Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="3" file="0117" n="117" rhead="DE CENTRO GRAVIT. SOLID."/>
            cta b d in g puncto, ducatur c g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">protrahatur ad circuli
              <lb/>
            uſque circumferentiam; </s>
            <s xml:space="preserve">quæ ſecet a e in h. </s>
            <s xml:space="preserve">Similiter conclu
              <lb/>
            demus c g per centrum circuli tranſire: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſecare
              <lb/>
            lineam a e; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">lineas b d, a e inter ſe æquidiſtantes eſſe.
              <lb/>
            </s>
            <s xml:space="preserve">Cumigitur c g per centrum circuli tranſeat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad punctũ
              <lb/>
            f perueniat neceſſe eſt: </s>
            <s xml:space="preserve">quòd c d e f ſit dimidium circumfe
              <lb/>
            rentiæ circuli. </s>
            <s xml:space="preserve">Quare in eadem
              <lb/>
              <anchor type="figure" xlink:label="fig-0117-01a" xlink:href="fig-0117-01"/>
            diametro c f erunt centra gra
              <lb/>
              <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/>
            uitatis triangulorum b c d,
              <lb/>
            a f e, & </s>
            <s xml:space="preserve">quadrilateri a b d e, ex
              <lb/>
              <anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/>
            quibus conſtat hexagonum a b
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            c d e f. </s>
            <s xml:space="preserve">perſpicuum eſt igitur in
              <lb/>
            ipſa c f eſſe circuli centrum, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum grauitatis hexagoni.
              <lb/>
            </s>
            <s xml:space="preserve">Rurſus ducta altera diametro
              <lb/>
            a d, eiſdem rationibus oſtende-
              <lb/>
            mus in ipſa utrumque cẽtrum
              <lb/>
            ineſſe. </s>
            <s xml:space="preserve">Centrum ergo grauita-
              <lb/>
            tis hexagoni, & </s>
            <s xml:space="preserve">centrum circuli idem erit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <figure xlink:label="fig-0117-01" xlink:href="fig-0117-01a">
              <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0117-01"/>
            </figure>
            <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">13. Archi
              <lb/>
            medis.</note>
            <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">9. @iuſdé.</note>
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          <p>
            <s xml:space="preserve">Sit heptagonum a b c d e f g æquilaterum atque æquian
              <lb/>
            gulum in circulo deſcriptum:
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0117-02a" xlink:href="fig-0117-02"/>
            & </s>
            <s xml:space="preserve">iungantur c e, b f, a g: </s>
            <s xml:space="preserve">di-
              <lb/>
            uiſa autem c e bifariam in pũ
              <lb/>
            cto h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta d h produca-
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            tur in k. </s>
            <s xml:space="preserve">non aliter demon-
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            ſtrabimus in linea d k eſſe cen
              <lb/>
            trum circuli, & </s>
            <s xml:space="preserve">centrum gra-
              <lb/>
            uitatis trianguli c d e, & </s>
            <s xml:space="preserve">tra-
              <lb/>
            peziorum b c e f, a b f g, hoc
              <lb/>
            eſt centrum totius heptago-
              <lb/>
            ni: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus eadem centra in
              <lb/>
            alia diametro cl ſimiliter du-
              <lb/>
            cta contineri. </s>
            <s xml:space="preserve">Quare & </s>
            <s xml:space="preserve">centrum grauitatis heptagoni, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum circuli in idem punctum conucniunt. </s>
            <s xml:space="preserve">Eodem mo</s>
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