Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s4485" xml:space="preserve">
              <pb file="0180" n="180" rhead="FED. COMMANDINI"/>
            fruſtum a d. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Sed pyramis q æqualis eſt fruſto à pyramide
              <lb/>
            abſciſſo, ut dem onſtrauimus. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4488" xml:space="preserve">conus, uel coni por-
              <lb/>
            tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
              <lb/>
            conſtat, & </s>
            <s xml:id="echoid-s4489" xml:space="preserve">altitudo eadem, quæ fruſti: </s>
            <s xml:id="echoid-s4490" xml:space="preserve">ipſi fruſto a d eſt æ-
              <lb/>
            qualis. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">atque illud eſt, quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s4492" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <head xml:id="echoid-head98" xml:space="preserve">THEOREMA XXI. PROPOSITIO XXVI.</head>
          <p>
            <s xml:id="echoid-s4493" xml:space="preserve">
              <emph style="sc">Cvivslibet</emph>
            fruſti à pyramide, uel cono,
              <lb/>
            uel coni portione abſcisſi, centrum grauitatis eſt
              <lb/>
            in axe, ita ut eo primum in duas portiones diui-
              <lb/>
            ſo, portio ſuperior, quæ minorem baſim attingit
              <lb/>
            ad portionem reliquam eam habeat proportio-
              <lb/>
            nem, quam duplum lateris, uel diametri maioris
              <lb/>
            baſis, vnà cum latere, uel diametro minoris, ipſi
              <lb/>
            reſpondente, habet ad duplum lateris, uel diame-
              <lb/>
            tri minoris baſis vnà cũ latere, uel diametro ma-
              <lb/>
            ioris: </s>
            <s xml:id="echoid-s4494" xml:space="preserve">deinde à puncto diuiſionis quarta parte ſu
              <lb/>
            perioris portionis in ipſa ſumpta: </s>
            <s xml:id="echoid-s4495" xml:space="preserve">& </s>
            <s xml:id="echoid-s4496" xml:space="preserve">rurſus ab in-
              <lb/>
            ferioris portionis termino, qui eſt ad baſim maio
              <lb/>
            rem, ſumpta quarta parte totius axis: </s>
            <s xml:id="echoid-s4497" xml:space="preserve">centrum ſit
              <lb/>
            in linea, quæ his finibus continetur, atque in eo li
              <lb/>
            neæ puncto, quo ſic diuiditur, ut tota linea ad par
              <lb/>
            tem propinquiorem minori baſi, eãdem propor-
              <lb/>
            tionem habeat, quam fruſtum ad pyramidẽ, uel
              <lb/>
            conum, uel coni portionem, cuius baſis ſit ea-
              <lb/>
            dem, quæ baſis maior, & </s>
            <s xml:id="echoid-s4498" xml:space="preserve">altitudo fruſti altitudini
              <lb/>
            æqualis.</s>
            <s xml:id="echoid-s4499" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum