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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        <div type="section" level="1" n="19">
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              <pb file="0028" n="28" rhead="ARCHIMEDIS"/>
            extra humidi ſuperficiem, axem habetin perpendiculari
              <lb/>
            per _k_: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propter ea, quæ ſuperius dicta ſunt, centrum gra-
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            uitatis ipſius eſt in linea n _k_, quod ſitr; </s>
            <s xml:space="preserve">totius autem por-
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            tionis centrum grauitatis eſt in linea f t, inter _k_ & </s>
            <s xml:space="preserve">f, quod
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            ſit x. </s>
            <s xml:space="preserve">reliquæ ergo figuræ, eius ſcilicet, quæ eſt in humido,
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            centrum erit in rectalinea r x producta ad partes x; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">aſ-
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              <anchor type="figure" xlink:label="fig-0028-01a" xlink:href="fig-0028-01"/>
            ſumpta ex ea linea quadam, quæ ad x r eandem habeat pro
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            portionem, quam grauitas portionis, quæ eſt extra humi-
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            dum, ad grauitatem figuræ, quæ in humido. </s>
            <s xml:space="preserve">Sit autem o
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            centrum dictæ figuræ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per o perpendicularis ducatur
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            l o. </s>
            <s xml:space="preserve">Feretur ergo grauitas portionis quidem, quæ eſt ex-
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            tra humidum, per rectam r l deorſum; </s>
            <s xml:space="preserve">figuræ autem, quæ
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            in humido, per rectam o l ſurſum. </s>
            <s xml:space="preserve">non manet igitur flgu-
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            ra; </s>
            <s xml:space="preserve">ſed partes eius, quæ ſuntad h, deorſum ferẽtur; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ
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            ad e ſurſum. </s>
            <s xml:space="preserve">atque hoc ſemper erit, donec f t ſecundum
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            perpendicularem fiat.</s>
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            <note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">A</note>
            <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a">
              <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0028-01"/>
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          <head xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:space="preserve">ITAQVE figura, quæ extra humidi ſuperficiem,
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              <anchor type="note" xlink:label="note-0028-01a" xlink:href="note-0028-01"/>
            axem habet in perpendiculari per _k_.</s>
            <s xml:space="preserve">]</s>
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            <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">A</note>
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              <emph style="sc">D_vcatvr_</emph>
            enim b c, quæ ſecet lineam n k in m: </s>
            <s xml:space="preserve">ipſa uero
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            n k circunferentiam a b c d ſecet in g. </s>
            <s xml:space="preserve">eodem modo, quo ſupra, de-</s>
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