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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            <s xml:space="preserve">_Etenim c b ad b d eſt ut ſex ad quindecim.</s>
            <s xml:space="preserve">]_ Poſuimus
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              <anchor type="note" xlink:label="note-0082-01a" xlink:href="note-0082-01"/>
            enim b K duplam eſſe ipſius K d. </s>
            <s xml:space="preserve">quare componendo b d ad k d erit,
              <lb/>
            ut tria ad unum; </s>
            <s xml:space="preserve">hoc eſt ut quindecim ad quinque. </s>
            <s xml:space="preserve">ſed b d ad K c
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            erat ut quídecim
              <lb/>
              <anchor type="figure" xlink:label="fig-0082-01a" xlink:href="fig-0082-01"/>
            ad quatuor. </s>
            <s xml:space="preserve">ergo
              <lb/>
            b d ad d c, ut quin
              <lb/>
            decim ad nouem:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſio
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            nem rationis, con
              <lb/>
            uertendôq; </s>
            <s xml:space="preserve">c b ad
              <lb/>
            b d, ut ſex ad quí
              <lb/>
            decim.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">N</note>
            <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a">
              <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0082-01"/>
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            <s xml:space="preserve">Etut c b ad
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              <anchor type="note" xlink:label="note-0082-02a" xlink:href="note-0082-02"/>
            b d, ita e b ad
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            b a, & </s>
            <s xml:space="preserve">d z ad
              <lb/>
            d a.</s>
            <s xml:space="preserve">] _Nam cum_
              <lb/>
            _triangula c b e,_
              <lb/>
            _d b a ſint ſimilia,_
              <lb/>
            _erit ut c b ad b e,_
              <lb/>
            _ita d b, ad b a & </s>
            <s xml:space="preserve">permutando, ut c b ad b d; </s>
            <s xml:space="preserve">ita e b ad b a. </s>
            <s xml:space="preserve">Rurſus_
              <lb/>
            _ut b c ad c e, ita b d ad d a: </s>
            <s xml:space="preserve">permutandôq; </s>
            <s xml:space="preserve">ut c b ad b d, ita c e, hoc_
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            _eſt d z ei æqualis ad d a._</s>
            <s xml:space="preserve"/>
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            <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">O</note>
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          <p>
            <s xml:space="preserve">Harum autem d z d a duplæ ſuntipſæ l i, la.</s>
            <s xml:space="preserve">] _Lineam_
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            _quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
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            _manifeſte conſtat. </s>
            <s xml:space="preserve">At uero l i ipſius d z dupla hoc pacto demon-_
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            _ſtrabitur. </s>
            <s xml:space="preserve">Quoniam enim z d ad d a eſt, ut duo ad quinque; </s>
            <s xml:space="preserve">erit có_
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            _uertendo, diuidendôq; </s>
            <s xml:space="preserve">a z, hoc eſt i z ad z d, ut tria ad duo: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _rurſus diuidendo i d ad d z, ut
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            m ad duo. </s>
            <s xml:space="preserve">erat autem z d ad_
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            _d a, hoc eſt ad d l, ut duo ad quinque. </s>
            <s xml:space="preserve">ergo ex æquali, conuertendóq;_
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            </s>
            <s xml:space="preserve">_l d ad d i, ut quinque ad unum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſionem rationis d l ad_
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            _li, ut quinque ad quatuor. </s>
            <s xml:space="preserve">ſed d z ad d l erat, ut duo ad quinque._ </s>
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              <lb/>
            _ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </s>
            <s xml:space="preserve">dupla eſt igitur_
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            _l i ipſius d z. </s>
            <s xml:space="preserve">quod demonſtrandum fuerat._</s>
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            <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">P</note>
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            <s xml:space="preserve">Et a d ad d i eam proportionem habet, quã quinque
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            </s>
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