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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          <p>
            <s xml:space="preserve">Ex demonſtratis perſpicue apparet, portioni
              <lb/>
            ſphæræ uel ſphæroidis, quæ dimidia maior eſt, cẽ
              <lb/>
            trum grauitatis in axe conſiſtere.</s>
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          </p>
          <p>
            <s xml:space="preserve">Data enim
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            qualibet maio
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            ri portiõe, quo
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            niã totius ſphæ
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            ræ, uel ſphæroi
              <lb/>
            dis grauitatis
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            centrum eſt in
              <lb/>
            axe; </s>
            <s xml:space="preserve">eſt autem
              <lb/>
            & </s>
            <s xml:space="preserve">in axe cen-
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            trum portio-
              <lb/>
            nis minoris:
              <lb/>
            </s>
            <s xml:space="preserve">reliquæ portionis uidelicet maioris centrum in axe neceſ-
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            ſario conſiſtet.</s>
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            <figure xlink:label="fig-0155-01" xlink:href="fig-0155-01a">
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        <div type="section" level="1" n="82">
          <head xml:space="preserve">THE OREMA XIII. PROPOSITIO XVII.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet pyramidis triã
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              <anchor type="figure" xlink:label="fig-0155-02a" xlink:href="fig-0155-02"/>
            gularem baſim habẽtis gra
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            uitatis centrum eſt in pun-
              <lb/>
            cto, in quo ipſius axes con-
              <lb/>
            ueniunt.</s>
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          </p>
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            <figure xlink:label="fig-0155-02" xlink:href="fig-0155-02a">
              <image file="0155-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0155-02"/>
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          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis trian
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            gulum a b c, axis d e: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">trian
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            guli b d c grauitatis centrum f:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur a f. </s>
            <s xml:space="preserve">erit & </s>
            <s xml:space="preserve">a faxis eiuſ
              <lb/>
            dem pyramidis ex tertia diffini-
              <lb/>
            tione huius. </s>
            <s xml:space="preserve">Itaque quoniam centrum grauitatis eſt in
              <lb/>
            axe d e; </s>
            <s xml:space="preserve">eſt autem & </s>
            <s xml:space="preserve">in axe a f; </s>
            <s xml:space="preserve">quod proxime demonſtraui</s>
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