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

Table of handwritten notes

< >
< >
page |< < (16) of 89 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div32" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s439" xml:space="preserve">
              <pb o="16" file="0028" n="28" rhead="PROMOTVS"/>
            dæ ſphæræ B, data diameter F, & </s>
            <s xml:id="echoid-s440" xml:space="preserve">oporteat inuenire quan
              <lb/>
            ta erit diameter ſolidæ ſphæræ A, ita faciendum erit.</s>
            <s xml:id="echoid-s441" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s442" xml:space="preserve">Accepto vt ſupra corpore ſolido D, & </s>
            <s xml:id="echoid-s443" xml:space="preserve">liquidi E, inuenta grauitate,
              <lb/>
            vt dictum eſt, fiat vt grauitas G, ad prauitatem H, ita cubus ex F, ad
              <lb/>
            alium cubum, cuius latus ſit C, Quoniam igitur eadem ratione qua
              <lb/>
            ſupra oſtendetur, vt grauitas G, ad grauitatem H, ita eſſe magnitudi-
              <lb/>
            nem ſphæræ B, ad ſphæræ A, magnitudinem, ſed magnitudo ſphæræ B,
              <lb/>
            ad magnitudinem ſphæræ A, triplicatam rationem habet eius,
              <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">18. 12.
                <lb/>
              Elem.</note>
            F, diameter ſphæræ B, ad diametrum ſphæræ A, ſimiliter, & </s>
            <s xml:id="echoid-s444" xml:space="preserve">cubus ex
              <lb/>
            F, ad cubum ex diametro
              <unsure/>
            ſphæræ A, triplicatã rationem habet
              <note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">33. 11.
                <lb/>
              Elem.</note>
            quam F, ad diametrum ſphæræ A, ergo, vt grauitas G, ad grauitatĕ
              <lb/>
            H, ita erit cubus ex F, ad cubum ex diametro ſphæræ A, ſed vt graui-
              <lb/>
            tas G, ad grauitatem H, ita eſt cubus ex F, ad cubum ex C, ergo cubus
              <lb/>
            ex C, æqualis erit cubo diametri ſphæræ A, quare, & </s>
            <s xml:id="echoid-s445" xml:space="preserve">latus C, æquabi-
              <lb/>
            tur ipſius ſphæræ A, diametro, inuenta igitur eſt quantitas diametri
              <lb/>
            ſolidæ ſphæræ A, quod facere oportebat.</s>
            <s xml:id="echoid-s446" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div35" type="section" level="1" n="20">
          <head xml:id="echoid-head23" xml:space="preserve">Exemplum.</head>
          <p>
            <s xml:id="echoid-s447" xml:space="preserve">Q Vidam proponit aliquod corpus liquidum notæ
              <lb/>
            magnitudinis, & </s>
            <s xml:id="echoid-s448" xml:space="preserve">vult inuenire quanta erit magni-
              <lb/>
            tudo alicuius ſolidi grauitatem habentis propoſi-
              <lb/>
            to corpori liquido æqualem.</s>
            <s xml:id="echoid-s449" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s450" xml:space="preserve">Sit propoſitum aliquod corpus aqueum B, cuius magnitudo ſit 115,
              <lb/>
            & </s>
            <s xml:id="echoid-s451" xml:space="preserve">oporteat inuenire quanta erit magnitudo plumbi grauitatem ha-
              <lb/>
            bentis æqualem propo ſitæ aquæ B, accipiatur aliquod corpus plumbeũ
              <lb/>
            D, cuius grauitas ſit verbi gratia 23, deinde aquæ magnitudinem ha-
              <lb/>
            bentis æqualem plumbo D, inueniatur grauitas quæ ſit 2. </s>
            <s xml:id="echoid-s452" xml:space="preserve">id autem do-
              <lb/>
            cuit propoſitionis octauæ exemplum, & </s>
            <s xml:id="echoid-s453" xml:space="preserve">fiat vi 23, ad 2, ita 115, ad
              <lb/>
            alium numerum qui ſit 10, is igitur numerus indicabit quanta erit
              <lb/>
            magnitudo plumbi grauitatem habentis æqualem propoſitæ aquæ B.</s>
            <s xml:id="echoid-s454" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s455" xml:space="preserve">Quod ſi propoſitum corpus aqueum B, ſit ſphæricum, cuius
              <lb/>
            ſphæræ diameter ſit 10, & </s>
            <s xml:id="echoid-s456" xml:space="preserve">oporteat inuenire quanta erit dia-
              <lb/>
            meter ſphæræ ex plumbo, grauitatem habentis æqualem pro-
              <lb/>
            poſitæ ſphæræ B, ita faciendum erit.</s>
            <s xml:id="echoid-s457" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s458" xml:space="preserve">Accepto, vt diximus aliquo corpore plumbeo D, cuius grauitas 23,
              <lb/>
            & </s>
            <s xml:id="echoid-s459" xml:space="preserve">aquæ magnitudinem habentis æqualem plumbo D, inuenta </s>
          </p>
        </div>
      </text>
    </echo>
Impressum