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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ARCHIMEDIS
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        <div type="section" level="1" n="39">
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              <pb file="0068" n="68" rhead="ARCHIMEDIS"/>
            _erit conuertendo tota portio ad partem ipſius demerſam, ut quadrd-_
              <lb/>
            _tum b d ad exceſſum, quo quadratum f q excedit. </s>
            <s xml:space="preserve">quare per conuer-_
              <lb/>
            _ſionem rationis tota portio ad eam, quæ extra humidum est ut_
              <lb/>
            _qu.</s>
            <s xml:space="preserve">idratum b d ad quadratum f q: </s>
            <s xml:space="preserve">nam quadratum b d tanto maius_
              <lb/>
            _est exceſſu, quo excedit quadratum f q, quantum est ipſum f q qua-_
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            _dratum_.</s>
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          </p>
          <div type="float" level="2" n="4">
            <note position="right" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">E</note>
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          <p style="it">
            <s xml:space="preserve">_Quoniam quæ ex parte 1 deorſum, quæ uero ex parte a_
              <lb/>
              <anchor type="note" xlink:label="note-0068-01a" xlink:href="note-0068-01"/>
            _ſurſum ferentur.</s>
            <s xml:space="preserve">]_ Hæc nos ita correximus, nam in translatione
              <lb/>
            mendoſe, ut opinor, legebatur, quoniam quæ ex parte l ad ſuperiora
              <lb/>
            ferentur, perpendicularis enim quæ tranſit per z ad partes l, & </s>
            <s xml:space="preserve">quæ
              <lb/>
            per g ad partes a cadit. </s>
            <s xml:space="preserve">quare centrum z unà cum p. </s>
            <s xml:space="preserve">trtibus ijs, quæ
              <lb/>
            ſunt ad l deorſum feretur, centrum uero g unà cum partibus quæ ad
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            a ſurſum.</s>
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            <note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">F</note>
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            <s xml:space="preserve">Similiter demonſtrabitur non manere portionem, ſed
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            inclinari, donec utique axis cum ſuperficie humidi faciat
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            angulum angulo b æqualem.</s>
            <s xml:space="preserve">] _Illud uero tum ex ijs, quæ in an_
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            _tecedenti dicta ſunt, tum ex figuris, quas appoſuimus, facile demon-_
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            _strari potest._</s>
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            <note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">G</note>
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          <head xml:space="preserve">PROPOSITIO X.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem, quàm
              <lb/>
            ut ad eam, quæ uſque ad axem proportionem ha-
              <lb/>
            beat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">in humidum
              <lb/>
            demiſſa, ita ut baſis ipſius non contingat humi-
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            dum: </s>
            <s xml:space="preserve">non nunquam quidem recta conſiſtet; </s>
            <s xml:space="preserve">non
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            nunquam inclinata: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">interdum adeo inclinata,
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              <anchor type="note" xlink:label="note-0068-04a" xlink:href="note-0068-04"/>
            ut baſis ipſius in uno puncto contingat ſuperfi-
              <lb/>
            ciem humidi: </s>
            <s xml:space="preserve">idq; </s>
            <s xml:space="preserve">in duabus diſpoſitionibus:</s>
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