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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FED. COMMANDINI
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            ut altitudo ad altitudinem & </s>
            <s xml:space="preserve">componendo conuertendo
              <lb/>
            que ſolidum a b g h, hoc eſt ſolidum a b c d ipſi æquale, ad
              <lb/>
              <anchor type="note" xlink:label="note-0158-01a" xlink:href="note-0158-01"/>
            ſolidum a b e f, ut altitudo ſolidi a b c d ad ſolidi a b e f al-
              <lb/>
            titudinem.</s>
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            <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a">
              <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0157-01"/>
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            <note position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">29. unde-
              <lb/>
            cimi</note>
            <note position="right" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">18. huius</note>
            <note position="left" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">7. quinti.</note>
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          <p>
            <s xml:space="preserve">Sint ſolida parallelepipeda a b, c d in æqualibus baſibus
              <lb/>
            conſtituta: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">b e altitudo ſolidi a b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidi c d altitudo
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            d f; </s>
            <s xml:space="preserve">quæ quidem maior ſit, quàm b e. </s>
            <s xml:space="preserve">Dico ſolidum a b ad
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            ſolidum c d eandem habere proportionem, quam be ad
              <lb/>
            d f. </s>
            <s xml:space="preserve">abſcindatur enim à linea d f æqualis ipſi b e, quæ ſit g f:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per g ducatur planum ſecans ſolidum c d; </s>
            <s xml:space="preserve">quod baſibus
              <lb/>
            æquidiſtet, faciatq; </s>
            <s xml:space="preserve">ſectionẽ h K. </s>
            <s xml:space="preserve">erunt ſolida a b, c k æque
              <lb/>
              <anchor type="note" xlink:label="note-0158-02a" xlink:href="note-0158-02"/>
            alta inter
              <lb/>
              <anchor type="figure" xlink:label="fig-0158-01a" xlink:href="fig-0158-01"/>
            ſe æqualia
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            cũ æqua-
              <lb/>
            les baſes
              <lb/>
            habeant.
              <lb/>
            </s>
            <s xml:space="preserve">Sed ſolidũ
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              <anchor type="note" xlink:label="note-0158-03a" xlink:href="note-0158-03"/>
            h d ad ſoli
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            dum c _K_
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            eſt, ut alti
              <lb/>
            tudo d g
              <lb/>
            ad g f alti-
              <lb/>
            tudinẽ ſe
              <lb/>
            catur enim ſolidum c d plano baſi
              <lb/>
              <anchor type="figure" xlink:label="fig-0158-02a" xlink:href="fig-0158-02"/>
            bus æquidiſtante: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus cõpo-
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            nendo, conuertendoq; </s>
            <s xml:space="preserve">ſolidũ c _k_
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            ad ſolidum c d, ut g f ad fd. </s>
            <s xml:space="preserve">ergo
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              <anchor type="note" xlink:label="note-0158-04a" xlink:href="note-0158-04"/>
            ſolidum a b, quod eſt æquale ipſi
              <lb/>
            c k ad ſolidum c d eam proportio
              <lb/>
            nem habet, quam altitudo g f, hoc
              <lb/>
            eſt b e ad d f altitudinem.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">31. unde
              <lb/>
            cimi</note>
            <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a">
              <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0158-01"/>
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            <note position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">18. huius</note>
            <figure xlink:label="fig-0158-02" xlink:href="fig-0158-02a">
              <image file="0158-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0158-02"/>
            </figure>
            <note position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">7. quinti.</note>
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          <p>
            <s xml:space="preserve">Sint deinde ſolida parallelepipe
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            da a b, a c in eadem baſi; </s>
            <s xml:space="preserve">quorum
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            axes d e, ſ e cum ipſa æquales angu</s>
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