitur per
                <expan abbr="communẽ">communem</expan>
              animi
                <expan abbr="ſententiã">ſententiam</expan>
              addito communi pondere a e,
                <lb/>
              erit pondus a b minus ſemper cum agina eſt in d, <08> in ullo alio lo­
                <lb/>
              co a b. </s>
              <s id="id001919">Ergo pondus a b apprehenſum in d
                <expan abbr="mouebit̃">mouebitur</expan>
              a b æquali ui
                <lb/>
                <arrow.to.target n="marg395"/>
                <lb/>
              maiore proportione, <08> in ullo alio loco. </s>
              <s id="id001920">Haſtile ergo in medio ap­
                <lb/>
              prehenſum maiore ui mouebitur, quàm in ulla alia parte. </s>
              <s id="id001921">Et ſi </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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