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="26" file="0163" n="163" rhead="DE CENTRO GRAVIT. SOLID."/>
            matis a e axis g h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſmatis a f axis l h. </s>
            <s xml:space="preserve">Dico priſma
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            a e ad priſma a f eam proportionem habere, quam g h ad
              <lb/>
            h l. </s>
            <s xml:space="preserve">ducantur à punctis g l perpendiculares ad baſis pla-
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            num g K, l m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur k h,
              <lb/>
              <anchor type="figure" xlink:label="fig-0163-01a" xlink:href="fig-0163-01"/>
            h m. </s>
            <s xml:space="preserve">Itaque quoniam anguli g h
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            k, l h m ſunt æquales, ſimiliter ut
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            ſupra demonſtrabimus, triangu-
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            la g h K, l h m ſimilia eſſe; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut g
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            K adlm, ita g h ad h l. </s>
            <s xml:space="preserve">habet au
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            tem priſma a e ad priſma a f ean
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            dem proportionem, quam altitu
              <lb/>
            do g k ad altitudinem l m, ſicuti
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            demonſtratum eſt. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ean-
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            dem habebit, quam g h, ad h l. </s>
            <s xml:space="preserve">py
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            ramis igitur a b c d g ad pyrami-
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            dem a b c d l eandem proportio-
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            nem habebit, quam axis g h ad h l axem.</s>
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            <figure xlink:label="fig-0163-01" xlink:href="fig-0163-01a">
              <image file="0163-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0163-01"/>
            </figure>
          </div>
          <figure>
            <image file="0163-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0163-02"/>
          </figure>
          <p>
            <s xml:space="preserve">Denique ſint priſmata a e, k o in æqualibus baſibus a b
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            c d, k l m n conſtituta; </s>
            <s xml:space="preserve">quorum axes cum baſibus æquales
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            faciant angulos: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">priſmatis a e axis f g, & </s>
            <s xml:space="preserve">altitudo f h:
              <lb/>
            </s>
            <s xml:space="preserve">priſmatis autem k o axis p q, & </s>
            <s xml:space="preserve">altitudo p r. </s>
            <s xml:space="preserve">Dico priſma
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            a e ad priſma k o ita eſſe, ut f g ad p q. </s>
            <s xml:space="preserve">iunctis enim g h,</s>
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