Valerio, Luca, De centro gravitatis solidorvm libri tres
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/079.jpg" pagenum="71"/>
              vt eſt HN, ad NG, ita fiat KM, ad ML, & GM, iun­
                <lb/>
              gatur: & vt eſt GO, ad ON, ita fiat GP, ad PM, & iun
                <lb/>
              gantur MN, OP, FG, GD, GE. </s>
              <s>Quoniam igitur re
                <lb/>
              cta KL, ſecat trapezij BCFE, latera parallela bifariam
                <lb/>
              in punctis K,L, & eſt vt HN, ad NG, hoc eſt vt duplum
                <lb/>
              lateris BC, vna cum latere EF, ad duplum lateris EF, vna
                <lb/>
              cum latere BC, ita KM, ad ML; erit punctum M, cen­
                <lb/>
              trum grauitatis trapezij BCFE, & pyramidis GBCFE,
                <lb/>
              axis GM. </s>
              <s>Et quoniam vt GO, ad ON, ita eſt GP, ad
                <lb/>
              PM, atque ideo GP, tripla ipſius PM, erit punctum P,
                <lb/>
              centrum grauitatis pyramidis GBCFE, atque ideo in
                <lb/>
              linea OP. </s>
              <s>Rurſus quoniam angulus ACB; æqualis eſt
                <lb/>
              angulo DFK: & vt AC, ad CK, ita eſt DF, ad FK:
                <lb/>
              eſt autem DF, parallela ipſi AC, & FK, ipſi CL; erit
                <lb/>
              reliqua DK, reliquæ AL, parallela; vnum igitur planum
                <lb/>
              eſt, ADKL, in quo iacet triangulum GMN; cum igitur
                <lb/>
              ſit parallela KH, ipſi GL, vtque HN, ad NG, ita
                <lb/>
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              M, ad ML; erit MN, ipſi LG, parallela: ſed OP, eſt
                <lb/>
              parallela ipſi MN; ſecant enim latera trianguli GMN,
                <lb/>
              in eaſdem rationes; igitur OP, erit LG, parallela. </s>
              <s>Simi­
                <lb/>
              liter ex puncto O, ad axes duarum pyramidum GABED,
                <lb/>
              GACFD, duæ aliæ rectæ lineæ ducerentur, quas & cen­
                <lb/>
              tra grauitatis pyramidum habere, & parallelas rectis GQ,
                <lb/>
              GR, alteram alteri eſse oſtenderemus, ſicut oſtendimus
                <lb/>
              OP, habentem centrum grauitatis pyramidis GBCFE,
                <lb/>
              ipſi GL, parallelam; ſed tres rectæ GL, GQ, GR, ſunt
                <lb/>
              in eodem plano trianguli nimirum ABC; tres igitur præ­
                <lb/>
              dictæ parallelæ, quæ ex puncto O, atque ideo trium præ­
                <lb/>
              dictarum pyramidum centra grauitatis erunt in eodem pla­
                <lb/>
              no, per punctum O, & trianguli ABC, parallelo. </s>
              <s>Quo­
                <lb/>
              niam igitur fruſti ABCDE, centrum grauitatis eſt in axe
                <lb/>
              GH; (manifeſtum hoc autem ex duobus centris grauitatis
                <lb/>
              pyramidis, cuius eſt prædictum fruſtum, & ablatæ, quæ
                <lb/>
              centra grauitatis ſunt in axe, cuius ſegmentum eſt axis </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum