Archimedes, Archimedis De insidentibvs aqvae

Page concordance

< >
Scan Original
41 13
42
43 14
44
45 15
46
47 16
48
49
50
< >
page |< < of 51 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div40" type="section" level="1" n="28">
          <p style="it">
            <s xml:id="echoid-s774" xml:space="preserve">
              <pb file="0044" n="44" rhead="DE INSIDENTIBVS AQVAE"/>
            ſcriptum eſt, et alia eadẽ diſponãtur, demõſtrabitur autẽ rurſum ꝙ t,
              <lb/>
            m, æquales exiſiens ipſi, f, i, & </s>
            <s xml:id="echoid-s775" xml:space="preserve">portiones a, f, q, a, b, Z, æquales inuicem
              <lb/>
            & </s>
            <s xml:id="echoid-s776" xml:space="preserve">quoniam in portionibus æqualibus, & </s>
            <s xml:id="echoid-s777" xml:space="preserve">ſimilib apol a, b, g, ſunt pro-
              <lb/>
            ductæ, quæ a, q, a, Z, æquales portiones auferentes æquales faciunt an-
              <lb/>
            gulos ad dyametros. </s>
            <s xml:id="echoid-s778" xml:space="preserve">portionum igitur a, h, b, Z, a, f, q, qui apud ſignal,
              <lb/>
            ***, anguli ſunt æquales. </s>
            <s xml:id="echoid-s779" xml:space="preserve">& </s>
            <s xml:id="echoid-s780" xml:space="preserve">quæ b, s, recta ipſi b, c, æqualis & </s>
            <s xml:id="echoid-s781" xml:space="preserve">quæ s,
              <lb/>
            r, ipſi r, c. </s>
            <s xml:id="echoid-s782" xml:space="preserve">Et quæ h, a, ipſi f, h, & </s>
            <s xml:id="echoid-s783" xml:space="preserve">quæ a, t, ipſi m, i. </s>
            <s xml:id="echoid-s784" xml:space="preserve">Et quoniam dupla
              <lb/>
            est, quæ f, x, ipſiy, i. </s>
            <s xml:id="echoid-s785" xml:space="preserve">Manifeſtum quòd quæ h, a, eſt maior, quàm dupla
              <lb/>
            ipſius a, t. </s>
            <s xml:id="echoid-s786" xml:space="preserve">Sit igitur quæ h, a, ipſi l, t, dupla. </s>
            <s xml:id="echoid-s787" xml:space="preserve">Rurſum autem ex hijs pa
              <lb/>
            lam quòd non manet portio ſed inclinabitur ex parte a, quoniam ſup
              <lb/>
            ponebatur portio, ſecundum unum ſignum tangere humidum palam
              <lb/>
            quòd ſecundum ampliorẽ locum baſis ab humido comprehendetur.</s>
            <s xml:id="echoid-s788" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s789" xml:space="preserve">HAbeat etiam rurſum portio ad humidum in grauitate propor-
              <lb/>
            tionem minorẽ ea, quam habet tetragonum, quod ab n, o, ad id q đ
              <lb/>
            a, b, d. </s>
            <s xml:id="echoid-s790" xml:space="preserve">Quam autem proportionem habet portio ad humidum in gra-
              <lb/>
            uitate, hanc habeat tetragonum, quod a, x, minorem autem eſt, quæ x,
              <lb/>
            quàm o, n. </s>
            <s xml:id="echoid-s791" xml:space="preserve">Rurſum igitur in aptetur quædam intermedia portionum
              <lb/>
            a, m, d, apol quæ p, i, æquedistanter ipſi b, d, producta æqualis ipſi x.
              <lb/>
            </s>
            <s xml:id="echoid-s792" xml:space="preserve">Secet autem ipſa intermedia coniſectione penes y, ipſam autem x, r,
              <lb/>
            rectam penes h, demonſtrabitur, autem quæ p, y, dupla ipſius y, i, ſicut
              <lb/>
            demonſtrata eſt, quæ, g, o, ipſius g, h, ducatur autem & </s>
            <s xml:id="echoid-s793" xml:space="preserve">quæ quidem
              <lb/>
            p, ***, contingens ſectionem apol ſecundum p, quæ autem p, e, perpen-
              <lb/>
            dicularis ſuper b, d, & </s>
            <s xml:id="echoid-s794" xml:space="preserve">a, i, copulata ducatur ad q. </s>
            <s xml:id="echoid-s795" xml:space="preserve">Erit autem quæ
              <lb/>
              <figure xlink:label="fig-0044-01" xlink:href="fig-0044-01a" number="34">
                <image file="0044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0044-01"/>
              </figure>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum