Commandino, Federico, Liber de centro gravitatis solidorum, 1565

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 101 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000082">
                <pb xlink:href="023/01/012.jpg"/>
              quæ quidem in centro conueniunt. </s>
              <s id="s.000083">idem igitur eſt centrum
                <lb/>
              grauitatis quadrati, & circuli centrum.</s>
            </p>
            <p type="margin">
              <s id="s.000084">
                <margin.target id="marg10"/>
              31. tertii.</s>
            </p>
            <p type="main">
              <s id="s.000085">Sit pentagonum æquilaterum, & æquiangulum in circu­
                <lb/>
                <figure id="id.023.01.012.1.jpg" xlink:href="023/01/012/1.jpg" number="4"/>
                <lb/>
              lo deſcriptum abcd e. </s>
              <s id="s.000086">& iun­
                <lb/>
              cta bd,
                <expan abbr="bifariamq́">bifariamque</expan>
              ; in f diuiſa,
                <lb/>
              ducatur cf, & producatur ad
                <lb/>
              circuli circumferentiam in g;
                <lb/>
              quæ lineam ae in h ſecet: de­
                <lb/>
              inde iungantur ac, cc. </s>
              <s id="s.000087">Eodem
                <lb/>
              modo, quo ſupra demonſtra­
                <lb/>
              bimus angulum bcf æqualem
                <lb/>
              eſſe. </s>
              <s id="s.000088">angulo dcf; & angulos
                <lb/>
              ad f utroſque rectos: & idcir­
                <lb/>
              co lineam cfg per circuli cen
                <lb/>
              trum tranſire. </s>
              <s id="s.000089">Quoniam igi­
                <lb/>
              tur latera cb, ba, & cd, de æqualia ſunt; & æquales anguli
                <lb/>
                <arrow.to.target n="marg11"/>
                <lb/>
              cba, cde: erit baſis ca baſi: ce, & angulus bca angulo
                <lb/>
              dce æqualis. </s>
              <s id="s.000090">ergo & reliquus ach, reliquo ech. </s>
              <s id="s.000091">eſt au­
                <lb/>
              tem ch utrique triangulo ach, ech communis. </s>
              <s id="s.000092">quare
                <lb/>
              baſis ah æqualis eſt baſi hc: & anguli, qui ad h recti:
                <expan abbr="ſuntq́">ſuntque</expan>
              ;
                <lb/>
                <arrow.to.target n="marg12"/>
                <lb/>
              recti, qui ad f. </s>
              <s id="s.000093">ergo lineæ ae, bd inter ſe ſe æquidiſtant. </s>
              <lb/>
              <s id="s.000094">Itaque cum trapezij abde latera bd, ae æquidiſtantia à li
                <lb/>
              nea fh bifariam diuidantur; centrum grauitatis ipſius erit
                <lb/>
                <arrow.to.target n="marg13"/>
                <lb/>
              in linea fh, ex ultima eiuſdem libri Archimedis. </s>
              <s id="s.000095">Sed trian­
                <lb/>
              guli bcd centrum grauitatis eſt in linea cf. </s>
              <s id="s.000096">ergo in eadem
                <lb/>
              linea ch eſt centrum grauitatis trapezij abde, & trian­
                <lb/>
              guli bcd: hoc eſt pentagoni ipſius centrum: & centrum
                <lb/>
              circuli. </s>
              <s id="s.000097">Rurſus ſi iuncta ad,
                <expan abbr="bifariamq́">bifariamque</expan>
              ; ſecta in k, duca­
                <lb/>
              tur ekl: demonſtrabimus in ipſa utrumque centrum in
                <lb/>
              eſſe. </s>
              <s id="s.000098">Sequitur ergo, ut punctum, in quo lineæ cg, el con­
                <lb/>
              ueniunt, idem ſit centrum circuli, & centrum grauitatis
                <lb/>
              pentagoni.</s>
            </p>
            <p type="margin">
              <s id="s.000099">
                <margin.target id="marg11"/>
              4. Primi.</s>
            </p>
            <p type="margin">
              <s id="s.000100">
                <margin.target id="marg12"/>
              28. primi.</s>
            </p>
            <p type="margin">
              <s id="s.000101">
                <margin.target id="marg13"/>
              13. Archi­
                <lb/>
              medis.</s>
            </p>
            <p type="main">
              <s id="s.000102">Sit hexagonum abcdef æquilaterum, & æquiangulum
                <lb/>
              in circulo deſignatum:
                <expan abbr="iunganturq́">iunganturque</expan>
              ; bd, ae: & bifariam </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum