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 |< < (3) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="64">
          <p>
            <s xml:space="preserve">
              <pb o="3" file="0117" n="117" rhead="DE CENTRO GRAVIT. SOLID."/>
            cta b d in g puncto, ducatur c g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">protrahatur ad circuli
              <lb/>
            uſque circumferentiam; </s>
            <s xml:space="preserve">quæ ſecet a e in h. </s>
            <s xml:space="preserve">Similiter conclu
              <lb/>
            demus c g per centrum circuli tranſire: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſecare
              <lb/>
            lineam a e; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">lineas b d, a e inter ſe æquidiſtantes eſſe.
              <lb/>
            </s>
            <s xml:space="preserve">Cumigitur c g per centrum circuli tranſeat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad punctũ
              <lb/>
            f perueniat neceſſe eſt: </s>
            <s xml:space="preserve">quòd c d e f ſit dimidium circumfe
              <lb/>
            rentiæ circuli. </s>
            <s xml:space="preserve">Quare in eadem
              <lb/>
              <anchor type="figure" xlink:label="fig-0117-01a" xlink:href="fig-0117-01"/>
            diametro c f erunt centra gra
              <lb/>
              <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/>
            uitatis triangulorum b c d,
              <lb/>
            a f e, & </s>
            <s xml:space="preserve">quadrilateri a b d e, ex
              <lb/>
              <anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/>
            quibus conſtat hexagonum a b
              <lb/>
            c d e f. </s>
            <s xml:space="preserve">perſpicuum eſt igitur in
              <lb/>
            ipſa c f eſſe circuli centrum, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum grauitatis hexagoni.
              <lb/>
            </s>
            <s xml:space="preserve">Rurſus ducta altera diametro
              <lb/>
            a d, eiſdem rationibus oſtende-
              <lb/>
            mus in ipſa utrumque cẽtrum
              <lb/>
            ineſſe. </s>
            <s xml:space="preserve">Centrum ergo grauita-
              <lb/>
            tis hexagoni, & </s>
            <s xml:space="preserve">centrum circuli idem erit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <figure xlink:label="fig-0117-01" xlink:href="fig-0117-01a">
              <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0117-01"/>
            </figure>
            <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">13. Archi
              <lb/>
            medis.</note>
            <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">9. @iuſdé.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit heptagonum a b c d e f g æquilaterum atque æquian
              <lb/>
            gulum in circulo deſcriptum:
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0117-02a" xlink:href="fig-0117-02"/>
            & </s>
            <s xml:space="preserve">iungantur c e, b f, a g: </s>
            <s xml:space="preserve">di-
              <lb/>
            uiſa autem c e bifariam in pũ
              <lb/>
            cto h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta d h produca-
              <lb/>
            tur in k. </s>
            <s xml:space="preserve">non aliter demon-
              <lb/>
            ſtrabimus in linea d k eſſe cen
              <lb/>
            trum circuli, & </s>
            <s xml:space="preserve">centrum gra-
              <lb/>
            uitatis trianguli c d e, & </s>
            <s xml:space="preserve">tra-
              <lb/>
            peziorum b c e f, a b f g, hoc
              <lb/>
            eſt centrum totius heptago-
              <lb/>
            ni: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus eadem centra in
              <lb/>
            alia diametro cl ſimiliter du-
              <lb/>
            cta contineri. </s>
            <s xml:space="preserve">Quare & </s>
            <s xml:space="preserve">centrum grauitatis heptagoni, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum circuli in idem punctum conucniunt. </s>
            <s xml:space="preserve">Eodem mo</s>
          </p>
        </div>
      </text>
    </echo>