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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          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_Sit ei, quæ uſque ad axem æqualis r h.</s>
            <s xml:space="preserve">]_ Ita legendum eſt,
              <lb/>
              <anchor type="note" xlink:label="note-0040-01a" xlink:href="note-0040-01"/>
            non r m, ut tranſlatio habet, quod ex ijs, quæ ſequuntur, manifeſte
              <lb/>
            conſtare poteſt.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">A</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Et oh dupla ipſius h m.</s>
            <s xml:space="preserve">]_ In tranſlatione mendoſe legeba-
              <lb/>
              <anchor type="note" xlink:label="note-0040-02a" xlink:href="note-0040-02"/>
            tur, on dupla ipſius rm.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">B</note>
          </div>
          <p>
            <s xml:space="preserve">Hoc enim ſupra demonſtratum eſt.</s>
            <s xml:space="preserve">] _In prima huius_.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">C</note>
          <p>
            <s xml:space="preserve">Et quam proportionem habet demerſa portio ad totã,
              <lb/>
              <anchor type="note" xlink:label="note-0040-04a" xlink:href="note-0040-04"/>
            eam quadratum p f habet ad n o quadratum.</s>
            <s xml:space="preserve">] _Hoc loco in_
              <lb/>
            _tranſlatione non nulli deſider abantur, quænos reſtituimus. </s>
            <s xml:space="preserve">Illud au_
              <lb/>
            _tem ab Archimede demonſtratum eſt in libro de conoidibus & </s>
            <s xml:space="preserve">ſphæ_
              <lb/>
            _roidibus propoſitione_ 26.</s>
            <s xml:space="preserve"/>
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            <note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">D</note>
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          <p style="it">
            <s xml:space="preserve">_Quare p f non eſt minor ipſa m o.</s>
            <s xml:space="preserve">]_ Nam ex decima quinti
              <lb/>
              <anchor type="note" xlink:label="note-0040-05a" xlink:href="note-0040-05"/>
            ſequitur, quadratum p f non eſſe minus quadrato m o. </s>
            <s xml:space="preserve">quare neque
              <lb/>
            linea p f minor erit linea m o ex 22 ſexti.</s>
            <s xml:space="preserve"/>
          </p>
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            <note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">E</note>
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          <p style="it">
            <s xml:space="preserve">_Nec b p item minor h o.</s>
            <s xml:space="preserve">]_ Eſt enim ut p f ad p b, ita m o,
              <lb/>
              <anchor type="note" xlink:label="note-0040-06a" xlink:href="note-0040-06"/>
            ad h o & </s>
            <s xml:space="preserve">permutando, ut p f ad mo, ita b p, ad b o. </s>
            <s xml:space="preserve">ſed p f non
              <lb/>
            est minor m o, ut oſtenſiim cst. </s>
            <s xml:space="preserve">ergo neque b p ipſa h o minor erit.</s>
            <s xml:space="preserve"/>
          </p>
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            <note position="left" xlink:label="note-0040-06" xlink:href="note-0040-06a" xml:space="preserve">F</note>
          </div>
          <note position="left" xml:space="preserve">14. quinti</note>
          <p>
            <s xml:space="preserve">Si igitur ab h
              <lb/>
              <anchor type="note" xlink:label="note-0040-08a" xlink:href="note-0040-08"/>
              <anchor type="figure" xlink:label="fig-0040-01a" xlink:href="fig-0040-01"/>
            ducatur linea ad
              <lb/>
            rectos angulos ip
              <lb/>
            ſi n o, coibit cum
              <lb/>
            b p, atque inter
              <lb/>
            b & </s>
            <s xml:space="preserve">p cadet.</s>
            <s xml:space="preserve">]
              <lb/>
            _Corruptus erat hic_
              <lb/>
            _locus in tranſlatio-_
              <lb/>
            _ne. </s>
            <s xml:space="preserve">Illud uero ita de-_
              <lb/>
            _monſtr abitur. </s>
            <s xml:space="preserve">Quo-_
              <lb/>
            _niam p f non eſt mi-_
              <lb/>
            _nor o m, nec p b ip-_
              <lb/>
            _ſa h o; </s>
            <s xml:space="preserve">ſi ponatur p f_
              <lb/>
            _æqualis o m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p b,_
              <lb/>
            _ipſi h o æqualis erit._</s>
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