Commandino, Federico, Liber de centro gravitatis solidorum, 1565

Page concordance

< >
Scan Original
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
< >
page |< < of 101 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="023/01/040.jpg"/>
            <p type="main">
              <s id="s.000375">SIT pyramis, cuius baſis triangulum abc; axis dc: &
                <lb/>
              ſecetur plano baſi æquidiſtante; quod
                <expan abbr="ſectionẽ">ſectionem</expan>
              faciat fgh;
                <lb/>
                <expan abbr="occurratq;">occurratque</expan>
              axi in puncto k. Dico fgh triangulum eſſe, ipſi
                <lb/>
              abc ſimile; cuius grauitatis centrum eſt K.
                <expan abbr="Quoniã">Quoniam</expan>
              enim
                <lb/>
              duo plana æquidiſtantia abc, fgh ſecantur à plano abd;
                <lb/>
              communes eorum ſectiones ab, fg æquidiſtantes erunt: &
                <lb/>
              eadem ratione æquidiſtantes ipſæ bc, gh: & ca, hf. </s>
              <s id="s.000376">Quòd
                <lb/>
              cum duæ lineæ fg, gh, duabus ab, bc æquidiſtent, nec
                <lb/>
              ſint in eodem plano; angulus ad g æqualis eſt angulo ad
                <lb/>
              b. </s>
              <s id="s.000377">& ſimiliter angulus ad h angulo ad c:
                <expan abbr="angulusq;">angulusque</expan>
              ad fci,
                <lb/>
              qui ad a eſt æqualis. </s>
              <s id="s.000378">triangulum igitur fgh ſimile eſt tri­
                <lb/>
              angulo abc. </s>
              <s id="s.000379">Atuero punctum k centrum eſſe grauita­
                <lb/>
              tis trianguli fgh hoc modo oſtendemus. </s>
              <s id="s.000380">Ducantur pla­
                <lb/>
              na per axem, & per lineas da, db, dc: erunt communes ſe­
                <lb/>
              ctiones fK, ae æquidiſtantes:
                <expan abbr="pariterq;">pariterque</expan>
              kg, eb; & kh, ec:
                <lb/>
              quare angulus kfh angulo eac; & angulus kfg ipſi eab
                <lb/>
                <figure id="id.023.01.040.1.jpg" xlink:href="023/01/040/1.jpg" number="30"/>
                <lb/>
              eſt æqualis. </s>
              <s id="s.000381">Eadem ratione
                <lb/>
              anguli ad g angulis ad b: &
                <lb/>
              anguli ad h iis, qui ad c æ­
                <lb/>
              quales erunt. </s>
              <s id="s.000382">ergo puncta
                <lb/>
              eK in triangulis abc, fgh
                <lb/>
              ſimiliter ſunt poſita, per ſe­
                <lb/>
              xtam poſitionem Archime­
                <lb/>
              dis in libro de centro graui­
                <lb/>
              tatis planorum. </s>
              <s id="s.000383">Sed cum e
                <lb/>
              ſit centrum grauitatis trian
                <lb/>
              guli abc, erit ex undecima
                <lb/>
              propoſitione eiuſdem libri,
                <lb/>
              & K trianguli fgh grauita
                <lb/>
              tis centrum. </s>
              <s id="s.000384">id quod demonſtrare oportebat. </s>
              <s id="s.000385">Non aliter
                <lb/>
              in ceteris pyramidibus, quod propoſitum eſt demonſtra­
                <lb/>
              bitur.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum