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="id001088">
                <pb pagenum="58" xlink:href="015/01/077.jpg"/>
              ius ſemidiameter eſt linea ducta à uertice portionis ad finem illius.</s>
            </p>
            <p type="margin">
              <s id="id001089">
                <margin.target id="marg204"/>
              1</s>
            </p>
            <p type="margin">
              <s id="id001090">
                <margin.target id="marg205"/>
              2</s>
            </p>
            <p type="margin">
              <s id="id001091">
                <margin.target id="marg206"/>
              3</s>
            </p>
            <p type="margin">
              <s id="id001092">
                <margin.target id="marg207"/>
              4</s>
            </p>
            <p type="margin">
              <s id="id001093">
                <margin.target id="marg208"/>
              5</s>
            </p>
            <p type="main">
              <s id="id001094">Quilibet ſector ſphæræ æqualis eſt cono, cuius baſis eſt circu­
                <lb/>
              lus æqualis ſuperficiei eiuſdem portionis, altitudo uerò ſphæræ ſe­
                <lb/>
              midiameter. </s>
              <s id="id001095">Proportio ſphæræ ad ſectorem datum, eſt duplica­
                <lb/>
              ta ei, quę eſt dimetientis ad lineam, quæ à uertice portionis ad lim­
                <lb/>
              bum. </s>
              <s id="id001096">Cum enim ſphæra ſit æqualis cono, cuius baſis eſt maior cir­
                <lb/>
              culus, altitudo uerò dupla dimetienti per tertiam harum, quæ hic
                <lb/>
                <arrow.to.target n="marg209"/>
                <lb/>
              proponuntur: erit ſphæra æqualis cono baſim habenti circulum,
                <lb/>
              cuius ſemidiameter ſit æqualis diametro ſphæræ, altitudo uerò ſe­
                <lb/>
              midiameter ſphæræ. </s>
              <s id="id001097">At per ſextam harum ſector ſphæræ eſt æqua­
                <lb/>
              lis cono habenti altitudinem ſemidiametrum ſphærę, baſim autem
                <lb/>
                <arrow.to.target n="marg210"/>
                <lb/>
              ipſam portionis ſuperficiem: igitur proportio ſphæræ ad ſecto­
                <lb/>
              rem, uelut circuli cuius diameter eſt dupla dimetienti ſphæræ ad
                <lb/>
              círculum æqualem ſuperficiei portionis: at ſuperficies portionis
                <lb/>
              per quintam harum eſt æqualis circulo, cuius ſemidiameter eſt li­
                <lb/>
              nea à uertice portionis ad limbum eiuſdem: ergo proportio ſphæ­
                <lb/>
              ræ ad ſuum ſectorem eſt uelut circuli, cuius dimetiens eſt duplus di
                <lb/>
              metienti ſphæræ, aut ſemidimetiens eſt æqualis dimetienti ſphæræ
                <lb/>
              ad circulum, cuius ſemidimetiens eſt linea à uertice portionis ad
                <lb/>
              limbum. </s>
              <s id="id001098">Sed proportio talium circulorum eſt duplicata propor­
                <lb/>
                <arrow.to.target n="marg211"/>
                <lb/>
              tioni ſemidimetientium, igitur proportio ſphæræ ad ſuum ſecto­
                <lb/>
              rem eſt ueluti dimetientis ſphæræ ad lineam, quæ á uertice portio­
                <lb/>
                <arrow.to.target n="marg212"/>
                <lb/>
              nis ad limbum duplicata. </s>
              <s id="id001099">Cuicunque portioni ſphæræ conus ille
                <lb/>
              habetur æqualis, qui baſim habeat eandem cum portione, altitudi­
                <lb/>
              nem uerò lineam rectam, quæ ad altitudinem portionis eandem
                <lb/>
              habeat proportionem, quam ſemidiametros ſphæræ unà cum alti­
                <lb/>
              tudine reliquæ portionis habet ad eandem reliquæ portionis alti­
                <lb/>
                <arrow.to.target n="marg213"/>
                <lb/>
              tudinem. </s>
              <s id="id001100">Earum ſphæræ portionum, quæ æqualibus ſuperfi­
                <lb/>
                <arrow.to.target n="marg214"/>
                <lb/>
              ciebus continentur medietas ſphæræ maxima exiſtit. </s>
              <s id="id001101">Proportio
                <lb/>
              ſuperficiei ſphæræ plano diuiſæ ad reliquæ portionis ſuperficiem,
                <lb/>
              & reſidui ſectoris ad ſectorem, eſt uelut quadratorum duarum li­
                <lb/>
              nearum quæ à uerticulis ſectionum ad communem ſuperficiem
                <lb/>
              plani portiones ſecantis deſcendunt: nam ſectorem ſphæræ, dico
                <lb/>
                <arrow.to.target n="marg215"/>
                <lb/>
              corpus compoſitum ex portione, & cono illo. </s>
              <s id="id001102">Ille idem etiam defi­
                <lb/>
              nit Ellipſim coni a cuti anguli ſectionem, quam dicit etiam fieri ſe­
                <lb/>
                <arrow.to.target n="marg216"/>
                <lb/>
              cto cylindro per planum non ad angulos rectos ſtante ſuper cylin­
                <lb/>
              dri axem. </s>
              <s id="id001103">Ab hac igitur coni acuti anguli ſectione ſeu ellipſi cir­
                <lb/>
                <arrow.to.target n="marg217"/>
                <lb/>
              cumacta figura ſphæroides corpus quod baſim rotundam habet,
                <lb/>
              uocat: id que duplex ob longum, quod fit diametro longiore quie­
                <lb/>
              ſcente, & prolatum quod fit quieſcente breuiore: ſicut reliquam ſci
                <lb/>
              licet parabolen aut hyperbolen, quia inferius non eſt terminata, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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