Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
< >
page |< < (33) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s4406" xml:space="preserve">
              <pb o="33" file="0177" n="177" rhead="DE CENTRO GRAVIT. SOLID."/>
            quod diuidat fruſtum in duo fruſta triangulares baſes ha-
              <lb/>
            bentia, uidelicet in fruſtum a b d e f h, & </s>
            <s xml:id="echoid-s4407" xml:space="preserve">in fruſtũ b c d f g h.
              <lb/>
            </s>
            <s xml:id="echoid-s4408" xml:space="preserve">erit triangulum k l n proportionale inter triangula a b d,
              <lb/>
            e f h: </s>
            <s xml:id="echoid-s4409" xml:space="preserve">& </s>
            <s xml:id="echoid-s4410" xml:space="preserve">triangulum l m n proportionale inter b c d, f g h. </s>
            <s xml:id="echoid-s4411" xml:space="preserve">
              <lb/>
            ſed pyramis æque alta, cuius baſis conſtat ex tribus trian-
              <lb/>
            gulis a b d, k l n, e f h, demonſtrata
              <lb/>
              <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a" number="132">
                <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0177-01"/>
              </figure>
            eſt ſruſto a b d e f h æqualis. </s>
            <s xml:id="echoid-s4412" xml:space="preserve">& </s>
            <s xml:id="echoid-s4413" xml:space="preserve">ſi-
              <lb/>
            militer pyramis, cuius baſis con-
              <lb/>
            ſtat ex triangulis b c d, l m n, f g h
              <lb/>
            æqualis fruſto b c d f g h: </s>
            <s xml:id="echoid-s4414" xml:space="preserve">compo-
              <lb/>
            nuntur autem tria quadrilatera a
              <lb/>
            b c d, _k_ l m n, e f g h è ſex triangu-
              <lb/>
            lis iam dictis. </s>
            <s xml:id="echoid-s4415" xml:space="preserve">pyramis igitur ba-
              <lb/>
            ſim habens æqualem tribus qua-
              <lb/>
            drilateris, & </s>
            <s xml:id="echoid-s4416" xml:space="preserve">altitudinem eandem
              <lb/>
            ipſi fruſto a g eſt æqualis. </s>
            <s xml:id="echoid-s4417" xml:space="preserve">Eodem
              <lb/>
            modo illud demõſtrabitur in aliis
              <lb/>
            eiuſmodi fruſtis.</s>
            <s xml:id="echoid-s4418" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4419" xml:space="preserve">Sit fruſtum coni, uel coni, uel coni portionis a d; </s>
            <s xml:id="echoid-s4420" xml:space="preserve">cuius maior ba-
              <lb/>
            ſis circulus, uel ellipſis circa diametrum a b; </s>
            <s xml:id="echoid-s4421" xml:space="preserve">minor circa
              <lb/>
            c d: </s>
            <s xml:id="echoid-s4422" xml:space="preserve">& </s>
            <s xml:id="echoid-s4423" xml:space="preserve">ſecetur plano, quod baſibus æquidiſtet, faciatq; </s>
            <s xml:id="echoid-s4424" xml:space="preserve">ſe-
              <lb/>
            ctionem circulum, uel ellipſim circa diametrum e f, ita ut
              <lb/>
            inter circulos, uel ellipſes a b, c d ſit proportionalis. </s>
            <s xml:id="echoid-s4425" xml:space="preserve">Dico
              <lb/>
            conum, uel coni portionem, cuius baſis eſt æqualis tribus
              <lb/>
            circulis, uel tribus ellipſibus a b, e f, c d; </s>
            <s xml:id="echoid-s4426" xml:space="preserve">& </s>
            <s xml:id="echoid-s4427" xml:space="preserve">altitudo eadem,
              <lb/>
            quæ fruſti a d, ipſi fruſto æqualem eſſe. </s>
            <s xml:id="echoid-s4428" xml:space="preserve">producatur enim
              <lb/>
            fruſti ſuperficies quouſque coeat in unum punctum, quod
              <lb/>
            ſit g: </s>
            <s xml:id="echoid-s4429" xml:space="preserve">& </s>
            <s xml:id="echoid-s4430" xml:space="preserve">coni, uel coni portionis a g b axis ſit g h, occurrens
              <lb/>
            planis a b, e f, c d in punctis h _k_ l: </s>
            <s xml:id="echoid-s4431" xml:space="preserve">circa circulum uero de-
              <lb/>
            ſcribatur quadratum m n o p, & </s>
            <s xml:id="echoid-s4432" xml:space="preserve">circa ellipſim rectangulũ
              <lb/>
            m n o p, quod ex ipſius diametris conſtat: </s>
            <s xml:id="echoid-s4433" xml:space="preserve">iunctisq; </s>
            <s xml:id="echoid-s4434" xml:space="preserve">g m,
              <lb/>
            g n, g o, g p, ex eodem uertice intelligatur pyramis baſim
              <lb/>
            habens dictum quadratum, uel rectangulum: </s>
            <s xml:id="echoid-s4435" xml:space="preserve">& </s>
            <s xml:id="echoid-s4436" xml:space="preserve">plana in
              <lb/>
            quibus ſunt circuli, uel ellipſes e f, c d uſque ad eius </s>
          </p>
        </div>
      </text>
    </echo>
Impressum