Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
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
< >
page |< < (37) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div157" type="section" level="1" n="51">
          <pb o="37" file="0085" n="85" rhead="DE IIS QVAE VEH. IN AQVA."/>
        </div>
        <div xml:id="echoid-div158" type="section" level="1" n="52">
          <head xml:id="echoid-head57" xml:space="preserve">DEMONSTRATIO SECVNDAE PARTIS.</head>
          <p>
            <s xml:id="echoid-s2176" xml:space="preserve">ITAQVE primum habeat portio ad humidum in
              <lb/>
            grauitate proportionem quidem maiorem, quàm qua dra
              <lb/>
            tum x o ad quadratum b d; </s>
            <s xml:id="echoid-s2177" xml:space="preserve">minorem uero, quàm quadra
              <lb/>
            tum, quod fit ab exceſſu, quo axis eſt maior, quàm ſeſquial-
              <lb/>
            ter eius, quæ uſque ad axem, ad quadratum b d: </s>
            <s xml:id="echoid-s2178" xml:space="preserve">& </s>
            <s xml:id="echoid-s2179" xml:space="preserve">quam
              <lb/>
            proportionem habet portio ad humidum in grauitate, eã
              <lb/>
            habeat quadratum, quod fit à linea ψ ad quadratum b d:
              <lb/>
            </s>
            <s xml:id="echoid-s2180" xml:space="preserve">erit ψ maior quidem, quàm x o, minor uero, quàm exceſ-
              <lb/>
              <note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">C</note>
            ſus, quo axis eſt maior, quàm ſeſquialter eius, quæ uſque ad
              <lb/>
            axem. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">aptetur quædam recta linea m n conicis ſectioni-
              <lb/>
            bus a m q l,
              <lb/>
              <figure xlink:label="fig-0085-01" xlink:href="fig-0085-01a" number="52">
                <image file="0085-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0085-01"/>
              </figure>
            a x d interiecta,
              <lb/>
            ac media, quæ li
              <lb/>
            neæ ψ ſit æqua-
              <lb/>
            lis; </s>
            <s xml:id="echoid-s2182" xml:space="preserve">ſecetq; </s>
            <s xml:id="echoid-s2183" xml:space="preserve">reli-
              <lb/>
            quã coni ſectio
              <lb/>
            nem in pun cto
              <lb/>
            h; </s>
            <s xml:id="echoid-s2184" xml:space="preserve">& </s>
            <s xml:id="echoid-s2185" xml:space="preserve">rectam li-
              <lb/>
            neam r g in u.
              <lb/>
            </s>
            <s xml:id="echoid-s2186" xml:space="preserve">demõſtrabitur
              <lb/>
              <note position="left" xlink:label="note-0085-02" xlink:href="note-0085-02a" xml:space="preserve">D</note>
            m h dupla ip-
              <lb/>
            ſius h n, ſicuti
              <lb/>
            demonſtratum
              <lb/>
            eſt o g ipſius g x
              <lb/>
            duplam eſſe. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">à
              <lb/>
            puncto autẽ m
              <lb/>
            ducatur m y contingens ſectionem a m q l in m: </s>
            <s xml:id="echoid-s2188" xml:space="preserve">& </s>
            <s xml:id="echoid-s2189" xml:space="preserve">m c a d
              <lb/>
            b d perpendicularis. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">poſtea ducta a n, & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">producta ad q li
              <lb/>
            neæ a n, n q inter ſe æquales erunt. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">quoniã enim in ſimi-
              <lb/>
              <note position="right" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve">E</note>
            libus portionibus a m q l, a x d ductæ ſunt à baſibus ad
              <lb/>
            portiones lineæ a q, a n, quæ æquales angulos continent
              <lb/>
            cum ipſis baſibus, eandem proportionem habebit q a ad
              <lb/>
            an, quam la ad a d. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">æqualis eſt ergo a n ipſi n q; </s>
            <s xml:id="echoid-s2194" xml:space="preserve">& </s>
            <s xml:id="echoid-s2195" xml:space="preserve">a q
              <lb/>
              <note position="right" xlink:label="note-0085-04" xlink:href="note-0085-04a" xml:space="preserve">F</note>
            </s>
          </p>
        </div>
      </text>
    </echo>