Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="34">
          <p>
            <s xml:space="preserve">
              <pb file="0054" n="54" rhead="ARCHIMEDIS"/>
            modo hum idi ſuperficiem continget.</s>
            <s xml:space="preserve">] _In translatione le-_
              <lb/>
            _gebatur ut baſis ipſius non tangat ſuperficiem humidi ſecundum_
              <lb/>
            _unum ſignum. </s>
            <s xml:space="preserve">nos autem ita uertere maluimus, & </s>
            <s xml:space="preserve">hic & </s>
            <s xml:space="preserve">in ijs,_
              <lb/>
            _quæ ſequuntur, quoniam græci οὐδὲ \~εις, οὐδὲ ἓν, pro οὐ δεὶς, &_</s>
            <s xml:space="preserve">
              <lb/>
            _οὐδε ν frequenter utútur. </s>
            <s xml:space="preserve">ut οὐδ ε ςιν οὐ δεὶς, nullus eſt: </s>
            <s xml:space="preserve">οὐ \’δ ὑφ
              <unsure/>
            ἑ νὸς,_
              <lb/>
            _ànullo & </s>
            <s xml:space="preserve">alia eiuſmodi._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">E</note>
          </div>
        </div>
        <div type="section" level="1" n="35">
          <head xml:space="preserve">PROPOSITIO VII.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem quidem
              <lb/>
            quàm ſeſquialtérum eius, quæ uſque ad axem;
              <lb/>
            </s>
            <s xml:space="preserve">minorem uero, quàm ut ad eam, quæ uſque ad
              <lb/>
            axem proportionem habeat, quam quindecim
              <lb/>
            ad quatuor: </s>
            <s xml:space="preserve">in humidum demiſſa, adeo ut baſis
              <lb/>
            ipſius tota ſitin humido; </s>
            <s xml:space="preserve">nunquam conſiſtet ita,
              <lb/>
            ut baſis contingat humidi ſuperficiem: </s>
            <s xml:space="preserve">ſed ut to-
              <lb/>
            ta in humido ſit, & </s>
            <s xml:space="preserve">nullo modo eius ſuperficiem
              <lb/>
            contingat.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demittatur in humidũ,
              <lb/>
            ut diximus, adeo ut baſis ipſius in uno puncto contingat
              <lb/>
            humidi ſuperficiem. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere ip-
              <lb/>
            ſam: </s>
            <s xml:space="preserve">ſed reuolui ita ut baſis fuperficiem humidi nullo mo-
              <lb/>
            do contingat. </s>
            <s xml:space="preserve">Secta enim ipſa plano per axem, recto ad ſu
              <lb/>
            perficiem humidi, ſectio ſit a p o l rectanguli coni ſectio:
              <lb/>
            </s>
            <s xml:space="preserve">ſuperficiei humidi ſectio ſit s 1: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectio-
              <lb/>
            nis diameter p f: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">p f in r quidem ita ut r p ſit
              <lb/>
            dupla ipſius r f; </s>
            <s xml:space="preserve">in ω autem ut p f ad r ω proportionem
              <lb/>
            habeat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ω k ipſi p f ad re-
              <lb/>
            ctos angulos ducatur erit r ω minor, quàm quæ uſque ad
              <lb/>
            axem. </s>
            <s xml:space="preserve">Itaque accipiatur ei, quæ uſque ad axem æqualis rh:</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>