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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            in linea e b punctũ g, it aut ſit g e æqualis e f. </s>
            <s xml:space="preserve">erit g por-
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            tionis a b c centrum. </s>
            <s xml:space="preserve">nam ſi hæ portiones, quæ æquales
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            & </s>
            <s xml:space="preserve">ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
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            & </s>
            <s xml:space="preserve">punctum b in d cadet, & </s>
            <s xml:space="preserve">g in f: </s>
            <s xml:space="preserve">figuris autem æquali-
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            bus, & </s>
            <s xml:space="preserve">ſimilibus inter ſe aptatis, centra quoque grauitatis
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            ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
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            medis in libro de centro grauitatis planorum. </s>
            <s xml:space="preserve">Quare cum
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            portionis a d c centrum grauitatis ſit ſ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portionis
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            a b c centrum g: </s>
            <s xml:space="preserve">magnitudinis; </s>
            <s xml:space="preserve">quæ ex utriſque efficitur:
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            </s>
            <s xml:space="preserve">hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
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            neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
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            dem libri Archimedis. </s>
            <s xml:space="preserve">ergo circuli, uel ellipſis centrum
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            grauitatis eſt idem, quod figuræ centrum. </s>
            <s xml:space="preserve">atque illud eſt,
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            quod demonſtrare oportebat.</s>
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            <figure xlink:label="fig-0123-02" xlink:href="fig-0123-02a">
              <image file="0123-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0123-02"/>
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            <s xml:space="preserve">Ex quibus ſequitur portionis circuli, uel ellip-
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            ſis, quæ dimidia maior ſit, centrum grauitatis in
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            diametro quoque ipſius conſiſtere.</s>
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          <figure>
            <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0124-01"/>
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            <s xml:space="preserve">Sit enim maior portio a b c, cu_i_us diameter b d, & </s>
            <s xml:space="preserve">com-
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            pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c, dia</s>
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