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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            <s xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c; </s>
            <s xml:space="preserve">axis d e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            ſecetur plano baſi æquidiſtante; </s>
            <s xml:space="preserve">quod ſectionẽ faciat f g h;
              <lb/>
            </s>
            <s xml:space="preserve">occurratq; </s>
            <s xml:space="preserve">axi in puncto k. </s>
            <s xml:space="preserve">Dico f g h triangulum eſſe, ipſi
              <lb/>
            a b c ſimile; </s>
            <s xml:space="preserve">cuius grauitatis centrum eſt K. </s>
            <s xml:space="preserve">Quoniã enim
              <lb/>
              <anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/>
            duo plana æquidiſtantia a b c, f g h ſecantur à plano a b d;
              <lb/>
            </s>
            <s xml:space="preserve">communes eorum ſectiones a b, f g æquidiſtantes erunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            eadem ratione æquidiſtantes ipſæ b c, g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">c a, h f. </s>
            <s xml:space="preserve">Quòd
              <lb/>
            cum duæ lineæ f g, g h, duabus a b, b c æquidiſtent, nec
              <lb/>
            ſintin eodem plano; </s>
            <s xml:space="preserve">angulus ad g æqualis eſt angulo ad
              <lb/>
              <anchor type="note" xlink:label="note-0144-02a" xlink:href="note-0144-02"/>
            b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimiliter angulus ad h angulo ad c: </s>
            <s xml:space="preserve">angulusq; </s>
            <s xml:space="preserve">ad f ei,
              <lb/>
            qui ad a eſt æqualis. </s>
            <s xml:space="preserve">triangulum igitur f g h ſimile eſt tri-
              <lb/>
            angulo a b c. </s>
            <s xml:space="preserve">At uero punctum k centrum eſſe grauita-
              <lb/>
            tis trianguli f g h hoc modo oſtendemus. </s>
            <s xml:space="preserve">Ducantur pla-
              <lb/>
            na per axem, & </s>
            <s xml:space="preserve">per lineas d a, d b, d c: </s>
            <s xml:space="preserve">erunt communes ſe-
              <lb/>
              <anchor type="note" xlink:label="note-0144-03a" xlink:href="note-0144-03"/>
            ctiones f K, a e æquidiſtantes: </s>
            <s xml:space="preserve">pariterq; </s>
            <s xml:space="preserve">k g, e b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">k h, e c:
              <lb/>
            </s>
            <s xml:space="preserve">quare angulus k f h angulo e a c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulus k f g ipſi e a b
              <lb/>
              <anchor type="note" xlink:label="note-0144-04a" xlink:href="note-0144-04"/>
            eſt æqualis. </s>
            <s xml:space="preserve">Eadem ratione
              <lb/>
              <anchor type="figure" xlink:label="fig-0144-01a" xlink:href="fig-0144-01"/>
            anguli ad g angulis ad b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            anguli ad h iis, qui ad c æ-
              <lb/>
            quales erunt. </s>
            <s xml:space="preserve">ergo puncta
              <lb/>
            e _K_ in triangulis a b c, f g h
              <lb/>
            ſimiliter ſunt poſita, per ſe-
              <lb/>
            xtam poſitionem Archime-
              <lb/>
            dis in libro de centro graui-
              <lb/>
            tatis planorum. </s>
            <s xml:space="preserve">Sed cum e
              <lb/>
            ſit centrum grauitatis trian
              <lb/>
            guli a b c, erit ex undecíma
              <lb/>
            propoſitione eiuſdem libri,
              <lb/>
            & </s>
            <s xml:space="preserve">K trianguli f g h grauita
              <lb/>
            tis centrum. </s>
            <s xml:space="preserve">id quod demonſtrare oportebat. </s>
            <s xml:space="preserve">Non aliter
              <lb/>
            in ceteris pyramidibus, quod propoſitum eſt demonſtra-
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            bitur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">16. unde
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            cimi</note>
            <note position="left" xlink:label="note-0144-02" xlink:href="note-0144-02a" xml:space="preserve">10. undeci
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            mi.</note>
            <note position="left" xlink:label="note-0144-03" xlink:href="note-0144-03a" xml:space="preserve">16. unde-
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            cimi</note>
            <note position="left" xlink:label="note-0144-04" xlink:href="note-0144-04a" xml:space="preserve">10. unde-
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            cimi</note>
            <figure xlink:label="fig-0144-01" xlink:href="fig-0144-01a">
              <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0144-01"/>
            </figure>
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