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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DE IIS QVAE VEH. IN AQVA.
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          <pb o="7" file="0025" n="25" rhead="DE IIS QVAE VEH. IN AQVA."/>
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        <div type="section" level="1" n="18">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">H_
              <emph style="sc">VIVS</emph>
            _ propoſitionis demonſtratio iniuria temporum deſidera-
              <lb/>
            tur, quam nos ita reſtituimus, ut ex figuris, quæ remanſerunt Archi
              <lb/>
            medem ſcripſiſſe colligi potuit: </s>
            <s xml:space="preserve">neque enim eas immutare uiſum est,
              <lb/>
            quæ uero ad declarationem, explicationémque addenda fuerant, in
              <lb/>
            commentarijs ſuppleuimus, id quod etiam præstitimus in ſecunda
              <lb/>
            propoſitione ſecundi libri.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">_SI aliqua magnitudo ſolida leuior humido.</s>
            <s xml:space="preserve">]_ Ea uerba,
              <lb/>
              <anchor type="note" xlink:label="note-0025-01a" xlink:href="note-0025-01"/>
            leuior bumido, nos addidimus, quæ in translatione non erant; </s>
            <s xml:space="preserve">quo-
              <lb/>
            niam de eiuſmodi magnitudinibus in bac propoſitione agitur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">A</note>
          </div>
          <p>
            <s xml:space="preserve">In humidũ demittatur, ita ut baſis portionis nõ tangat hu
              <lb/>
              <anchor type="note" xlink:label="note-0025-02a" xlink:href="note-0025-02"/>
            midum.</s>
            <s xml:space="preserve">] _Hoc est in humidum ita demitt atur, ut baſis ſurſum ſpe_
              <lb/>
            _ctet; </s>
            <s xml:space="preserve">uertex autem deorſum. </s>
            <s xml:space="preserve">quod quidem opponitur ei, quod in ſe-_
              <lb/>
            _quenti dixit._ </s>
            <s xml:space="preserve">In humidum demittatur, ita ut baſis tota ſit in
              <lb/>
            humido. </s>
            <s xml:space="preserve">_His enim uerbis ſignificat portionem oppoſito modo in_
              <lb/>
            _humidum demitti, ut ſcilicet uertex ſurſum; </s>
            <s xml:space="preserve">baſis autem deorſum_
              <lb/>
            _uergat. </s>
            <s xml:space="preserve">eodem dicendi modo frequenter uſus est in ſecundo libro; </s>
            <s xml:space="preserve">in_
              <lb/>
            _quo de portionibus conoidis rectangulitractatur._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0025-02" xlink:href="note-0025-02a" xml:space="preserve">B</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Quoniã igitur unaquæq; </s>
            <s xml:space="preserve">ſphæræ portio axẽ habet in linea,_
              <lb/>
              <anchor type="note" xlink:label="note-0025-03a" xlink:href="note-0025-03"/>
            _quæ à cẽtro ſphæræ ad eius baſim perpẽdicularis ducitur.</s>
            <s xml:space="preserve">]_
              <lb/>
            Iungatur enim b c, & </s>
            <s xml:space="preserve">k l ſecet circunferentiam a b c d in puncto g;
              <lb/>
            </s>
            <s xml:space="preserve">lineam uero rectam b c in m. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam duo circuli a b c d, e f b
              <lb/>
            ſecant ſe ſe in punctis b c; </s>
            <s xml:space="preserve">recta linea, quæ ipſorum centra coniun-
              <lb/>
            git, uidelicet k l lineam b c bifariam, & </s>
            <s xml:space="preserve">ad angulos rectos ſecat: </s>
            <s xml:space="preserve">
              <lb/>
            ut in commentarij s in Ptolemæi planiſpbærium oſtendimus. </s>
            <s xml:space="preserve">quare
              <lb/>
            portionis circuli b n c diameter eſt m n; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portionis b g c diame-
              <lb/>
              <anchor type="note" xlink:label="note-0025-04a" xlink:href="note-0025-04"/>
            ter m g: </s>
            <s xml:space="preserve">nam rectæ lineæ, quæ ipſi b c æquidistantes ex utraque
              <lb/>
            parte ducuntur, cum linea n g rectos angulos faciunt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco ab
              <lb/>
              <anchor type="note" xlink:label="note-0025-05a" xlink:href="note-0025-05"/>
            ipſa bifariam ſecantur. </s>
            <s xml:space="preserve">portionis igitur ſpbæræ b n c axis eſt n m;
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portionis b g c axis m g. </s>
            <s xml:space="preserve">ex quo ſequitur, portionis in bumido
              <lb/>
            demerſæ axem eſſe in linea k l; </s>
            <s xml:space="preserve">ipſam ſcilicet n g. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum grauita-
              <lb/>
            tis centrum cuius libet ſpbæræ portionis ſit in axe; </s>
            <s xml:space="preserve">quod nos in libro</s>
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