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="043/01/029.jpg" pagenum="21"/>
              erit axis DE, pyramidis ABCD, cuius axis ſegmentum
                <lb/>
              DP eſt triplum ipſius PE: igitur P centrum erit pyra­
                <lb/>
              midis ABCD. </s>
              <s>Et quoniam tres rectæ FK, KH, HF,
                <lb/>
              ſunt parallelæ tribus BD, DC, CB, pro vt inter ſe reſpon
                <lb/>
              dent, vt KH, ipſi LG, quoniam vtraque lateri DC, ob
                <lb/>
              latera triangulorum ſecta proportionaliter in punctis K, H,
                <lb/>
              L, G: & ſic de reliquis; erit pyramis A
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              FH, ſimilis toti
                <lb/>
              pyramidi ABCD. </s>
              <s>Similiter vnaquæque trium aliarum
                <lb/>
              pyramidum abſciſſarum, videlicet FLBG, GHMC,
                <lb/>
              KDLM, ſimilis erit pyramidi ABCD, atque ideo in­
                <lb/>
              ter ſe ſimiles. </s>
              <s>Rurſus,
                <lb/>
              quoniam pyramidum
                <lb/>
              ſimilium latus AD eſt
                <lb/>
              duplum lateris AK, ho
                <lb/>
              mologi; pyramis AB­
                <lb/>
              CD, octupla erit py­
                <lb/>
              ramidis AKFH, ob
                <lb/>
              triplicatam laterum ho
                <lb/>
              mologorum proportio
                <lb/>
              nem. </s>
              <s>Similiter
                <expan abbr="vna-qũæque">vna­
                  <lb/>
                qunæque</expan>
              trium reliqua­
                <lb/>
              rum pyramidum abſciſ
                <lb/>
              ſarum erit octaua pars
                <lb/>
              pyramidis ABCD;
                <lb/>
                <figure id="id.043.01.029.1.jpg" xlink:href="043/01/029/1.jpg" number="15"/>
                <lb/>
              quatuor igitur pyramides abſciſſæ ſimul ſumptæ dimi­
                <lb/>
              dium erit pyramidis ABCD: & reliquum igitur ſoli­
                <lb/>
              dum demptis quatuor pyramidibus, dimidium pyramidis
                <lb/>
              ABCD. </s>
              <s>Dico reliquum ſolidum LKMGFH, eſſe
                <lb/>
              octaedrum. </s>
              <s>Nam octo triangulis ipſum contineri mani­
                <lb/>
              feſtum eſt. </s>
              <s>bina autem oppoſita eſſe parallela, & æqualia,
                <lb/>
              & ſimilia, ſic oſtendimus. </s>
              <s>Quoniam enim triangulum
                <lb/>
              FGH, eſt in plano trianguli ABC, plano trianguli KLM
                <lb/>
              parallelo; erit triangulum FGH, parallelum triangu-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum