Valerio, Luca, De centro gravitatis solidorum, 1604

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/028.jpg" pagenum="20"/>
              liter igitur vt ante oſtenderemus, vnamquamque qua­
                <lb/>
              tuor pyramidum, quarum communis vertex S, baſes au­
                <lb/>
              tem triangula, quæ ſunt circa pyramidem ABCD, eſse
                <lb/>
              quartam partem pyramidis ABCD. </s>
              <s>Siue igitur pun­
                <lb/>
              ctum S, cadat intra vnam priorum quatuor pyrami­
                <lb/>
              dum, ſiue in earum aliquo latere, ſeu triangulo; neceſ­
                <lb/>
              ſario erit pars æquali toti; tam enim tota vna pyramis
                <lb/>
              quatuor priorum, quarum communis vertex F, quàm eius
                <lb/>
              pars, vna quatuor pyramidum poſteriorum, quarum com­
                <lb/>
              munis vertex S, erit eiuſdem ABCD, pyramidis pars
                <lb/>
              quarta. </s>
              <s>Ex abſurdo igitur non in alio puncto à puncto F
                <lb/>
              ſecabunt ſe in eaſdem rationes quatuor rectæ, quæ ab angu
                <lb/>
              lis ad oppoſita triangula pyramidis ABCD, ducantur.
                <lb/>
              </s>
              <s>Manifeſtum eſt igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO IX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis pyramis baſim habens triangulam di­
                <lb/>
              uiditur in quatuor pyra mides æquales, & ſimiles
                <lb/>
              inter ſe, & toti, & vnum octaedrum totius pyrami­
                <lb/>
              dis dimidium, ip ſi que concentricum. </s>
            </p>
            <p type="main">
              <s>Sit pyramis ABCD, cuius baſis triangulum ABC,
                <lb/>
              ſectisque omnibus lateribus bifariam, iungantur rectæ FG,
                <lb/>
              GH, HF, FK, KL, LM, M
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              , KH, HM, GL, LF.
                <lb/>
              </s>
              <s>Dico quatuor pyramides DKLM, LFBG, KHFA,
                <lb/>
              MHGC, æquales eſse, & ſimiles inter ſe, & toti pyrami­
                <lb/>
              di ABCD: octaedrum autem eſse LFGM
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              H, & di­
                <lb/>
              midium pyramidis ABCD, ipſique concentricum. </s>
              <s>Du­
                <lb/>
              cantur enim rectæ DNH, BQH, LN: & poſita BE, du
                <lb/>
              pla ipſius BH, iungatur DOC, in triangulo DBH, &
                <lb/>
              ponatur DP, ipſius PE, tripla, & connectantur rectæ LP,
                <lb/>
              PH. </s>
              <s>Quoniam igitur E, eſt centrum trianguli ABC, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum