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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          <head xml:space="preserve">PROPOSITIO VI.</head>
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              <emph style="sc">Solidae</emph>
            magnitudines humido leuiores, in
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            humidum impulſæ ſurſum feruntur tanta ui, quã
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            to humidum molem habens magnitudini æqua-
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            lem, grauius eſt ipſa magnitudine.</s>
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            <s xml:space="preserve">SIT enim magnitudo aleuior humido: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit magnitu
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            dinis quidem a grauitas b: </s>
            <s xml:space="preserve">humidi uero molem habentis
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            æqualem ipſi a, grauitas ſit b c. </s>
            <s xml:space="preserve">demonſtrandum eſt magni
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            tudinem a in humidum impulſam tanta ui ſurſum ferri,
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            quanta eſt grauitas c. </s>
            <s xml:space="preserve">accipiatur enim quædam magnitu-
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            do, in qua d habens grauitatem ipſi c æqualem. </s>
            <s xml:space="preserve">Itaque
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            magnitudo ex utriſque magnitudinibus conſtans, in qui-
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            bus a d, leuior eſt humido: </s>
            <s xml:space="preserve">nam magnitudinis quidem quæ
              <lb/>
            ex utriſque conſtat grauitas eſt b c; </s>
            <s xml:space="preserve">humidi uero habentis
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            molem ipſis æ qualem grauitas maior eſt, quàm b c: </s>
            <s xml:space="preserve">quo-
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            niam b c grauitas eſt humidi
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              <anchor type="figure" xlink:label="fig-0020-01a" xlink:href="fig-0020-01"/>
            molẽ habentis æqualem ipſia.
              <lb/>
            </s>
            <s xml:space="preserve">Si ergo demittatur in humidũ
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            magnitudo ex utriſque a d con
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            ſtans; </s>
            <s xml:space="preserve">uſque eò demergetur, ut
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            tanta moles humidi, quanta eſt
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            pars magnitudinis demerſa eã
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            dem, quam tota magnitudo
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            grauitatem habeat. </s>
            <s xml:space="preserve">hoc enim
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            iam demonſtratum eſt. </s>
            <s xml:space="preserve">ſit autẽ
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            ſuperſicies humidi alicuius a b
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            c d circunferentia. </s>
            <s xml:space="preserve">Quoniam igitur tanta moles humidi,
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            quanta eſt magnitudo a grauitatem habet eandem, quam
              <lb/>
            magnitudines a d: </s>
            <s xml:space="preserve">perſpicuum eſt partem ipſius demer-
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            ſam eſſe magnitudinem a; </s>
            <s xml:space="preserve">reliquam uero d totam ex hu-</s>
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