Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
[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.]
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ARCHIMEDIS
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            & </s>
            <s xml:space="preserve">per conuer-
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              <anchor type="figure" xlink:label="fig-0078-01a" xlink:href="fig-0078-01"/>
            ſionem rationis
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            ut e b ad e g,
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            ita f d ad f h.
              <lb/>
            </s>
            <s xml:space="preserve">eſt autem ut a e
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            ad e b, ita c f
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            ad f d. </s>
            <s xml:space="preserve">ex æqua
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            li igitur ut a e
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            ad e g, ita c f
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            ad f h.</s>
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          </p>
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            <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a">
              <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0078-01"/>
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              <emph style="sc">A_liter_</emph>
            . </s>
            <s xml:space="preserve">Aptentur lineæ a b, c d inter ſe ſe, ita ut ad partes
              <lb/>
            a c angulum faciant; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſint a c in uno atque eodem puncto: </s>
            <s xml:space="preserve">deinde
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            iungantur d b, h g, fe. </s>
            <s xml:space="preserve">cum igitur ſit ut a e ad e b, ita c f, hoc eſt
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            a f ad f d; </s>
            <s xml:space="preserve">æquidiſtabit fe ipſi d b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimiliter h g eidem d b
              <lb/>
              <anchor type="note" xlink:label="note-0078-01a" xlink:href="note-0078-01"/>
            æquidiſtabit: </s>
            <s xml:space="preserve">quoniam a h ad h d eſt, ut a g ad g b. </s>
            <s xml:space="preserve">ergo f c, h g
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            inter ſe ſe æquidiſtant: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco ut a e ad e g, ita a f; </s>
            <s xml:space="preserve">hoc eſt c f ad
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            fh. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
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            <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">2. ſexti:</note>
            <note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">30. primi</note>
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        <div type="section" level="1" n="46">
          <head xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:space="preserve">Sint rurſus duæ portiones ſimiles, contentæ rectis li-
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            neis, & </s>
            <s xml:space="preserve">rectangulorum conorum ſectionibus, ut in ſupe-
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            riori figura a b c, cuius diameter b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">e f c, cuius
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            diameter f g: </s>
            <s xml:space="preserve">ducaturque à puncto e linea e h, diame-
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            tris b d, f g æquidiſtans, quæ ſectionem a b c in _k_ ſe-
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            cet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto c ducatur c h contingens ſectionem
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            a b c in c conueniensque cumlinea e h in h, quæ ſectio
              <lb/>
            nem quoque e f c in eodem c puncto continget, ut demon
              <lb/>
            strabitur. </s>
            <s xml:space="preserve">Dico lineam ductam ab ipſa c h uſque ad ſe-
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            ctionem e f c, ita ut lineæ e h æquidistet, in eandem pro
              <lb/>
            portionem diuidi à ſectione a b c; </s>
            <s xml:space="preserve">in quam linea c a à</s>
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