Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div206" type="section" level="1" n="68">
          <p>
            <s xml:id="echoid-s3149" xml:space="preserve">
              <pb file="0124" n="124" rhead="FED. COMMANDINI"/>
            in linea e b punctũ g, it aut ſit g e æqualis e f. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">erit g por-
              <lb/>
            tionis a b c centrum. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">nam ſi hæ portiones, quæ æquales
              <lb/>
            & </s>
            <s xml:id="echoid-s3152" xml:space="preserve">ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
              <lb/>
            & </s>
            <s xml:id="echoid-s3153" xml:space="preserve">punctum b in d cadet, & </s>
            <s xml:id="echoid-s3154" xml:space="preserve">g in f: </s>
            <s xml:id="echoid-s3155" xml:space="preserve">figuris autem æquali-
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s3156" xml:space="preserve">ſimilibus inter ſe aptatis, centra quoque grauitatis
              <lb/>
            ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
              <lb/>
            medis in libro de centro grauitatis planorum. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">Quare cum
              <lb/>
            portionis a d c centrum grauitatis ſit ſ: </s>
            <s xml:id="echoid-s3158" xml:space="preserve">& </s>
            <s xml:id="echoid-s3159" xml:space="preserve">portionis
              <lb/>
            a b c centrum g: </s>
            <s xml:id="echoid-s3160" xml:space="preserve">magnitudinis; </s>
            <s xml:id="echoid-s3161" xml:space="preserve">quæ ex utriſque efficitur:
              <lb/>
            </s>
            <s xml:id="echoid-s3162" xml:space="preserve">hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
              <lb/>
            neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
              <lb/>
            dem libri Archimedis. </s>
            <s xml:id="echoid-s3163" xml:space="preserve">ergo circuli, uel ellipſis centrum
              <lb/>
            grauitatis eſt idem, quod figuræ centrum. </s>
            <s xml:id="echoid-s3164" xml:space="preserve">atque illud eſt,
              <lb/>
            quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s3165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3166" xml:space="preserve">Ex quibus ſequitur portionis circuli, uel ellip-
              <lb/>
            ſis, quæ dimidia maior ſit, centrum grauitatis in
              <lb/>
            diametro quoque ipſius conſiſtere.</s>
            <s xml:id="echoid-s3167" xml:space="preserve"/>
          </p>
          <figure number="81">
            <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0124-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3168" xml:space="preserve">Sit enim maior portio a b c, cu_i_us diameter b d, & </s>
            <s xml:id="echoid-s3169" xml:space="preserve">com-
              <lb/>
            pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c, </s>
          </p>
        </div>
      </text>
    </echo>