Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
[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.]
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ARCHIMEDIS
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        <div type="section" level="1" n="36">
          <p>
            <s xml:space="preserve">
              <pb file="0060" n="60" rhead="ARCHIMEDIS"/>
            tur centrum grauitatis eius, quæ extra humidum in pro-
              <lb/>
            tracta, quod ſit g. </s>
            <s xml:space="preserve">Itaque per z g ductis perpendiculari-
              <lb/>
              <anchor type="note" xlink:label="note-0060-01a" xlink:href="note-0060-01"/>
            bus ad humidi ſuperficiem, quæ ipſi t h æquidiſtent; </s>
            <s xml:space="preserve">ſequi-
              <lb/>
            tur portionem ipſam non manere, fed reuolui adeo, ut a-
              <lb/>
            xis cum ſuperficie
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              <anchor type="figure" xlink:label="fig-0060-01a" xlink:href="fig-0060-01"/>
            humidi angulum
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            faciat maiorẽ eo,
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            quem nunc facit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">C</note>
            <figure xlink:label="fig-0057-01" xlink:href="fig-0057-01a">
              <image file="0057-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0057-01"/>
            </figure>
            <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">D</note>
            <note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">E</note>
            <note position="right" xlink:label="note-0057-04" xlink:href="note-0057-04a" xml:space="preserve">F</note>
            <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">G</note>
            <note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">13. quin-
              <lb/>
            ti.</note>
            <note position="left" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve">H</note>
            <note position="left" xlink:label="note-0058-04" xlink:href="note-0058-04a" xml:space="preserve">K</note>
            <figure xlink:label="fig-0058-01" xlink:href="fig-0058-01a">
              <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0058-01"/>
            </figure>
            <note position="left" xlink:label="note-0058-05" xlink:href="note-0058-05a" xml:space="preserve">L</note>
            <note position="left" xlink:label="note-0058-06" xlink:href="note-0058-06a" xml:space="preserve">M</note>
            <note position="left" xlink:label="note-0058-07" xlink:href="note-0058-07a" xml:space="preserve">N</note>
            <note position="right" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve">O</note>
            <figure xlink:label="fig-0059-01" xlink:href="fig-0059-01a">
              <image file="0059-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0059-01"/>
            </figure>
            <note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">P</note>
            <figure xlink:label="fig-0060-01" xlink:href="fig-0060-01a">
              <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0060-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Et quoniam cũ
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            antea poſuiſſem´
              <unsure/>
              <lb/>
            facere angulũ ma
              <lb/>
            iorem angulo b,
              <lb/>
            portio neque tũc
              <lb/>
            cõſiſtebat; </s>
            <s xml:space="preserve">perſpi
              <lb/>
            cuũ eſt ipſam con
              <lb/>
            ſiſtere, ſi angulum
              <lb/>
            fecerit angulo b
              <lb/>
            æqualem. </s>
            <s xml:space="preserve">Sic e-
              <lb/>
              <anchor type="note" xlink:label="note-0060-02a" xlink:href="note-0060-02"/>
            nim eriti o æqua-
              <lb/>
            lis ψ b: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">ω i
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            æqualis ψ r: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p h ipſi f. </s>
            <s xml:space="preserve">erit igitur m p ſeſquialtera p h;
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p h dupla h m. </s>
            <s xml:space="preserve">quare cum h ſit centrum grauitatis eius
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            partis, quæ eſt in humido, per eandem perpendicularem,
              <lb/>
            & </s>
            <s xml:space="preserve">ipſa ſurſum, & </s>
            <s xml:space="preserve">quæ extra eſt feretur deorſum. </s>
            <s xml:space="preserve">mane-
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            bitigitur portio; </s>
            <s xml:space="preserve">quoniam altera pars ab altera non re-
              <lb/>
            pelletur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0060-02" xlink:href="note-0060-02a" xml:space="preserve">Q</note>
          </div>
        </div>
        <div type="section" level="1" n="37">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_E T ſit c b ſeſquialtera b r. </s>
            <s xml:space="preserve">erit & </s>
            <s xml:space="preserve">c d ipſius k r ſeſqui-_
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              <anchor type="note" xlink:label="note-0060-03a" xlink:href="note-0060-03"/>
            _altera_.</s>
            <s xml:space="preserve">] In translatione ita legebatur. </s>
            <s xml:space="preserve">ſit autem & </s>
            <s xml:space="preserve">c b quidem
              <lb/>
            hemiolia ipſius b r: </s>
            <s xml:space="preserve">c d autem ipſius K r. </s>
            <s xml:space="preserve">Sed nos quod postremo
              <lb/>
            loco legitur, idcirco corrigendum duximus, quoniam illud non po-
              <lb/>
            nitur ita eſſe, ſed ex ijs, quæ poſita ſunt, neceſſario colligitur. </s>
            <s xml:space="preserve">ſi enim</s>
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