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 |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div192" type="section" level="1" n="64">
          <p>
            <s xml:id="echoid-s2875" xml:space="preserve">
              <pb file="0116" n="116" rhead="FED. COMMANDINI"/>
            quæ quidem in centro conueniunt. </s>
            <s xml:id="echoid-s2876" xml:space="preserve">idem igitur eſt centrum
              <lb/>
            grauitatis quadrati, & </s>
            <s xml:id="echoid-s2877" xml:space="preserve">circuli centrum.</s>
            <s xml:id="echoid-s2878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2879" xml:space="preserve">Sit pentagonum æquilaterum, & </s>
            <s xml:id="echoid-s2880" xml:space="preserve">æquiangulum in circu-
              <lb/>
            lo deſcriptum a b c d e: </s>
            <s xml:id="echoid-s2881" xml:space="preserve">& </s>
            <s xml:id="echoid-s2882" xml:space="preserve">iun-
              <lb/>
              <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="72">
                <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0116-01"/>
              </figure>
            cta b d, bifariamq́; </s>
            <s xml:id="echoid-s2883" xml:space="preserve">in ſ diuiſa,
              <lb/>
            ducatur c f, & </s>
            <s xml:id="echoid-s2884" xml:space="preserve">producatur ad
              <lb/>
            circuli circumferentiam in g;
              <lb/>
            </s>
            <s xml:id="echoid-s2885" xml:space="preserve">quæ lineam a e in h ſecet: </s>
            <s xml:id="echoid-s2886" xml:space="preserve">de-
              <lb/>
            inde iungantur a c, c e. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">Eodem
              <lb/>
            modo, quo ſupra demonſtra-
              <lb/>
            bimus angulum b c f æqualem
              <lb/>
            eſſe angulo d c f; </s>
            <s xml:id="echoid-s2888" xml:space="preserve">& </s>
            <s xml:id="echoid-s2889" xml:space="preserve">angulos
              <lb/>
            ad f utroſque rectos: </s>
            <s xml:id="echoid-s2890" xml:space="preserve">& </s>
            <s xml:id="echoid-s2891" xml:space="preserve">idcir-
              <lb/>
            colineam c f g per circuli cen
              <lb/>
            trum tranſire. </s>
            <s xml:id="echoid-s2892" xml:space="preserve">Quoniam igi-
              <lb/>
            tur latera c b, b a, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">c d, d e æqualia ſunt; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">& </s>
            <s xml:id="echoid-s2895" xml:space="preserve">æquales anguli
              <lb/>
            c b a, c d e: </s>
            <s xml:id="echoid-s2896" xml:space="preserve">erit baſis c a baſi c e, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">angulus b c a angulo
              <lb/>
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">4. Primi.</note>
            d c e æqualis. </s>
            <s xml:id="echoid-s2898" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2899" xml:space="preserve">reliquus a c h, reliquo e c h. </s>
            <s xml:id="echoid-s2900" xml:space="preserve">eſt au-
              <lb/>
            tem c h utrique triangulo a c h, e c h communis. </s>
            <s xml:id="echoid-s2901" xml:space="preserve">quare
              <lb/>
            baſis a h æqualis eſt baſi h e: </s>
            <s xml:id="echoid-s2902" xml:space="preserve">& </s>
            <s xml:id="echoid-s2903" xml:space="preserve">anguli, quiad h recti: </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ſuntq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2905" xml:space="preserve">recti, qui ad f. </s>
            <s xml:id="echoid-s2906" xml:space="preserve">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">08. primi.</note>
            Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
              <lb/>
            nea fh bifariam diuidantur; </s>
            <s xml:id="echoid-s2908" xml:space="preserve">centrum grauitatis ipſius erit
              <lb/>
            in linea f h, ex ultima eiuſdem libri Archimedis. </s>
            <s xml:id="echoid-s2909" xml:space="preserve">Sed trian-
              <lb/>
              <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">13. Archi-
                <lb/>
              medis.</note>
            guli b c d centrum grauitatis eſt in linea c f. </s>
            <s xml:id="echoid-s2910" xml:space="preserve">ergo in eadem
              <lb/>
            linea c h eſt centrum grauitatis trapezij a b d e, & </s>
            <s xml:id="echoid-s2911" xml:space="preserve">trian-
              <lb/>
            guli b c d: </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc eſt pentagoni ipſius centrum & </s>
            <s xml:id="echoid-s2913" xml:space="preserve">centrum
              <lb/>
            circuli. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">Rurſus ſi iuncta a d, bifariamq́; </s>
            <s xml:id="echoid-s2915" xml:space="preserve">ſecta in k, duca-
              <lb/>
            tur e k l: </s>
            <s xml:id="echoid-s2916" xml:space="preserve">demonſtrabimus in ipſa utrumque centrum in
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s2917" xml:space="preserve">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
              <lb/>
            ueniunt, idem ſit centrum circuli, & </s>
            <s xml:id="echoid-s2918" xml:space="preserve">centrum grauitatis
              <lb/>
            pentagoni.</s>
            <s xml:id="echoid-s2919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2920" xml:space="preserve">Sit hexagonum a b c d e f æquilaterum, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">æquiangulum
              <lb/>
            in circulo deſignatum: </s>
            <s xml:id="echoid-s2922" xml:space="preserve">iunganturq́; </s>
            <s xml:id="echoid-s2923" xml:space="preserve">b d, a c: </s>
            <s xml:id="echoid-s2924" xml:space="preserve">& </s>
            <s xml:id="echoid-s2925" xml:space="preserve">bifariam </s>
          </p>
        </div>
      </text>
    </echo>