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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FED. COMMANDINI
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        <div type="section" level="1" n="93">
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              <pb file="0194" n="194" rhead="FED. COMMANDINI"/>
            tionem cadet: </s>
            <s xml:space="preserve">Itaque cum à portione conoidis, cuius gra-
              <lb/>
            uitatis centrum e auferatur inſcripta figura, centrum ha-
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            bens p: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit l e ad e p, ut figura inſcripta ad portiones reli
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            quas: </s>
            <s xml:space="preserve">erit magnitudinis, quæ ex reliquis portionibus con
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            ſtat, centrum grauitatis punctum l, extra portionem ca-
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            dens. </s>
            <s xml:space="preserve">quod fieri nequit. </s>
            <s xml:space="preserve">ergo linea p e minor eſt ip ſa g li-
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            nea propoſita.</s>
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          </p>
          <div type="float" level="2" n="2">
            <figure xlink:label="fig-0193-02" xlink:href="fig-0193-02a">
              <image file="0193-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0193-02"/>
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          <p>
            <s xml:space="preserve">Ex quibus perſpicuum eſt centrum grauitatis
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            figuræ inſcriptæ, & </s>
            <s xml:space="preserve">circumſcriptæ eo magis acce
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            dere ad portionis centrum, quo pluribus cylin-
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            dris, uel cylindri portionibus conſtet: </s>
            <s xml:space="preserve">fiatq́ figu
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            ra inſcripta maior, & </s>
            <s xml:space="preserve">circumſcripta minor. </s>
            <s xml:space="preserve">& </s>
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            quanquam continenter ad portionis centrū pro-
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            pius admoueatur nunquam tamen ad ipſum per
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            ueniet. </s>
            <s xml:space="preserve">ſequeretur enim figuram inſcriptam, nó
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            ſolum portioni, ſed etiam circumſcriptæ figuræ
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            æqualem eſſe. </s>
            <s xml:space="preserve">quod eſt abſurdum.</s>
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        <div type="section" level="1" n="94">
          <head xml:space="preserve">THE OREMA XXIII. PROPOSITIO XXIX.</head>
          <p>
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              <emph style="sc">Cvivslibet</emph>
            portionis conoidis rectangu-
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            li axis à cẽtro grauitatis ita diuiditur, ut pars quæ
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            terminatur ad uerticem, reliquæ partis, quæ ad ba
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            ſim ſit dupla.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">SIT portio conoidis rectanguli uel abſciſſa plano ad
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            axem recto, uel non recto: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa altero plano per axé
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            ſit ſuperſiciei ſe ctio a b c r ectanguli coni ſectio, uel parabo
              <lb/>
            le; </s>
            <s xml:space="preserve">plani abſcindentis portionem ſectio ſit recta linea a c:
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            </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis diameter b d. </s>
            <s xml:space="preserve">Sumatur autem
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            in linea b d punctum e, ita ut b e ſit ipſius e d dupla. </s>
            <s xml:space="preserve">Dico</s>
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