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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        <div type="section" level="1" n="34">
          <p>
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              <pb file="0054" n="54" rhead="ARCHIMEDIS"/>
            modo hum idi ſuperficiem continget.</s>
            <s xml:space="preserve">] _In translatione le-_
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            _gebatur ut baſis ipſius non tangat ſuperficiem humidi ſecundum_
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            _unum ſignum. </s>
            <s xml:space="preserve">nos autem ita uertere maluimus, & </s>
            <s xml:space="preserve">hic & </s>
            <s xml:space="preserve">in ijs,_
              <lb/>
            _quæ ſequuntur, quoniam græci οὐδὲ \~εις, οὐδὲ ἓν, pro οὐ δεὶς, &_</s>
            <s xml:space="preserve">
              <lb/>
            _οὐδε ν frequenter utútur. </s>
            <s xml:space="preserve">ut οὐδ ε ςιν οὐ δεὶς, nullus eſt: </s>
            <s xml:space="preserve">οὐ \’δ ὑφ
              <unsure/>
            ἑ νὸς,_
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            _ànullo & </s>
            <s xml:space="preserve">alia eiuſmodi._</s>
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            <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">E</note>
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        </div>
        <div type="section" level="1" n="35">
          <head xml:space="preserve">PROPOSITIO VII.</head>
          <p>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            leuior humido axem habuerit maiorem quidem
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            quàm ſeſquialtérum eius, quæ uſque ad axem;
              <lb/>
            </s>
            <s xml:space="preserve">minorem uero, quàm ut ad eam, quæ uſque ad
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            axem proportionem habeat, quam quindecim
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            ad quatuor: </s>
            <s xml:space="preserve">in humidum demiſſa, adeo ut baſis
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            ipſius tota ſitin humido; </s>
            <s xml:space="preserve">nunquam conſiſtet ita,
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            ut baſis contingat humidi ſuperficiem: </s>
            <s xml:space="preserve">ſed ut to-
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            ta in humido ſit, & </s>
            <s xml:space="preserve">nullo modo eius ſuperficiem
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            contingat.</s>
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            <s xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demittatur in humidũ,
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            ut diximus, adeo ut baſis ipſius in uno puncto contingat
              <lb/>
            humidi ſuperficiem. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere ip-
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            ſam: </s>
            <s xml:space="preserve">ſed reuolui ita ut baſis fuperficiem humidi nullo mo-
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            do contingat. </s>
            <s xml:space="preserve">Secta enim ipſa plano per axem, recto ad ſu
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            perficiem humidi, ſectio ſit a p o l rectanguli coni ſectio:
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            </s>
            <s xml:space="preserve">ſuperficiei humidi ſectio ſit s 1: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectio-
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            nis diameter p f: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">p f in r quidem ita ut r p ſit
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            dupla ipſius r f; </s>
            <s xml:space="preserve">in ω autem ut p f ad r ω proportionem
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            habeat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ω k ipſi p f ad re-
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            ctos angulos ducatur erit r ω minor, quàm quæ uſque ad
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            axem. </s>
            <s xml:space="preserve">Itaque accipiatur ei, quæ uſque ad axem æqualis rh:</s>
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