Archimedes, Archimedis De insidentibvs aqvae

Table of contents

< >
< >
page |< < of 51 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div38" type="section" level="1" n="27">
          <pb file="0034" n="34" rhead="DE INSIDENTIBVS AQVAE"/>
          <figure number="27">
            <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0034-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s540" xml:space="preserve">ES to portio, qualis dicta _est_, & </s>
            <s xml:id="echoid-s541" xml:space="preserve">ponatur, quæ d, b, æqualis axi por-
              <lb/>
            tionis, & </s>
            <s xml:id="echoid-s542" xml:space="preserve">quæ quidem b, k, ſit dupla ipſius K, d. </s>
            <s xml:id="echoid-s543" xml:space="preserve">Quæ autem K, r,
              <lb/>
            æqualis ei, quæ uſque ad axem, quę autem c, b, hemiolia ipſius b, r.
              <lb/>
            </s>
            <s xml:id="echoid-s544" xml:space="preserve">Quam autem proportionem habet portio ad bumidum in grauitate,
              <lb/>
            banc habeat exceſſus, quo excedit tetragonum, quod a, b, d, tetragonum
              <lb/>
            quod a, b, f, q, ad tetragonum, quod a, b, d, ſit autem quæ f, dupla ipſius q. </s>
            <s xml:id="echoid-s545" xml:space="preserve">
              <lb/>
            Palam igitur, quòd exceßus, quo excidit tetragonum, quod a, b, d, tetra-
              <lb/>
            gonum, quod a, b, c, ad tetragonum, quod a, b, d, quo axis portionis eſt ma
              <lb/>
            ior, quàm hemiolius eius, quæ uſque ad axem minor eſt in maiori ergo te
              <lb/>
            tragonum, quod a, b, d, excedit id, quod a, b, f, q, quàm tetragonum quod
              <lb/>
            a, b, d, excedat tetragonum, quod a, b, c. </s>
            <s xml:id="echoid-s546" xml:space="preserve">Quare quæ f, q, eſt minor, quàm
              <lb/>
            b, c. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s548" xml:space="preserve">quæ f, quàm b, r. </s>
            <s xml:id="echoid-s549" xml:space="preserve">Sit igitur ipſi f, æqualis, quæ r, x, & </s>
            <s xml:id="echoid-s550" xml:space="preserve">quæ x,
              <lb/>
            e, recta ducatur ſuper b, d, potens medietatem eius, quòd continetur ſub
              <lb/>
            K, r, x, b, dico quòd portio demißa in bumidũ ita, ut baſis ipſius tota ſit
              <lb/>
            in humido conſistat, ita ut axis ipſius ad ſuperficiem humidt
              <unsure/>
            faciat angu
              <lb/>
            lum æqualem angulo b. </s>
            <s xml:id="echoid-s551" xml:space="preserve">Demittatur quidem enim portio in humidum,
              <lb/>
            ut dictum eſt & </s>
            <s xml:id="echoid-s552" xml:space="preserve">non faciat axis ad ſuperficiem humidi angulum æqua-
              <lb/>
            lem b, ſed maiorem primo. </s>
            <s xml:id="echoid-s553" xml:space="preserve">Secta autem ipſa plano recto ad ſuperficiem
              <lb/>
            bumidi porti
              <unsure/>
            onis ſectio ſit, quę apol. </s>
            <s xml:id="echoid-s554" xml:space="preserve">rectanguli coniſectio ſuperficiei au-
              <lb/>
            tem humidi, quæ c, i, axis autem portionis, & </s>
            <s xml:id="echoid-s555" xml:space="preserve">dyameter ſit quę n, o, & </s>
            <s xml:id="echoid-s556" xml:space="preserve">
              <lb/>
            ſit ſecta ſecundum ***, t, ut & </s>
            <s xml:id="echoid-s557" xml:space="preserve">prius ducatur autem quæ quidem y, p,
              <lb/>
            æquedistanter ipſi c, i, contingens ſectionem ſecundum p. </s>
            <s xml:id="echoid-s558" xml:space="preserve">Quæ autem m,
              <lb/>
            p, æquediſtanter ipſi n, o. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Quæ uero p, s, perpendicularis ſuper axé, quo-
              <lb/>
            niam egit axis portionis ad ſuperficiem bumidi facit angulum maiorem
              <lb/>
            angulo b. </s>
            <s xml:id="echoid-s560" xml:space="preserve">Erit utique & </s>
            <s xml:id="echoid-s561" xml:space="preserve">angulus, qui ſub s, y, p, maior angulo b, tetrago
              <lb/>
            num ergo quod a, p, s, ad tetragonum quod a, b, s, y, habet proportionem
              <lb/>
            matorem, quàm tetragonum, quod a, x, e, ad tetragonum, quod a, x, b.</s>
            <s xml:id="echoid-s562" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum