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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ARCHIMEDIS
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            <s xml:space="preserve">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
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            ipſis ſectionibus in eandem proportionem ſecari. </s>
            <s xml:space="preserve">eſt enim
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            diuidendo, conuertendoque cm ad mb, & </s>
            <s xml:space="preserve">cf ad fb, ut
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            ce ad ea.</s>
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        <div type="section" level="1" n="44">
          <head xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">illud constare potest; </s>
            <s xml:space="preserve">lineas, quæ in portioni-
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            bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
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            les angulos contineant, ab ipſis ſimiles quoque portiones
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            abſcindere: </s>
            <s xml:space="preserve">hoc eſt, ut in propoſita figura, portiones h b c,
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            m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
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            ſimiles eſſe.</s>
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            <s xml:space="preserve">
              <emph style="sc">D_ividantvr_</emph>
            enim ch, cm bifariam in punctis p q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
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            ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </s>
            <s xml:space="preserve">erit portio-
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            nis b s c diameter p s, & </s>
            <s xml:space="preserve">portionis m u c diameter q u. </s>
            <s xml:space="preserve">Itaque fiat
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            ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
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            quæ ſit s x: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut quadratum c t ad quadratum c q, ita fiat f o ad
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            u y. </s>
            <s xml:space="preserve">iam exijs
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              <anchor type="figure" xlink:label="fig-0076-01a" xlink:href="fig-0076-01"/>
            quæ demóſtra
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            uimus in com-
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            mentarijs in
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            quartam pro-
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            poſitioné. </s>
            <s xml:space="preserve">Ar-
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            chrmedis de co
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            noidibus, & </s>
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              <lb/>
            ſphæroidibus,
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            patet quadra-
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            tum c p æqua-
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            le eſſe rectan-
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            gulo p s x:</s>
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