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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ARCHIMEDIS
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          <p>
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              <pb file="0042" n="42" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">ſectionis diameter no: </s>
            <s xml:space="preserve">ſuperſiciei autem humidi ſectio
              <lb/>
            ſit is. </s>
            <s xml:space="preserve">Quoniam igitur axis non eſt ſecundum perpendicu
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            larem; </s>
            <s xml:space="preserve">ipſa no cum is non faciet angulos æquales. </s>
            <s xml:space="preserve">Du-
              <lb/>
            catur k ω contingens ſectionem apol in p; </s>
            <s xml:space="preserve">atque ipſi is
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            æquidiſtans: </s>
            <s xml:space="preserve">per p autem ducatur p f æquidiſtās ipſi n o:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumantur grauitatum centra: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius a p o l ſolidi
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            centrum r; </s>
            <s xml:space="preserve">eius quod extra humidum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta br
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            producatur adg,
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              <anchor type="figure" xlink:label="fig-0042-01a" xlink:href="fig-0042-01"/>
            quodſit centrum
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            grauitatis ſolidi ĩ
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            humido demerſi:
              <lb/>
            </s>
            <s xml:space="preserve">ſumatur præterea
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            r h æ qualis ei, quæ
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            uſque ad axẽ: </s>
            <s xml:space="preserve">o h
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            autem dupla ipſi-
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            us h m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia fiãt,
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            ſicuti ſuperius di-
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            ctum eſt. </s>
            <s xml:space="preserve">Itaque
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            cum portio ad hu
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            midum in grauita
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            te non maiorem
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            proportionem ha
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            bere ponatur, quã
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            exceſſus, quo quadratum n o excedit quadratum m o, ad
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            ipſum n o quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem in grauita
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            te portio habet ad humidum æqualis molis, eandem ha-
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            beat magnitudo portionis demerſa ad totam portio-
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            nem, quod demonſtratum eſt in prima propoſitione: </s>
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              <lb/>
            magnitudo demerſa non maiorem proportionem ha-
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              <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
            bebit ad totam portionem, quàm ſit dicta illa propor-
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            portio. </s>
            <s xml:space="preserve">quare non maiorem proportionem habet tota
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              <anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
            portio ad eam quæ eſt extra humidum, quàm quadratum
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            no ad quadratum m o. </s>
            <s xml:space="preserve">habet autem tota portio ad eam,
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              <anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
            quæ extra humidum proportionem eandem, quam qua-</s>
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