Valerio, Luca, De centro gravitatis solidorvm libri tres

List of thumbnails

< >
31
31
32
32
33
33
34
34
35
35
36
36
37
37
38
38
39
39
40
40
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/031.jpg" pagenum="23"/>
              per conuerſionem rationis, vt NL ad LO, ita QH, ad
                <lb/>
              HE: & permutando, vt LN ad QH, ita LO ad EH:
                <lb/>
              ſed LN, oſtenſa eſt æqualis QH; æqualis igitur LO,
                <lb/>
              erit ipſi EH; ſed & OP, eſt æqualis ipſi PE, vt oſten­
                <lb/>
              dimus: duæ igitur LO, OP, duabus HE, EP æqua­
                <lb/>
              les erunt altera alteri, & angulos æquales continent LOP,
                <lb/>
              PEH, parallelis exiſtentibus LN, BH ſectionibus tri­
                <lb/>
              anguli DBH, quæ fiunt à duobus planis parallelis; ba­
                <lb/>
              ſis igitur LP, trianguli LOP, æqualis eſt baſi PH,
                <lb/>
              trianguli PEH, & angulus OPL, angulo EPH in pla­
                <lb/>
              no trianguli DBH, in quo DPE, eſt vna recta linea;
                <lb/>
              igitur LPH, erit vna recta linea, quæ cum ſit axis octa­
                <lb/>
              edri LKMGFH, & ſectus ſit in puncto P, bifariam,
                <lb/>
              erit punctum P, centrum octaedri LKMGEH. ſed &
                <lb/>
              centrum pyramidis ABCD. </s>
              <s>Manifeſtum eſt igitur pro­
                <lb/>
              poſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO X.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omne fruſtum pyramidis triangulam baſim
                <lb/>
              habentis, ſiue coni, ad pyramidem, vel conum, cu­
                <lb/>
              ius baſis eſt eadem, quæ maior baſis fruſti, & ea­
                <lb/>
              dem altitudo, eam habet proportionem, quam duo
                <lb/>
              latera homologa, vel duæ diametri baſium ipſius
                <lb/>
              fruſti, vnà cum tertia minori proportionali ad
                <lb/>
              prædicta duo latera, vel diametros; ad maioris ba­
                <lb/>
              ſis latus, vel diametrum. </s>
              <s>Ad priſma autem, vel
                <lb/>
              cylindrum, cuius eadem eſt baſis, quæ maior baſis
                <lb/>
              fruſti, & eadem altitudo; vt tres prædictæ deìn­
                <lb/>
              ceps proportionales ſimul, ad triplam lateris, vel
                <lb/>
              diametri maioris baſis. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>