Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
< >
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>
Impressum