Archimedes, Archimedis De insidentibvs aqvae

List of thumbnails

< >
11
11 (4) 		12
12
13
13 (5) 		14
14
15
15 (6) 		16
16
17
17 		18
18
19
19 (2) 		20
20
< >
page |< < (8) of 51 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div36" type="section" level="1" n="26">
          <p style="it">
            <s xml:id="echoid-s463" xml:space="preserve">
              <pb o="8" file="0031" n="31" rhead="LIBER II."/>
            axem. </s>
            <s xml:id="echoid-s464" xml:space="preserve">Quæ ergo f, q, erit minor ipſa b, c. </s>
            <s xml:id="echoid-s465" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s466" xml:space="preserve">quàm f, minor ipſæ
              <lb/>
            b, r. </s>
            <s xml:id="echoid-s467" xml:space="preserve">Sit autem ipſi f, æqualis, quæ r, x, & </s>
            <s xml:id="echoid-s468" xml:space="preserve">ſuper ipſa b, d, recta ducatur,
              <lb/>
            quæ x, e, quæ poſſit dimidium eius, quod ſub K, r, x, & </s>
            <s xml:id="echoid-s469" xml:space="preserve">copuletur quæ b, e,
              <lb/>
            demonſtrandum quòd portio dimißa in bumidum, vt dictum est, conſi-
              <lb/>
            ſtet inclinata ita, ut axis ad ſuperficiem bumidi faciat angulum æqualé
              <lb/>
            angulo e, b, x, demonstratur enim aliqua portio in bumidum, & </s>
            <s xml:id="echoid-s470" xml:space="preserve">baſis ip
              <lb/>
            ſius non tang at ſuperficiem bumidi. </s>
            <s xml:id="echoid-s471" xml:space="preserve">Et ſi poſſibile eſt axis ipſius ad ſu-
              <lb/>
            perficiem bumidi non faciat angulum æqualem angulo b, ſed primo ma-
              <lb/>
            iorem: </s>
            <s xml:id="echoid-s472" xml:space="preserve">ſecta autem portione per axem plano recto ad ſuperficiem bu-
              <lb/>
            midi. </s>
            <s xml:id="echoid-s473" xml:space="preserve">Sectio erit quàm apol. </s>
            <s xml:id="echoid-s474" xml:space="preserve">rectanguli coni ſectio. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Superficies autem
              <lb/>
            bumidi, quæ x, s. </s>
            <s xml:id="echoid-s476" xml:space="preserve">Axis autem, & </s>
            <s xml:id="echoid-s477" xml:space="preserve">dyameter portionis, quæ n, o, duca-
              <lb/>
            tur autem, & </s>
            <s xml:id="echoid-s478" xml:space="preserve">quæ quidem p, y, æquediſtanter ipſi x, s, contingens ſectio
              <lb/>
            nem apol. </s>
            <s xml:id="echoid-s479" xml:space="preserve">ſecundum p. </s>
            <s xml:id="echoid-s480" xml:space="preserve">Quæ autem p, m, æquediſtanter ipſi n, o. </s>
            <s xml:id="echoid-s481" xml:space="preserve">Quæ au
              <lb/>
            tem p, i, perpendicularis, ſuper n, o, & </s>
            <s xml:id="echoid-s482" xml:space="preserve">quæ quidem b, r, ſit æqualis ipſi i,
              <lb/>
            ***. </s>
            <s xml:id="echoid-s483" xml:space="preserve">Quæ autem r, K, ipſin, o, & </s>
            <s xml:id="echoid-s484" xml:space="preserve">quæ ***, b, rectam ſuper axem.
              <lb/>
            </s>
            <s xml:id="echoid-s485" xml:space="preserve">
              <figure xlink:label="fig-0031-01" xlink:href="fig-0031-01a" number="25">
                <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0031-01"/>
              </figure>
            Quoniam igitur ſupponitur axis portionis ad ſuperficiem bumidi facere
              <lb/>
            angulum maiorem angulo b, palam quòd angulo p, i, n, angulus, qui ad
              <lb/>
            p, i, m, _est_ maior angulo b, maiorem igitur proportionem habet tetrago
              <lb/>
            num, quod a, p, i, ad tetragonum quod ab i, quàm tetra-
              <lb/>
            gonum, quod ab e, x, ad tetragonum quòd a, x, o Sed quam quidem pro-
              <lb/>
            portionem habet tetragonum, quod a, p, i, ad id, quod ab i.
              <lb/>
            </s>
            <s xml:id="echoid-s486" xml:space="preserve">hanc habet quæ K, r, ad i. </s>
            <s xml:id="echoid-s487" xml:space="preserve">Quam autem proportionem habet te
              <lb/>
            tragonum, quod ab e, x, ad tetragonum a, x, b, hanc habet medietas ip-
              <lb/>
            ſius K, r, ad x, b, maiorem ergo proportionem habet, quàm K, r, ad
              <lb/>
            i, quàm medietas ipſius k, r, ad x, b. </s>
            <s xml:id="echoid-s488" xml:space="preserve">Minor ergo eſt, quàm dupla, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum