Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="8" file="0127" n="127" rhead="DE CENTRO GRAVIT. SOLID."/>
            æquidiſtant autem c g o, m n p. </s>
            <s xml:space="preserve">ergo parallelogrãma ſunt
              <lb/>
            o n, g m, & </s>
            <s xml:space="preserve">linea m n æqualis c g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">n p ipſi g o. </s>
            <s xml:space="preserve">aptatis igi-
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            tur
              <emph style="sc">K</emph>
            l m, a b c triãgulis, quæ æqualia & </s>
            <s xml:space="preserve">ſimilia sũt; </s>
            <s xml:space="preserve">linea m p
              <lb/>
            in c o, & </s>
            <s xml:space="preserve">punctum n in g cadet. </s>
            <s xml:space="preserve">Quòd cũ g ſit centrum gra-
              <lb/>
            uitatis trianguli a b c, & </s>
            <s xml:space="preserve">n trianguli
              <emph style="sc">K</emph>
            l m grauitatis cen-
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            trum erit id, quod demonſtrandum relinquebatur. </s>
            <s xml:space="preserve">Simili
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            ratione idem contingere demonſtrabimus in aliis priſma-
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            tibus, ſiue quadrilatera, ſiue plurilatera habeant plana,
              <lb/>
            quæ opponuntur.</s>
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          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">10. unde
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            cimi</note>
            <note position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">10. unde-
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            cimi</note>
            <note position="left" xlink:label="note-0126-03" xlink:href="note-0126-03a" xml:space="preserve">4. ſexti</note>
            <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a">
              <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0126-01"/>
            </figure>
            <note position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">per 5. pe-
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            titionem
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            Archime
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            dis.</note>
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        </div>
        <div type="section" level="1" n="70">
          <head xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:space="preserve">Exiam demonſtratis perſpicue apparet, cuius
              <lb/>
            Iibet priſmatis axem, parallelogrammorum lat eri
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            bus, quæ ab oppoſitis planis ducũtur æquidiſtare.</s>
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          </p>
        </div>
        <div type="section" level="1" n="71">
          <head xml:space="preserve">THEOREMA VI. PROPOSITIO VI.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet priſmatis centrum grauitatis eſt in
              <lb/>
            plano, quod oppoſitis planis æquidiſtans, reli-
              <lb/>
            quorum planorum latera bifariam diuidit.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit priſma, in quo plana, quæ opponuntur ſint trian-
              <lb/>
            gula a c e, b d f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">parallelogrammorum latera a b, c d,
              <lb/>
            e f bifariam diuidãtur in punctis g h _K_: </s>
            <s xml:space="preserve">per diuiſiones au-
              <lb/>
            tem planum ducatur; </s>
            <s xml:space="preserve">cuius ſectio figura g h _K_. </s>
            <s xml:space="preserve">eritlinea
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              <anchor type="note" xlink:label="note-0127-01a" xlink:href="note-0127-01"/>
            g h æquidiſtans lineis a c, b d & </s>
            <s xml:space="preserve">h k ipſis c e, d f. </s>
            <s xml:space="preserve">quare ex
              <lb/>
            decimaquinta undecimi elementorum, planum illud pla
              <lb/>
            nis a c e, b d f æquidiſtabit, & </s>
            <s xml:space="preserve">ſaciet ſectionem figu-
              <lb/>
              <anchor type="note" xlink:label="note-0127-02a" xlink:href="note-0127-02"/>
            ram ipſis æqualem, & </s>
            <s xml:space="preserve">ſimilem, ut proxime demonſtra-
              <lb/>
            uimus. </s>
            <s xml:space="preserve">Dico centrum grauitatis priſmatis eſſe in plano
              <lb/>
            g h
              <emph style="sc">K</emph>
            . </s>
            <s xml:space="preserve">Si enim fieri poteſt, ſit eius centrum l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur
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            l m uſque ad planum g h
              <emph style="sc">K</emph>
            , quæ ipſi a b æquidiſtet.</s>
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          </p>
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