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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            At cum e f ſit ſexta pars axis
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            ſphæræ, crit d e tripla e f. </s>
            <s xml:space="preserve">ergo
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            punctum e eſt grauitatis cen-
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            trum ipſius pyramidis: </s>
            <s xml:space="preserve">quod
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            in uigeſima ſecunda huius de-
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            monſtratum fuit. </s>
            <s xml:space="preserve">Sed e eſt cen
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            trum ſphæræ. </s>
            <s xml:space="preserve">Sequitur igitur,
              <lb/>
            ut centrum grauitatis pyrami-
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            dis in ſphæra deſcriptæ idem
              <lb/>
            ſit, quod ipſius ſphæræ cen-
              <lb/>
            trum.</s>
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            <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a">
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          <p>
            <s xml:space="preserve">Sit cubus in ſphæra deſcriptus a b, & </s>
            <s xml:space="preserve">oppoſitorum pla-
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            norum lateribus bifariam diuiſis, per puncta diuiſionum
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            plana ducantur, ut communis ipſorum ſectio ſit recta li-
              <lb/>
            nea c d. </s>
            <s xml:space="preserve">Itaque ſi ducatur a b, ſolidi ſcilicet diameter, lineæ
              <lb/>
            a b, c d ex trigeſimanona undecimi ſeſe bifariam ſecabunt.
              <lb/>
            </s>
            <s xml:space="preserve">ſecent autem in puncto e. </s>
            <s xml:space="preserve">erit
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              <anchor type="figure" xlink:label="fig-0188-02a" xlink:href="fig-0188-02"/>
            e centrũ grauitatis ſolidi a b,
              <lb/>
            id quod demonſtratum eſt in
              <lb/>
            octaua huius. </s>
            <s xml:space="preserve">Sed quoniam ab
              <lb/>
            eſt ſphæræ diametro æqualis,
              <lb/>
            ut in decima quinta propoſi-
              <lb/>
            tione tertii decimi libri elemẽ
              <lb/>
            torum oſtenditur: </s>
            <s xml:space="preserve">punctum e
              <lb/>
            ſphæræ quoque centrum erit.
              <lb/>
            </s>
            <s xml:space="preserve">Cubi igitur in ſphæra deſcri-
              <lb/>
            pti grauitatis centrum idem
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            eſt, quod centrum ipſius ſphæræ.</s>
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            <figure xlink:label="fig-0188-02" xlink:href="fig-0188-02a">
              <image file="0188-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0188-02"/>
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            <s xml:space="preserve">Sit octahedrum a b c d e f, in ſphæra deſcriptum, cuius
              <lb/>
            ſphæræ centrum ſit g. </s>
            <s xml:space="preserve">Dico punctum g ipſius octahedri
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            grauitatis centrum eſſe. </s>
            <s xml:space="preserve">Conſtat enim ex iis, quæ demon-
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            ſtrata ſunt à Campano in quinto decimo libro elemento-
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            rum, propoſitione ſextadecima eiuſimodi ſolidum diuidi
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            in duas pyramides æquales, & </s>
            <s xml:space="preserve">ſimiles; </s>
            <s xml:space="preserve">uidelicetin pyrami-</s>
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