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 |< < (32) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <pb o="32" file="0175" n="175" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:id="echoid-s4367" xml:space="preserve">SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
              <lb/>
            cuius maior baſis a b, minor c d. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">& </s>
            <s xml:id="echoid-s4369" xml:space="preserve">ſecetur altero plano
              <lb/>
            baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
              <lb/>
            baſes a b, c d. </s>
            <s xml:id="echoid-s4370" xml:space="preserve">conſtituatur autẽ pyramis, uel conus, uel co-
              <lb/>
            ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
              <lb/>
            ſti, & </s>
            <s xml:id="echoid-s4371" xml:space="preserve">altitudo æqualis. </s>
            <s xml:id="echoid-s4372" xml:space="preserve">Di-
              <lb/>
              <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a" number="129">
                <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-01"/>
              </figure>
            co fruſtum a d ad pyrami-
              <lb/>
            dem, uel conum, uel coni
              <lb/>
            portionem a g b eandem
              <lb/>
            proportionẽ habere, quã
              <lb/>
            utræque baſes, a b, c d unà
              <lb/>
            cum e f ad baſim a b. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">eſt
              <lb/>
            enim fruſtum a d æquale
              <lb/>
            pyramidi, uel cono, uel co-
              <lb/>
            ni portioni, cuius baſis ex
              <lb/>
            tribus baſibus a b, e f, c d
              <lb/>
            conſtat; </s>
            <s xml:id="echoid-s4374" xml:space="preserve">& </s>
            <s xml:id="echoid-s4375" xml:space="preserve">altitudo ipſius
              <lb/>
            altitudini eſt æqualis: </s>
            <s xml:id="echoid-s4376" xml:space="preserve">quod mox oſtendemus. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Sed pyrami
              <lb/>
            des, coni, uel coni portiões,
              <lb/>
              <figure xlink:label="fig-0175-02" xlink:href="fig-0175-02a" number="130">
                <image file="0175-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-02"/>
              </figure>
            quæ ſunt æquali altitudine,
              <lb/>
            eãdem inter ſe, quam baſes,
              <lb/>
            proportionem habent, ſicu-
              <lb/>
            ti demonſtratum eſt, partim
              <lb/>
            ab Euclide in duodecimo li-
              <lb/>
              <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">6. 11. duo
                <lb/>
              decimi</note>
            bro elementorum, partim à
              <lb/>
            nobis in cõmentariis in un-
              <lb/>
            decimam propoſitionẽ Ar-
              <lb/>
            chimedis de conoidibus, & </s>
            <s xml:id="echoid-s4378" xml:space="preserve">
              <lb/>
            ſphæroidibus. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">quare pyra-
              <lb/>
            mis, uel conus, uel coni por-
              <lb/>
            tio, cuius baſis eſt tribus illis
              <lb/>
            baſibus æqualis ad a g b eam
              <lb/>
            habet proportionem, quam
              <lb/>
            baſes a b, e f, c d ad ab bafim. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">Fruſtum igitur a d ad a g </s>
          </p>
        </div>
      </text>
    </echo>