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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DE IIS QVAE VEH. IN AQVA.
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          <p style="it">
            <s xml:space="preserve">
              <pb o="8" file="0027" n="27" rhead="DE IIS QVAE VEH. IN AQVA."/>
            neas; </s>
            <s xml:space="preserve">neutra alteri obſistit, quo minus moueatur; </s>
            <s xml:space="preserve">ídq; </s>
            <s xml:space="preserve">continenter
              <lb/>
            fiat, dum portio in rectum fuerit conſtituta: </s>
            <s xml:space="preserve">tunc enim utrarumque
              <lb/>
            magnitudinum grauitatis centra in unam, eandémq; </s>
            <s xml:space="preserve">perpendicula-
              <lb/>
            rum conueniunt, uidelicet in axem portionis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quanto conatu, im
              <lb/>
            petùue ea, quæ in humido eſt ſurſum, tanto quæ extra humidum de-
              <lb/>
            orſum per eandem lineam contendit. </s>
            <s xml:space="preserve">quare cum altera alteram non
              <lb/>
            ſuperet, non amplius mouebitur portio; </s>
            <s xml:space="preserve">ſed conſiſtet, manebítq; </s>
            <s xml:space="preserve">in
              <lb/>
            eodem ſemper ſitu; </s>
            <s xml:space="preserve">niſi forte aliqua cauſſa extrinſecus acceſſerit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve">F</note>
          </div>
        </div>
        <div type="section" level="1" n="19">
          <head xml:space="preserve">PROPOSITIO IX.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Qvòd</emph>
            ſi figura humido leuior in humidum
              <lb/>
            demittatur, ita ut baſis tota ſit in humido; </s>
            <s xml:space="preserve">inſide
              <lb/>
            bit recta, ita ut axis ipſius ſecundum perpendicu
              <lb/>
            larem conſtituatur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">INTELLIGATVR enim magnitudo aliqua, qua-
              <lb/>
            lis dicta eſt, in humidum demiſſa: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">intelligatur planum
              <lb/>
            per axem portionis, & </s>
            <s xml:space="preserve">per centrum terræ ductum: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſu
              <lb/>
            perficiei quidem humidi ſectio a b c d circunferentia; </s>
            <s xml:space="preserve">figu
              <lb/>
            ræ autem ſectio circun ferentia e f h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit e h recta linea:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis portionis f t. </s>
            <s xml:space="preserve">Si igitur fieri poteſt, non ſit f t ſecun
              <lb/>
            dum perpendicularem.</s>
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          </p>
          <figure>
            <image file="0027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0027-01"/>
          </figure>
          <p>
            <s xml:space="preserve">Demonſtrandum eſt non
              <lb/>
            manerefiguram; </s>
            <s xml:space="preserve">ſed in re
              <lb/>
            ctum reſtitui. </s>
            <s xml:space="preserve">eſt autem
              <lb/>
            centrum ſphæræ in linea
              <lb/>
            f t: </s>
            <s xml:space="preserve">rurſus enim ſit figu-
              <lb/>
            ra primo maior dimidia
              <lb/>
            ſphæra: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſphæræ centrũ
              <lb/>
            in dimidia ſphæra ſit pun-
              <lb/>
            ctum t; </s>
            <s xml:space="preserve">in minore portione p; </s>
            <s xml:space="preserve">in maiori uero ſit _k_: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            _k_, & </s>
            <s xml:space="preserve">terræ centrum l ducatur _k_ l. </s>
            <s xml:space="preserve">Itaque figura quæ eſt
              <lb/>
              <anchor type="note" xlink:label="note-0027-01a" xlink:href="note-0027-01"/>
            </s>
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