Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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            <s xml:space="preserve">SIT cylindrus, uel cylindri po rtio a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">plano per a-
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            xem ducto ſecetur; </s>
            <s xml:space="preserve">cuius ſectio ſit parallelogrammum a b
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            c d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam diuiſis a d, b c parallelogrammi lateribus,
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            per diuiſionum puncta e f planum baſi æquidiſtans duca-
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            tur; </s>
            <s xml:space="preserve">quod faciet ſectionem, in cy lindro quidem circulum
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            æqualem iis, qui ſunt in baſibus, ut demonſtrauit Serenus
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            in libro cylindricorum, propoſitione quinta: </s>
            <s xml:space="preserve">in cylindri
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            uero portione ellipſim æqualem, & </s>
            <s xml:space="preserve">ſimilem eis, quæ ſunt
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            in oppoſitis planis, quod nos
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              <anchor type="figure" xlink:label="fig-0130-01a" xlink:href="fig-0130-01"/>
            demonſtrauimus in commen
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            tariis in librum Archimedis
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            de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidi-
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            bus. </s>
            <s xml:space="preserve">Dico centrum grauita-
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            tis cylindri, uel cylindri por-
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            tionis eſſe in plano e f. </s>
            <s xml:space="preserve">Si enĩ
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            fieri poteſt, fit centrum g: </s>
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            ducatur g h ipſi a d æquidi-
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            ſtans, uſque ad e f planum.
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            </s>
            <s xml:space="preserve">Itaque linea a e continenter
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            diuiſa bifariam, erit tandem
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            pars aliqua ipſius k e, minor
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            g h. </s>
            <s xml:space="preserve">Diuidantur ergo lineæ
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            a e, e d in partes æquales ipſi
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            k e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per diuiſiones plana ba
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            ſibus æquidiſtantia ducãtur. </s>
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              <lb/>
            erunt iam ſectiones, figuræ æ-
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            quales, & </s>
            <s xml:space="preserve">ſimiles eis, quæ ſunt
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            in baſibus: </s>
            <s xml:space="preserve">atque erit cylindrus in cylindros diuiſus: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cy
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            lindri portio in portiones æquales, & </s>
            <s xml:space="preserve">ſimiles ipſi k f. </s>
            <s xml:space="preserve">reli-
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            qua ſimiliter, ut ſuperius in priſmate concludentur.</s>
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