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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DE CENTRO GRAVIT. SOLID.
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              <pb o="29" file="0169" n="169" rhead="DE CENTRO GRAVIT. SOLID."/>
            l h eandem habet proportionem, quam e m ad m k, uideli-
              <lb/>
            cet triplam. </s>
            <s xml:space="preserve">quare linea l m ipſam e f ſecabit in puncto g:
              <lb/>
            </s>
            <s xml:space="preserve">etenim e g ad g f eſt, ut el ad l h. </s>
            <s xml:space="preserve">præterea quoniam h k, l m
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            æquidiſtant, erunt triangula h e f, l e g ſimilia: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">inter
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            ſe ſimilia f e k, g e m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut e fad e g, ita h fad l g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita f _K_ ad
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            g m. </s>
            <s xml:space="preserve">ergo uth fadlg, ita f k ad g m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando uth f
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            ad f _K_, ita l g ad g m. </s>
            <s xml:space="preserve">ſed cum h ſit centrum trianguli a b d; </s>
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              <lb/>
            & </s>
            <s xml:space="preserve">K triãguli b c d: </s>
            <s xml:space="preserve">punctũ uero f totius quadrilateri a b c d
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            centrum: </s>
            <s xml:space="preserve">erit ex 8. </s>
            <s xml:space="preserve">Archimedis de centro grauitatis plano
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            rum h fad f
              <emph style="sc">K</emph>
            , ut triangulum b c d ad triangulum a b d: </s>
            <s xml:space="preserve">ut
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            autem b c d triangulum ad triangulum a b d, ita pyramis
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            b c d e ad pyramidem a b d e. </s>
            <s xml:space="preserve">ergo
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              <anchor type="figure" xlink:label="fig-0169-01a" xlink:href="fig-0169-01"/>
            linea lg ad g m erit, ut pyramis
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            b c d e ad pyramidé a b d e. </s>
            <s xml:space="preserve">ex quo
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            ſequitur, ut totius pyramidis
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            a b c d e punctum g ſit grauitatis
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            centrum. </s>
            <s xml:space="preserve">Rurſus ſit pyramis ba-
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            ſim habens pentagonum a b c d e:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axem f g: </s>
            <s xml:space="preserve">diuidaturq; </s>
            <s xml:space="preserve">axis in pũ
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            cto h, ita ut fh ad h g triplam habe
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            at proportionem. </s>
            <s xml:space="preserve">Dico h grauita-
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            tis centrũ eſſe pyramidis a b c d e f. </s>
            <s xml:space="preserve">
              <lb/>
            iungatur enim e b: </s>
            <s xml:space="preserve">intelligaturq; </s>
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            pyramis, cuius uertex f, & </s>
            <s xml:space="preserve">baſis
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            triangulum a b e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia pyramis
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            intelligatur eundem uerticem ha-
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            bens, & </s>
            <s xml:space="preserve">baſim b c d e quadrilaterũ: </s>
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            ſit autem pyramidis a b e faxis f
              <emph style="sc">K</emph>
            ,
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            & </s>
            <s xml:space="preserve">grauitatis centrum l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyrami
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            dis b c d e faxis f m, & </s>
            <s xml:space="preserve">centrum gra
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            uitatis n: </s>
            <s xml:space="preserve">iunganturq; </s>
            <s xml:space="preserve">
              <emph style="sc">K</emph>
            m, l n; </s>
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              <lb/>
            quæ per puncta g h tranſibunt. </s>
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              <lb/>
            Rurſus eodem modo, quo ſup ra,
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            demonſtrabimus lineas K g m, l h n ſibiipſis æ quidiſtare</s>
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