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="4" file="0019" n="19" rhead="DE IIS QVAE VEH. IN AQVA."/>
            premitur pars humidi, quæ eſt ſub ſuperficie o p. </s>
            <s xml:space="preserve">quare ex-
              <lb/>
            pellet partem minus preſſam, & </s>
            <s xml:space="preserve">non manebit humidum.
              <lb/>
            </s>
            <s xml:space="preserve">ponebatur autem manens. </s>
            <s xml:space="preserve">non igitur demergetur tota,
              <lb/>
            ſed aliqua pars ipſius ex humidi ſuperficie extabit.</s>
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            <figure xlink:label="fig-0018-01" xlink:href="fig-0018-01a">
              <image file="0018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0018-01"/>
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          <head xml:space="preserve">PROPOSITIO V.</head>
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              <emph style="sc">Solidarvm</emph>
            magnitudinum quæcunque le
              <lb/>
            uior humido fuerit, demiſſa in humidum vſque
              <lb/>
            eô demergetur, vt tanta moles humidi, quanta
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            eſt partis demerſæ, eandem, quam tota magnitu-
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            do, grauitatem habeat.</s>
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            <s xml:space="preserve">DISPONANTVR eadem, quæſupra: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">humi-
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            dum manens: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">magnitudo e h t f humido leuior. </s>
            <s xml:space="preserve">Si igitur
              <lb/>
            humidum manet, ſimiliter prementur eius partes, quæ æ-
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            qualiter iacent. </s>
            <s xml:space="preserve">ſimiliter ergo premetur humidum ſub ſu-
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            perficiebus x o o p.
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            </s>
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              <anchor type="figure" xlink:label="fig-0019-01a" xlink:href="fig-0019-01"/>
            quare æ qualis eſt graui-
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            tas, qua premuntur. </s>
            <s xml:space="preserve">eſt
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            autem & </s>
            <s xml:space="preserve">grauitas humi
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            di, quod in prima pyra-
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            mide abſque ſolido b h
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            t c, æqualis grauitati hu
              <lb/>
            midi, quod in altera py-
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            ramide abſq; </s>
            <s xml:space="preserve">r s q y hu-
              <lb/>
            mido. </s>
            <s xml:space="preserve">perſpicuum eſt
              <lb/>
            igitur grauitatem ma-
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            gnitudinis e h t f grauitati humidi r s q y æqualem eſſe. </s>
            <s xml:space="preserve">ex
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            quibus conſtat, tantam humidi molem, quanta eſt pars de
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            merſa ſolidæ magnitudinis, eandem, quam tota magnitu-
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            do habere grauitatem.</s>
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