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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FED. COMMANDINI
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            mus: </s>
            <s xml:space="preserve">erit utique grauitatis centrum pyramidis punctum
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            g: </s>
            <s xml:space="preserve">in quo ſcilicet ipſi axes conueniunt.</s>
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          <head xml:space="preserve">THEOREMA XIIII. PROPOSITIO XVIII.</head>
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              <emph style="sc">Si</emph>
            ſolidum parallelepipedum ſecetur plano
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            baſibus æquidiſtante; </s>
            <s xml:space="preserve">erit ſolidum ad ſolidum,
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            ſicut altitudo ad altitudinem, uel ſicut axisad
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            axem.</s>
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            <s xml:space="preserve">Sit ſolidum parallelepipe
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              <anchor type="figure" xlink:label="fig-0156-01a" xlink:href="fig-0156-01"/>
            dum a b c d e f g h, cuius axis
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            k 1: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">plano baſibus
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            æquidiſtante, quod faciat
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            fectionem m n o p; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axi in
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            puncto q occurrat. </s>
            <s xml:space="preserve">Dico
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            ſolidum g m ad ſolidum m c
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            eam proportionem habere,
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            quam altitudo ſolidi g m ha-
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            betad ſolidi m c altitudi-
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            nem; </s>
            <s xml:space="preserve">uel quam axis k q ad
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            axem q l. </s>
            <s xml:space="preserve">Sienim axis K l ad
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            baſis planum ſit perpendicu
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            laris, & </s>
            <s xml:space="preserve">linea g c, quæ ex quin
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            ta huius ipſi k l æquidiſtat,
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            perpendicularis erit ad idẽ
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            planum, & </s>
            <s xml:space="preserve">ſolidi altitudi-
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            nem dimetietur. </s>
            <s xml:space="preserve">Itaqueſo-
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              <anchor type="note" xlink:label="note-0156-01a" xlink:href="note-0156-01"/>
            lidum g m ad ſolidum m c
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            eam proportionem habet,
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            quam parallelogrammũ g n
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            ad parallelogrammum n c,
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            hoc eſt quam linea g o, quæ
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              <anchor type="note" xlink:label="note-0156-02a" xlink:href="note-0156-02"/>
            </s>
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