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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DE IIS QVAE VEH. IN AQVA.
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          <pb o="37" file="0073" n="73" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:space="preserve">Cum ergo tres portiones ſint a p o i, a ei, atd, con-
              <lb/>
              <anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/>
            tentæ rectis lineis, & </s>
            <s xml:space="preserve">rectãgulorum conorum ſectionibus;
              <lb/>
            </s>
            <s xml:space="preserve">rectæq;</s>
            <s xml:space="preserve">, ſimiles, & </s>
            <s xml:space="preserve">inæquales, quæ contingunt ſe ſe ſuper
              <lb/>
            unam quamque baſim.</s>
            <s xml:space="preserve">] _Poſt ea uerba, ſuper unamquanque_
              <lb/>
            _baſim, in trans latione aliqua deſiderari uidentur. </s>
            <s xml:space="preserve">Ad borum autem_
              <lb/>
            _demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
              <lb/>
            _quæ ſequuntur, neceſſaria erunt._</s>
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          </p>
          <div type="float" level="2" n="11">
            <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">M</note>
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        </div>
        <div type="section" level="1" n="42">
          <head xml:space="preserve">LEMMA I.</head>
          <p style="it">
            <s xml:space="preserve">Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
              <lb/>
            æquidiſtantes a c, d e, ita ut quam proportionem ba-
              <lb/>
            bet a b ad b d, eandern haheat a c ad de. </s>
            <s xml:space="preserve">Dico li-
              <lb/>
            neam, quæ c b puncta coniungit, etiam per ipſum e
              <lb/>
            tr anſire.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
              <lb/>
            </s>
            <s xml:space="preserve">tranſeat primum infra, ut per f. </s>
            <s xml:space="preserve">erunt triangula a b c, d b f inter ſe
              <lb/>
            ſimilia. </s>
            <s xml:space="preserve">quare ut a b ad b d, ita a c ad d f. </s>
            <s xml:space="preserve">ſed ut a b ad bd, ita
              <lb/>
              <anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/>
            erat a c ad d e. </s>
            <s xml:space="preserve">ergo d f ipſi d e æqualis erit, uidelicet pars to-
              <lb/>
              <anchor type="note" xlink:label="note-0073-03a" xlink:href="note-0073-03"/>
            ti, quod eſt
              <lb/>
              <anchor type="figure" xlink:label="fig-0073-01a" xlink:href="fig-0073-01"/>
            cbſurdum.
              <lb/>
            </s>
            <s xml:space="preserve">Idem ab-
              <lb/>
            ſurdum ſe
              <lb/>
            quetur, ſi
              <lb/>
            linea c b
              <lb/>
            ſupra e pú
              <lb/>
            ctum tran
              <lb/>
            ſire pona-
              <lb/>
            tur. </s>
            <s xml:space="preserve">quare
              <lb/>
            c b etiam
              <lb/>
            per e ne-
              <lb/>
            ceſſario tranſibit. </s>
            <s xml:space="preserve">quod oportebat demonſtrare.</s>
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            <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">9. quinti.</note>
            <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a">
              <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0073-01"/>
            </figure>
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