Valerio, Luca, De centro gravitatis solidorvm libri tres

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
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>