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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              <pb o="3" file="0017" n="17" rhead="DE IIS QVAE VEH. IN AQVA."/>
            iuncta, & </s>
            <s xml:space="preserve">continuata: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſectio planorũ ipſius K m K n:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in humido intelligatur quædam magnitudo r s q y ex ip
              <lb/>
            ſo humido conſtans, æqualis, & </s>
            <s xml:space="preserve">ſimilis ſolidæ b h t c, quæ
              <lb/>
            quidem pars eſt ſolidæ magnitudinis in humido demerſa. </s>
            <s xml:space="preserve">
              <lb/>
            partes igitur humidi, quæ ſcilicet in prima pyramide ſuper
              <lb/>
            ficie x o continetur, & </s>
            <s xml:space="preserve">quæ in altera continetur p o, æquali
              <lb/>
            ter ſunt poſitæ, & </s>
            <s xml:space="preserve">continuatæ ſed non ſimiliter premun-
              <lb/>
            tur. </s>
            <s xml:space="preserve">nam contenta quidem x o, premitur ſolido e h t f, & </s>
            <s xml:space="preserve">
              <lb/>
            humido interiecto inter ſuperficies x o, l m, & </s>
            <s xml:space="preserve">plana pyra-
              <lb/>
            midis; </s>
            <s xml:space="preserve">contenta uero p o premitur ſolido r s q y, & </s>
            <s xml:space="preserve">humi-
              <lb/>
            do inter ſuperficies o p, m n, & </s>
            <s xml:space="preserve">pyramidis plana interiecto. </s>
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              <lb/>
            minor autem eſt grauitas humidi, quod eſt inter m n, o p,
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            quàm eius, quod inter l m, x o. </s>
            <s xml:space="preserve">ſolidum enim r s q y eſt mi
              <lb/>
            nus ſolido e h t f: </s>
            <s xml:space="preserve">cum ſit æquale ipſi b h t c; </s>
            <s xml:space="preserve">quia magnitu
              <lb/>
            dine æquale, & </s>
            <s xml:space="preserve">æque graue ponitur ſolidum, atque humi-
              <lb/>
            dum: </s>
            <s xml:space="preserve">reliquum autem reliquo inæquale eſt. </s>
            <s xml:space="preserve">conſtatigitur
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            partem contentã ſuperficie o p, expelli ab ea, quæ ipſa x o
              <lb/>
            continetur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non conſiſtere humidum. </s>
            <s xml:space="preserve">ponebatur au-
              <lb/>
            tem conſiſtens, & </s>
            <s xml:space="preserve">manens: </s>
            <s xml:space="preserve">non ergo ex ſuperficie humidi
              <lb/>
            extat aliquid ſolidæ magnitudinis. </s>
            <s xml:space="preserve">ſed neque demerſum
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            ſolidum ad inferiora feretur. </s>
            <s xml:space="preserve">Similiter enim prementur
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            omnes partes humidi æqualiter poſitæ, cum ſolidum ſit æ-
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            que graue, atque humidum.</s>
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            <figure xlink:label="fig-0016-01" xlink:href="fig-0016-01a">
              <image file="0016-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0016-01"/>
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          <head xml:space="preserve">PROPOSITIO IIII.</head>
          <p>
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              <emph style="sc">Solidarvm</emph>
            magnitudinum, quæcunque
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            leuior humido fuerit, demiſſa in humidum non
              <lb/>
            demergetur tota, ſed aliqua pars ipſius ex humi-
              <lb/>
            di ſuperficie extabit.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">SIT magnitudo ſolida humido leuior; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demiſſa in hu
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            midum demergatur tota, ſi fieri poteſt, ut nulla pars ipſius</s>
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