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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              <pb file="0178" n="178" rhead="FED. COMMANDINI"/>
            producantur. </s>
            <s xml:space="preserve">Quoniam igitur pyramis ſecatur planis bafi
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            æquidiſtantibus, ſectiones ſimiles erunt: </s>
            <s xml:space="preserve">atque erunt qua-
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              <anchor type="note" xlink:label="note-0178-01a" xlink:href="note-0178-01"/>
            drata, uel rectangula circa circulos, uel ellipſes deſcripta,
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            quemadmodum & </s>
            <s xml:space="preserve">in ipſa baſi. </s>
            <s xml:space="preserve">Sed cum circuli inter ſe eã
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            proportionem habeant, quam diametrorum quadrata:
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            </s>
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              <anchor type="note" xlink:label="note-0178-02a" xlink:href="note-0178-02"/>
            itemq; </s>
            <s xml:space="preserve">ellipſes eam quam rectangula ex ipſarum diametris
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            conſtantia: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit circulus, uel ellipſis circa diametrum e f
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              <anchor type="figure" xlink:label="fig-0178-01a" xlink:href="fig-0178-01"/>
              <anchor type="note" xlink:label="note-0178-03a" xlink:href="note-0178-03"/>
            proportionalis inter circulos, uel ellipſes a b, c d; </s>
            <s xml:space="preserve">erit re-
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            ctangulum e f etiam inter rectangula a b, c d proportio-
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            nale: </s>
            <s xml:space="preserve">per rectangulum enim nunc breuitatis cauſa etiã ip-
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            ſum quadratum intelligemus. </s>
            <s xml:space="preserve">quare ex iis, quæ proxime
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            dicta ſunt, pyramis baſim habens æqualem dictis rectangu
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            lis, & </s>
            <s xml:space="preserve">altitudinem eandem, quam fruſtum a d, ipſi fruſto à
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            pyramide abſciſſo æqualis probabitur. </s>
            <s xml:space="preserve">ut autem rectangu
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            lum c d ad rectangulũ e f, ita circulus, uel ellipſis c d a d e f
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            circulum, uel ellipſim: </s>
            <s xml:space="preserve">componendoq; </s>
            <s xml:space="preserve">ut rectangula c d,
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            e f, ad e f rectangulum, ita circuli, uel ellipſes e d, e f, ad e f:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut rectangulum e f ad rectangulum a b, ita cir culus, uel
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            cllipſis e f ad a b circulum, uel ellipſim. </s>
            <s xml:space="preserve">ergo ex æquali, & </s>
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            componendo, utrectãgula c d, e f, a b ad ipſum a b, ita cir-</s>
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