Ghetaldi, Marino, Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis

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            <s xml:id="echoid-s853" xml:space="preserve">
              <pb o="35" file="0047" n="47" rhead="ARCHIMEDES."/>
            datur quæſita grauitas lib. </s>
            <s xml:id="echoid-s854" xml:space="preserve">97, vnc. </s>
            <s xml:id="echoid-s855" xml:space="preserve">6, ſcrup. </s>
            <s xml:id="echoid-s856" xml:space="preserve">19, gran. </s>
            <s xml:id="echoid-s857" xml:space="preserve">11 {1/37}.</s>
            <s xml:id="echoid-s858" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s859" xml:space="preserve">Quæris denique grauitatem ſphæræ stanneæ, diametrum babentis
              <lb/>
            vnius pedis. </s>
            <s xml:id="echoid-s860" xml:space="preserve">in linea vnius pedis, ſeu 12, vnciarum, ſub titulo graui-
              <lb/>
            tatis ſphæræ ſtanneæ, datur quæſita ſphæræ grauitas lib. </s>
            <s xml:id="echoid-s861" xml:space="preserve">304, adun-
              <lb/>
            quem. </s>
            <s xml:id="echoid-s862" xml:space="preserve">Atque ita reliquarum ſphærarum in tabula nominatarum, ex
              <lb/>
            data diametrorum magnitudine, grauitates inuenies.</s>
            <s xml:id="echoid-s863" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div60" type="section" level="1" n="35">
          <head xml:id="echoid-head38" xml:space="preserve">Qua ratione hanc Tabulam compoſuimus.</head>
          <p style="it">
            <s xml:id="echoid-s864" xml:space="preserve">Primum inueniendam curauimus gra
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            uitatem alicuius ſphæræ, da-
              <lb/>
            tam babentis diametrum, & </s>
            <s xml:id="echoid-s865" xml:space="preserve">ad boc faciendum, oportebat aliquam
              <lb/>
            ſphæram efficere, ſed quoniam ad ill am efficiendam, exactam bumana
              <lb/>
            diligentia non ſufficit, fieri curauimus Cylindrum ex ſtanno, altitu-
              <lb/>
            dine æqualem diametro circuli, qui baſis eſt ipſius Cylindri, is enim
              <lb/>
            torno fieri poteſt multo exactior quam ſphæra, & </s>
            <s xml:id="echoid-s866" xml:space="preserve">facilius. </s>
            <s xml:id="echoid-s867" xml:space="preserve">buius au-
              <lb/>
            tem Cylindri altitudo, vel diameter ipſius baſis, erat duarum vncia-
              <lb/>
            rum prædicti pedis Romani, grauitas vero duarum librarum, cum
              <lb/>
            vna vncia, & </s>
            <s xml:id="echoid-s868" xml:space="preserve">octo ſcrupulis, ſiue vt boc pondus ad grana reducamus,
              <lb/>
            Cylindri grauitas erat Gran. </s>
            <s xml:id="echoid-s869" xml:space="preserve">14592. </s>
            <s xml:id="echoid-s870" xml:space="preserve">abstulimns ab bac Cylindri
              <lb/>
            grauitate partem tertiam, id est 4864, reliquum, quod est 9728. </s>
            <s xml:id="echoid-s871" xml:space="preserve">ſer-
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            uauimus, pro grauitate ſphæræ, diametrum babentis æqualem altitu-
              <lb/>
            dini Cylindri, oſtenſum enim est ab Archimede propoſ 32, lib. </s>
            <s xml:id="echoid-s872" xml:space="preserve">1, de
              <lb/>
            ſphæra, & </s>
            <s xml:id="echoid-s873" xml:space="preserve">Cylindro, Cylindrum, qui baſim babeat maximo in ſphæra
              <lb/>
            circulo æqualem, & </s>
            <s xml:id="echoid-s874" xml:space="preserve">altitudinem æqualem diametro ſphæræ, ad ipſam
              <lb/>
            ſphæram ſeſquialterum eſſe; </s>
            <s xml:id="echoid-s875" xml:space="preserve">itaque grauitatem ſphæræ, diametrum
              <lb/>
            babentis duarum vnciarum inuenimus eſſe gran. </s>
            <s xml:id="echoid-s876" xml:space="preserve">9728.</s>
            <s xml:id="echoid-s877" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s878" xml:space="preserve">Inuenta igitur grauitate ſphæræ, cuius diameter est duarum vn-
              <lb/>
            ciarum, facile inuenientur reliquarum ſphærarũ grauitates, ſi enim
              <lb/>
            inuenienda ſit grauitas ſphæræ stannea babentis diametrum {1/4}. </s>
            <s xml:id="echoid-s879" xml:space="preserve">vn-
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            ciæ. </s>
            <s xml:id="echoid-s880" xml:space="preserve">fiat vt cubus ex 2, ad cubum ex {1/4}, boc est vt 512, ad 1, ita 9728,
              <lb/>
            ad alium numerum, qui ſit 19, ſphæræ igitur cuius diameter eſt {1/4},
              <lb/>
            vnciæ, grauitas erit gran. </s>
            <s xml:id="echoid-s881" xml:space="preserve">19, ostenſum enim est prop. </s>
            <s xml:id="echoid-s882" xml:space="preserve">17, buius, ſphæ-
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            ras eiuſdem generis inter ſe eſſe in grauitate, vt diametrorum cubi in
              <lb/>
            magnitudine.</s>
            <s xml:id="echoid-s883" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s884" xml:space="preserve">Rurſus ſit inuenienda grauitas ſphæræ stannæ babentis diame-
              <lb/>
            trum {1/2}, vnciæ, fiat vt cubus ex {1/4}, ad cubum ex {1/2}, boc est vt 1, ad 8,
              <lb/>
            ita 19, ad 152, ſphæra igitur, cuius diameter eſt {1/2}, vnciæ, babebit gra-
              <lb/>
            uitatem gran. </s>
            <s xml:id="echoid-s885" xml:space="preserve">152.</s>
            <s xml:id="echoid-s886" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s887" xml:space="preserve">Sit denique inuenienda grauitas ſphæræ stannæ, diametrum ba-
              <lb/>
            bentis {3/4}, vnciæ, fiat vt cubus ex {1/4}, ad cubum ex {3/4}, boc eſt vt 1, ad 27,
              <lb/>
            ita 19, ad 513, grauitas igitur ſphæræ babentis diametrum {3/4}, vnciæ,</s>
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