Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="64">
          <p>
            <s xml:space="preserve">
              <pb file="0116" n="116" rhead="FED. COMMANDINI"/>
            quæ quidem in centro conueniunt. </s>
            <s xml:space="preserve">idem igitur eſt centrum
              <lb/>
            grauitatis quadrati, & </s>
            <s xml:space="preserve">circuli centrum.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <figure xlink:label="fig-0115-02" xlink:href="fig-0115-02a">
              <image file="0115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-02"/>
            </figure>
            <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">51. tortil.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit pentagonum æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum in circu-
              <lb/>
            lo deſcriptum a b c d e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iun-
              <lb/>
              <anchor type="figure" xlink:label="fig-0116-01a" xlink:href="fig-0116-01"/>
            cta b d, bifariamq́; </s>
            <s xml:space="preserve">in ſ diuiſa,
              <lb/>
            ducatur c f, & </s>
            <s xml:space="preserve">producatur ad
              <lb/>
            circuli circumferentiam in g;
              <lb/>
            </s>
            <s xml:space="preserve">quæ lineam a e in h ſecet: </s>
            <s xml:space="preserve">de-
              <lb/>
            inde iungantur a c, c e. </s>
            <s 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:space="preserve">& </s>
            <s xml:space="preserve">angulos
              <lb/>
            ad f utroſque rectos: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcir-
              <lb/>
            colineam c f g per circuli cen
              <lb/>
            trum tranſire. </s>
            <s xml:space="preserve">Quoniam igi-
              <lb/>
            tur latera c b, b a, & </s>
            <s xml:space="preserve">c d, d e æqualia ſunt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">æquales anguli
              <lb/>
            c b a, c d e: </s>
            <s xml:space="preserve">erit baſis c a baſi c e, & </s>
            <s xml:space="preserve">angulus b c a angulo
              <lb/>
              <anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/>
            d c e æqualis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquus a c h, reliquo e c h. </s>
            <s xml:space="preserve">eſt au-
              <lb/>
            tem c h utrique triangulo a c h, e c h communis. </s>
            <s xml:space="preserve">quare
              <lb/>
            baſis a h æqualis eſt baſi h e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli, quiad h recti: </s>
            <s xml:space="preserve">ſuntq́;
              <lb/>
            </s>
            <s xml:space="preserve">recti, qui ad f. </s>
            <s xml:space="preserve">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0116-02a" xlink:href="note-0116-02"/>
            Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
              <lb/>
            nea fh bifariam diuidantur; </s>
            <s xml:space="preserve">centrum grauitatis ipſius erit
              <lb/>
            in linea f h, ex ultima eiuſdem libri Archimedis. </s>
            <s xml:space="preserve">Sed trian-
              <lb/>
              <anchor type="note" xlink:label="note-0116-03a" xlink:href="note-0116-03"/>
            guli b c d centrum grauitatis eſt in linea c f. </s>
            <s xml:space="preserve">ergo in eadem
              <lb/>
            linea c h eſt centrum grauitatis trapezij a b d e, & </s>
            <s xml:space="preserve">trian-
              <lb/>
            guli b c d: </s>
            <s xml:space="preserve">hoc eſt pentagoni ipſius centrum & </s>
            <s xml:space="preserve">centrum
              <lb/>
            circuli. </s>
            <s xml:space="preserve">Rurſus ſi iuncta a d, bifariamq́; </s>
            <s xml:space="preserve">ſecta in k, duca-
              <lb/>
            tur e k l: </s>
            <s xml:space="preserve">demonſtrabimus in ipſa utrumque centrum in
              <lb/>
            eſſe. </s>
            <s xml:space="preserve">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
              <lb/>
            ueniunt, idem ſit centrum circuli, & </s>
            <s xml:space="preserve">centrum grauitatis
              <lb/>
            pentagoni.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a">
              <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0116-01"/>
            </figure>
            <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">4. Primi.</note>
            <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">08. primi.</note>
            <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">13. Archi-
              <lb/>
            medis.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit hexagonum a b c d e f æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum
              <lb/>
            in circulo deſignatum: </s>
            <s xml:space="preserve">iunganturq́; </s>
            <s xml:space="preserve">b d, a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſe-</s>
          </p>
        </div>
      </text>
    </echo>