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="id002134">
                <pb pagenum="119" xlink:href="015/01/138.jpg"/>
              o a, ad o c, igitur clauus eſt longè potentior in comparatione ueli
                <lb/>
              d, quam f, ergo uelum d minus agit nauim, quam f. </s>
              <s id="id002135">Sed ut extrema
                <lb/>
              ſe habent, ita medium eorum comparatione, igitur malus b e uali­
                <lb/>
              dior eſt, multo d a, & infirmior c f. </s>
              <s id="id002136">Verùm, ut dixi, ob ſitum ſimpli­
                <lb/>
              citer ualidius eſt, uelum e quam f, & etiam quia, ut dixi, altior &
                <lb/>
              craſsior ſolet eſſe, ideo multo ualidior tribus his cauſis, quàm e f:
                <lb/>
              adde quartam quòd uelum habet maius, antiquo tempore uoca­
                <lb/>
              tum acatius. </s>
              <s id="id002137">At ut etiam docui c b non eſt in medio, nec æquidiſtat
                <lb/>
              ab a d & c f, ſed inclinatur ad proram ideoque imbecillior: cum ergo
                <lb/>
              ſit æqualium, & paulo maiorum uirium, quàm c f, & tutior, & me­
                <lb/>
              lius agatur per
                <expan abbr="clauũ">clauum</expan>
              quàm c f, & ſit a d nimis iuſto imbecillis, pro­
                <lb/>
              pterea b e mali, & ueli maximus eſt uſus: adeò mali nomen per an­
                <lb/>
              tonomaſiam de ipſo ſimpliciter intelligatur.</s>
            </p>
            <p type="main">
              <s id="id002138">Propoſitio centeſima uigeſima prima.</s>
            </p>
            <p type="main">
              <s id="id002139">Flabelli uires, at que naturam declarare.</s>
            </p>
            <p type="main">
              <s id="id002140">Sit flabellum a b c appenſum, ut ſolet, in a, & moueatur motu </s>
            </p>
            <p type="main">
              <s id="id002141">
                <arrow.to.target n="marg413"/>
                <lb/>
              quaſi circa axem p a q in parte inferiore, & aër comprehenſus ſub
                <lb/>
              b h k, & ſpatium ſit 1 m figuræ nauicularis, quæ conſtat eſſe par­
                <lb/>
              tem cylindri inanis ex formatione ab Euclide ſcripta: nam ſi pro­
                <lb/>
              poneretur p a q ad perpendiculum ſuperſtans plano, fieret circum­
                <lb/>
              ducta a b c ſuperficie, quæ eſſet lata ſuperius, ſicut etiam inferius
                <lb/>
                <arrow.to.target n="marg414"/>
                <lb/>
              cylindrus: at ſuperius a b tenuis eſt, & anguſta, ergo fiet pars cy­
                <lb/>
              lindri inanis: quia non circumuoluitur, donec redeat. </s>
              <s id="id002142">Ergo per di­
                <lb/>
              cta ſuperius ſectio illius p r q s per axem eſt pars cuiuſdam elly­
                <lb/>
                <arrow.to.target n="marg415"/>
                <lb/>
              pſis. </s>
              <s id="id002143">Et ſectio quæuis planæ ſuperficiei æquidiſtans a b c uelut tu,
                <lb/>
              item que æquidiſtans axi p a q eſt ſuperficies rectangula, quarum
                <lb/>
              una eſt ſimilis, & æqualis b h k, eſt in una ſuperficie cum axe p a q
                <lb/>
              alia uerò eſt æquidiſtans eidem axi maior aut minor æquidiſtanti­
                <lb/>
              um, & ipſa laterum, at que rectangula ac ſi cylindrus ſtans axi plano
                <lb/>
              æquidiſtanti ſecaretur iuxta longitudinem ſeu altitudinem ſuam:
                <lb/>
              & manifeſtum eſt, quod iſta duo plana, & eorum ſuperficies ſecant
                <lb/>
              ſe mutuò ad rectos angulos.</s>
            </p>
            <p type="margin">
              <s id="id002144">
                <margin.target id="marg413"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="margin">
              <s id="id002145">
                <margin.target id="marg414"/>
              L
                <emph type="italics"/>
              ib.
                <emph.end type="italics"/>
              11.
                <lb/>
                <emph type="italics"/>
              diff.
                <emph.end type="italics"/>
              21.</s>
            </p>
            <p type="margin">
              <s id="id002146">
                <margin.target id="marg415"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              69.</s>
            </p>
            <p type="main">
              <s id="id002147">Quibus conſtitutis, qui ſtabunt iuxta l, & m longitudines aëris
                <lb/>
              moti, & loci, per quem tranſit flabellum, ſentient magnum uentum,
                <lb/>
              quoniam cum corpus m x l ab extremis partibus ſit elatius a b ex­
                <lb/>
              tremis, ſtantes, & alti tangentur à uento agitato. </s>
              <s id="id002148">Si uero ſedeant, aer
                <lb/>
              primum non attinget illos, ut etiam quia ſurſum pellitur non per­
                <lb/>
              ueniet ad illos, imò diffugiet, ergo non refrigerabuntur. </s>
              <s id="id002149">Qui uerò
                <lb/>
              à lateribus l x m
                <expan abbr="ſtabũt">ſtabunt</expan>
              hiccinde, uelut in f g, ſi ſteterint,
                <expan abbr="nõ">non</expan>
              refrigera
                <lb/>
                <expan abbr="bũtur">buntur</expan>
              , quia
                <expan abbr="quãdo">quando</expan>
              flabellum erit in l, uel m aer deſcendet, ergo fugi
                <lb/>
              et ab illis, cum autem fuerit in x, erit in loco humiliori, & </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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