Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
< >
page |< < (17) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div224" type="section" level="1" n="74">
          <pb o="17" file="0145" n="145" rhead="DE CENTRO GRAVIT. SOLID."/>
        </div>
        <div xml:id="echoid-div226" type="section" level="1" n="75">
          <head xml:id="echoid-head82" xml:space="preserve">PROBLEMA I. PROPOSITIO X.</head>
          <p>
            <s xml:id="echoid-s3677" xml:space="preserve">
              <emph style="sc">Data</emph>
            qualibet pyramide, fieri poteſt, ut fi-
              <lb/>
            gura ſolida in ipſa in ſcribatur, & </s>
            <s xml:id="echoid-s3678" 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:id="echoid-s3679" xml:space="preserve"/>
          </p>
          <figure number="99">
            <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0145-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3680" xml:space="preserve">Sit pyramis, cuius baſis
              <lb/>
            triangulũ a b c; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:id="echoid-s3682" xml:space="preserve">Sitq; </s>
            <s xml:id="echoid-s3683" xml:space="preserve">priſma, quod eandẽ
              <lb/>
            baſim habeat, & </s>
            <s xml:id="echoid-s3684" xml:space="preserve">axem eun
              <lb/>
            dem. </s>
            <s xml:id="echoid-s3685" 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:id="echoid-s3686" xml:space="preserve">quod
              <lb/>
            quidem baſim eandem ha
              <lb/>
            beat, quam pyramis, & </s>
            <s xml:id="echoid-s3687" xml:space="preserve">a-
              <lb/>
            xem e f. </s>
            <s xml:id="echoid-s3688" 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:id="echoid-s3689" xml:space="preserve">& </s>
            <s xml:id="echoid-s3690" xml:space="preserve">per
              <lb/>
            diuiſiones plana ducãtur: </s>
            <s xml:id="echoid-s3691" 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:id="echoid-s3692" xml:space="preserve">ab uno
              <lb/>
            quoque autẽ horum trian
              <lb/>
            gulorum duo priſmata cõ
              <lb/>
            ſtruantur; </s>
            <s xml:id="echoid-s3693" xml:space="preserve">unum quidem
              <lb/>
            ad partes e; </s>
            <s xml:id="echoid-s3694" xml:space="preserve">alterum </s>
          </p>
        </div>
      </text>
    </echo>