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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="29" file="0069" n="69" rhead="DE IIS QVAE VEH. IN AQVA."/>
            interdũ quidem ita, ut baſis in humidum magis
              <lb/>
              <anchor type="note" xlink:label="note-0069-01a" xlink:href="note-0069-01"/>
            demergatur: </s>
            <s xml:space="preserve">interdum uero ita, ut ſuperficiem
              <lb/>
              <anchor type="note" xlink:label="note-0069-02a" xlink:href="note-0069-02"/>
            humidi nullo modo contingat; </s>
            <s xml:space="preserve">ſecundum pro-
              <lb/>
              <anchor type="note" xlink:label="note-0069-03a" xlink:href="note-0069-03"/>
            portionem, quam habet ad humidum in grauita-
              <lb/>
            te. </s>
            <s xml:space="preserve">Eorum quæ dicta ſunt, ſingula inferius de-
              <lb/>
            monſtrabuntur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0068-04" xlink:href="note-0068-04a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">D</note>
            <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">E</note>
          </div>
          <p>
            <s xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa plano per axẽ.
              <lb/>
            </s>
            <s xml:space="preserve">recto ad ſuperficiem humidi, ſectio ſit a p o l rectanguli co
              <lb/>
            ni ſeccio: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:space="preserve">ſece-
              <lb/>
            turq; </s>
            <s xml:space="preserve">b d in puncto quidem _k_ ita, ut b k dupla ſitipſius
              <lb/>
            _k_ d: </s>
            <s xml:space="preserve">in c uero ita, ut b d ad
              <emph style="sc">K C</emph>
            proportionẽ habeat ean-
              <lb/>
            dem, quam quindecim ad quatuor. </s>
            <s xml:space="preserve">conſtat igitur k c ma-
              <lb/>
              <anchor type="note" xlink:label="note-0069-04a" xlink:href="note-0069-04"/>
            iorem eſſe, quàm quæ uſque ad axem. </s>
            <s xml:space="preserve">Sit ei quæ uſque ad
              <lb/>
              <anchor type="note" xlink:label="note-0069-05a" xlink:href="note-0069-05"/>
            axem æqualis k r: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ipſius k r ſeſquialtera d s. </s>
            <s xml:space="preserve">Eſt autem
              <lb/>
              <anchor type="note" xlink:label="note-0069-06a" xlink:href="note-0069-06"/>
            & </s>
            <s xml:space="preserve">s b ſeſquial-
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              <anchor type="figure" xlink:label="fig-0069-01a" xlink:href="fig-0069-01"/>
            tera ipſius b r.
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            </s>
            <s xml:space="preserve">Itaque iũgatur
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            a b, & </s>
            <s xml:space="preserve">per c du
              <lb/>
            catur c e per-
              <lb/>
            pẽdicularis ad
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            b d, quæ lineã
              <lb/>
            a b in puncto
              <lb/>
            e ſecet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            e ducatur e z
              <lb/>
            æquidiſtãs b d. </s>
            <s xml:space="preserve">
              <lb/>
            Rurſus ipſa a b
              <lb/>
            bifariã in t di-
              <lb/>
            uiſa, ducatur t
              <lb/>
            h eidem b d æ-
              <lb/>
            quidiſtans: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            intelligantur rectanguli coni ſectiones deſcriptæ a e i qui-</s>
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