Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
< >
page |< < (17) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="74">
          <pb o="17" file="0145" n="145" rhead="DE CENTRO GRAVIT. SOLID."/>
        </div>
        <div type="section" level="1" n="75">
          <head xml:space="preserve">PROBLEMA I. PROPOSITIO X.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Data</emph>
            qualibet pyramide, fieri poteſt, ut fi-
              <lb/>
            gura ſolida in ipſa in ſcribatur, & </s>
            <s xml:space="preserve">altera circũſcri-
              <lb/>
            batur ex priſmatibus æqualem aItitudinem ha-
              <lb/>
            bẽtibus, ita ut cir cumſcripta inſcriptam excedat
              <lb/>
            magnitudine, quæ minor ſit quacũque ſolida ma
              <lb/>
            gnitudine propoſita.</s>
            <s xml:space="preserve"/>
          </p>
          <figure>
            <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0145-01"/>
          </figure>
          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis
              <lb/>
            triangulũ a b c; </s>
            <s xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:space="preserve">Sitq; </s>
            <s xml:space="preserve">priſma, quod eandẽ
              <lb/>
            baſim habeat, & </s>
            <s xml:space="preserve">axem eun
              <lb/>
            dem. </s>
            <s xml:space="preserve">Itaque hoc priſma-
              <lb/>
            te continenter ſecto bifa-
              <lb/>
            riam, plano baſi æquidiftã
              <lb/>
            te, relinquetur tãdem priſ
              <lb/>
            ma quoddam minus pro-
              <lb/>
            poſita magnitudine: </s>
            <s xml:space="preserve">quod
              <lb/>
            quidem baſim eandem ha
              <lb/>
            beat, quam pyramis, & </s>
            <s xml:space="preserve">a-
              <lb/>
            xem e f. </s>
            <s xml:space="preserve">diuidatur d e in
              <lb/>
            partes æquales ipſi e f in
              <lb/>
            punctis g h k l m n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            diuiſiones plana ducãtur: </s>
            <s xml:space="preserve">
              <lb/>
            quæ baſibus æquidiſtent,
              <lb/>
            erunt ſectiones, triangula
              <lb/>
            ipſi a b c ſimilia, ut proxi-
              <lb/>
            me oſtendimus. </s>
            <s xml:space="preserve">ab uno
              <lb/>
            quoque autẽ horum trian
              <lb/>
            gulorum duo priſmata cõ
              <lb/>
            ſtruantur; </s>
            <s xml:space="preserve">unum quidem
              <lb/>
            ad partes e; </s>
            <s xml:space="preserve">alterum ad</s>
          </p>
        </div>
      </text>
    </echo>