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="17" file="0145" n="145" rhead="DE CENTRO GRAVIT. SOLID."/>
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          <head xml:space="preserve">PROBLEMA I. PROPOSITIO X.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Data</emph>
            qualibet pyramide, fieri poteſt, ut fi-
              <lb/>
            gura ſolida in ipſa in ſcribatur, & </s>
            <s xml:space="preserve">altera circũſcri-
              <lb/>
            batur ex priſmatibus æqualem aItitudinem ha-
              <lb/>
            bẽtibus, ita ut cir cumſcripta inſcriptam excedat
              <lb/>
            magnitudine, quæ minor ſit quacũque ſolida ma
              <lb/>
            gnitudine propoſita.</s>
            <s xml:space="preserve"/>
          </p>
          <figure>
            <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0145-01"/>
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          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis
              <lb/>
            triangulũ a b c; </s>
            <s xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:space="preserve">Sitq; </s>
            <s xml:space="preserve">priſma, quod eandẽ
              <lb/>
            baſim habeat, & </s>
            <s xml:space="preserve">axem eun
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            dem. </s>
            <s xml:space="preserve">Itaque hoc priſma-
              <lb/>
            te continenter ſecto bifa-
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            riam, plano baſi æquidiftã
              <lb/>
            te, relinquetur tãdem priſ
              <lb/>
            ma quoddam minus pro-
              <lb/>
            poſita magnitudine: </s>
            <s xml:space="preserve">quod
              <lb/>
            quidem baſim eandem ha
              <lb/>
            beat, quam pyramis, & </s>
            <s xml:space="preserve">a-
              <lb/>
            xem e f. </s>
            <s xml:space="preserve">diuidatur d e in
              <lb/>
            partes æquales ipſi e f in
              <lb/>
            punctis g h k l m n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            diuiſiones plana ducãtur: </s>
            <s xml:space="preserve">
              <lb/>
            quæ baſibus æquidiſtent,
              <lb/>
            erunt ſectiones, triangula
              <lb/>
            ipſi a b c ſimilia, ut proxi-
              <lb/>
            me oſtendimus. </s>
            <s xml:space="preserve">ab uno
              <lb/>
            quoque autẽ horum trian
              <lb/>
            gulorum duo priſmata cõ
              <lb/>
            ſtruantur; </s>
            <s xml:space="preserve">unum quidem
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            ad partes e; </s>
            <s xml:space="preserve">alterum ad</s>
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