Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
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
< >
page |< < (35) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <pb o="35" file="0181" n="181" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:id="echoid-s4500" xml:space="preserve">Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
              <lb/>
            beat abſciſſum: </s>
            <s xml:id="echoid-s4501" xml:space="preserve">cuius maior baſis triangulum a b c, minor
              <lb/>
            d e f; </s>
            <s xml:id="echoid-s4502" xml:space="preserve">& </s>
            <s xml:id="echoid-s4503" xml:space="preserve">axis g h. </s>
            <s xml:id="echoid-s4504" xml:space="preserve">ducto autem plano per axem & </s>
            <s xml:id="echoid-s4505" xml:space="preserve">per lineã
              <lb/>
            d a, quod ſectionem faciat d a k l quadrilaterum; </s>
            <s xml:id="echoid-s4506" xml:space="preserve">puncta
              <lb/>
            K l lineas b c, e f bifariam ſecabunt. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">nam cum g h ſit axis
              <lb/>
            ſruſti: </s>
            <s xml:id="echoid-s4508" xml:space="preserve">erit h centrum grauitatis trianguli a b c: </s>
            <s xml:id="echoid-s4509" xml:space="preserve">& </s>
            <s xml:id="echoid-s4510" xml:space="preserve">g
              <lb/>
            centrum trianguli d e f: </s>
            <s xml:id="echoid-s4511" xml:space="preserve">cen-
              <lb/>
              <figure xlink:label="fig-0181-01" xlink:href="fig-0181-01a" number="134">
                <image file="0181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0181-01"/>
              </figure>
              <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">3. diffi. hu
                <lb/>
              ius.</note>
            trum uero cuiuslibet triangu
              <lb/>
            li eſt in recta linea, quæ ab an-
              <lb/>
            gulo ipſius ad dimidiã baſim
              <lb/>
            ducitur ex decimatertia primi
              <lb/>
            libri Archimedis de cẽtro gra
              <lb/>
            uitatis planorum. </s>
            <s xml:id="echoid-s4512" xml:space="preserve">quare cen-
              <lb/>
              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">Vltima e-
                <lb/>
              auſdẽ libri
                <lb/>
              Archime-
                <lb/>
              dis.</note>
            trũ grauitatis trapezii b c f e
              <lb/>
            eſt in linea _K_ l, quod ſit m: </s>
            <s xml:id="echoid-s4513" xml:space="preserve">& </s>
            <s xml:id="echoid-s4514" xml:space="preserve">à
              <lb/>
            puncto m ad axem ducta m n
              <lb/>
            ipſi a k, uel d l æquidiſtante;
              <lb/>
            </s>
            <s xml:id="echoid-s4515" xml:space="preserve">erit axis g h diuiſus in portio-
              <lb/>
            nes g n, n h, quas diximus: </s>
            <s xml:id="echoid-s4516" xml:space="preserve">ean
              <lb/>
            dem enim proportionem ha-
              <lb/>
            bet g n ad n h, quã l m ad m _k_. </s>
            <s xml:id="echoid-s4517" xml:space="preserve">
              <lb/>
            At l m ad m K habet eam, quã
              <lb/>
            duplum lateris maioris baſis
              <lb/>
            b c una cum latere minoris e f
              <lb/>
            ad duplum lateris e f unà cum
              <lb/>
            later b c, ex ultima eiuſdem
              <lb/>
            libri Archimedis. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Itaque à li-
              <lb/>
            nea n g abſcindatur, quarta
              <lb/>
            pars, quæ ſit n p: </s>
            <s xml:id="echoid-s4519" xml:space="preserve">& </s>
            <s xml:id="echoid-s4520" xml:space="preserve">ab axe h g abſcindatur itidem
              <lb/>
            quarta pars h o: </s>
            <s xml:id="echoid-s4521" xml:space="preserve">& </s>
            <s xml:id="echoid-s4522" xml:space="preserve">quam proportionem habet fruſtum ad
              <lb/>
            pyramidem, cuius maior baſis eſt triangulum a b c, & </s>
            <s xml:id="echoid-s4523" xml:space="preserve">alti-
              <lb/>
            tudo ipſi æqualis; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">habeat o p ad p q. </s>
            <s xml:id="echoid-s4525" xml:space="preserve">Dico centrum graui-
              <lb/>
            tatis fruſti eſſe in linea p o, & </s>
            <s xml:id="echoid-s4526" xml:space="preserve">in puncto q. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">namque ipſum
              <lb/>
            eſſe in linea g h manifeſte conſtat. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">protractis enim fruſti </s>
          </p>
        </div>
      </text>
    </echo>
Impressum