Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < (30) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div120" type="section" level="1" n="40">
          <p>
            <s xml:id="echoid-s1732" xml:space="preserve">
              <pb o="30" file="0071" n="71" rhead="DE IIS QVAE VEH. IN AQVA."/>
            eadem ratione oſtẽdetur p y ipſius y f dupla. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">Itaque quo
              <lb/>
            niam d s ſeſquialtera eſt ipſius _k_ r; </s>
            <s xml:id="echoid-s1734" xml:space="preserve">erit b s exceſſus, quo
              <lb/>
            axis eſt maior, quàm ſeſquialter eius, quæ uſque ad axem.
              <lb/>
            </s>
            <s xml:id="echoid-s1735" xml:space="preserve">Si igitur portio ad humidũ in grauitate eã habet propor-
              <lb/>
            tionem, quam quadratum, quod fit à linea b ſ ad quadra-
              <lb/>
            tum, quod à b d, aut maiorem; </s>
            <s xml:id="echoid-s1736" xml:space="preserve">in hnmidum demiſſa, ita
              <lb/>
            ut baſis ipſius non contingat humidum, recta conſiſtet. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">de
              <lb/>
            monſtratum eſt enim ſuperius, portionem, cuius axis eſt
              <lb/>
              <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">R</note>
            maior, quàm ſeſquiaiter eius, quæ uſque ad axem, ſi ad hu-
              <lb/>
            midum in grauitate non minorem proportionem habeat,
              <lb/>
            quàm quadratum, quod fit ab exceſſu, quo axis maior eſt,
              <lb/>
            quam ſeſquialter eius, quæ uſque ad axem, ad quadratum,
              <lb/>
            quod ab axe; </s>
            <s xml:id="echoid-s1738" xml:space="preserve">demiſſam in humidum, ita ut dictum eſt, re-
              <lb/>
            ctam conſiſtere.</s>
            <s xml:id="echoid-s1739" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div123" type="section" level="1" n="41">
          <head xml:id="echoid-head46" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s1740" xml:space="preserve">_
              <emph style="sc">Qvae</emph>
            _ hac decima propoſitione continentur, Archimedes in
              <lb/>
            quinque partes diſſecuit, & </s>
            <s xml:id="echoid-s1741" xml:space="preserve">ſingulas ſeorſum demonſtrauit.</s>
            <s xml:id="echoid-s1742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1743" xml:space="preserve">Nonnunquam quidem recta conſiſtat.</s>
            <s xml:id="echoid-s1744" xml:space="preserve">] _Hæc eſt prima_
              <lb/>
              <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">A</note>
            _pars, cuius demonstr ationem ſtatim ſubiungit._</s>
            <s xml:id="echoid-s1745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1746" xml:space="preserve">Etinterdum adeo inclinata, ut baſis ipſius in uno pun-
              <lb/>
              <note position="right" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">B</note>
            cto contingat ſuperficiem humidi; </s>
            <s xml:id="echoid-s1747" xml:space="preserve">idq; </s>
            <s xml:id="echoid-s1748" xml:space="preserve">in duabus diſpoſi-
              <lb/>
            tionibus.</s>
            <s xml:id="echoid-s1749" xml:space="preserve">] _Demonſtratum eſt illud in tertia parte._</s>
            <s xml:id="echoid-s1750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1751" xml:space="preserve">Interdum ita, ut baſis in humidum magis demergatur.</s>
            <s xml:id="echoid-s1752" xml:space="preserve">]
              <lb/>
              <note position="right" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">C</note>
            _Pertinet id ad quartam partem._</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1754" xml:space="preserve">Interdum uero ita, ut ſuperficiem humidi nullo modo
              <lb/>
              <note position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve">D</note>
            contingat.</s>
            <s xml:id="echoid-s1755" xml:space="preserve">] _Hoc duobus item modis fit, quorum unus in ſecunda,_
              <lb/>
            _alter in quarta parte explicatur._</s>
            <s xml:id="echoid-s1756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">Secundum proportionem, quam habet ad humidum in
              <lb/>
              <note position="right" xlink:label="note-0071-06" xlink:href="note-0071-06a" xml:space="preserve">E</note>
            grauitate.</s>
            <s xml:id="echoid-s1758" xml:space="preserve">] _In translatione ita legebatur, quam autem proportio_
              <lb/>
            _nem habet ad humidum in grauitate._</s>
            <s xml:id="echoid-s1759" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1760" xml:space="preserve">_Conſtat igitur k c maiorem eſſe, quàm quæ uſque ad_
              <lb/>
              <note position="right" xlink:label="note-0071-07" xlink:href="note-0071-07a" xml:space="preserve">F</note>
            _axem.</s>
            <s xml:id="echoid-s1761" xml:space="preserve">]_ Nam cum b d ad k c eandem habeat proportionem, quam</s>
          </p>
        </div>
      </text>
    </echo>