Commandino, Federico, Liber de centro gravitatis solidorum, 1565

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 101 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="25" xlink:href="023/01/057.jpg"/>
            <p type="main">
              <s id="s.000517">Sint duo priſmata ae, af, quorum eadem baſis quadri­
                <lb/>
              latera abcd:
                <expan abbr="ſitq;">ſitque</expan>
              priſmatis ae altitudo eg; & priſmatis
                <lb/>
              af altitudo fh. </s>
              <s id="s.000518">Dico priſma ae ad priſma af eam habere
                <lb/>
              proportionem, quam eg ad fh. </s>
              <s id="s.000519">iungatur enim ac: & in
                <lb/>
              unoquoque priſmate duo priſmata intelligantur, quorum
                <lb/>
                <figure id="id.023.01.057.1.jpg" xlink:href="023/01/057/1.jpg" number="49"/>
                <lb/>
              baſes ſint triangu
                <lb/>
              la abc, acd. </s>
              <s id="s.000520">habe
                <lb/>
              bunt duo priſma­
                <lb/>
              te in eadem baſi
                <lb/>
              abc conſtituta,
                <lb/>
              proportionem
                <expan abbr="eã">eam</expan>
                <lb/>
              dem, quam ipſo­
                <lb/>
              rum altitudines e
                <lb/>
              g, fh, ex iam de­
                <lb/>
              monſtratis. </s>
              <s id="s.000521">& ſi­
                <lb/>
              militer alia duo,
                <lb/>
              quæ ſunt in baſi a
                <lb/>
                <arrow.to.target n="marg62"/>
                <lb/>
              c d. </s>
              <s id="s.000522">quare totum priſma ae ad priſma af eandem propor
                <lb/>
              tionem habebit, quam altitudo eg ad fh altitudinem. </s>
              <lb/>
              <s id="s.000523">Quòd cum priſmata ſint pyramidum tripla, & ipſæ pyrami
                <lb/>
              des, quarum eadem eſt baſis quadrilatera, & altitudo priſ­
                <lb/>
              matum altitudini æqualis, eam inter ſe proportionem ha­
                <lb/>
              bebunt, quam altitudines.</s>
            </p>
            <p type="margin">
              <s id="s.000524">
                <margin.target id="marg62"/>
              12. quinti</s>
            </p>
            <p type="main">
              <s id="s.000525">Si uero priſmata baſes æquales habeant,
                <expan abbr="nõ">non</expan>
              eaſdem, ſint
                <lb/>
              duo eiuſmodi priſmata ae, fl: & ſit baſis priſmatis ae qua
                <lb/>
              drilaterum abcd; & priſmatis fl quadrilaterum fghk. </s>
              <lb/>
              <s id="s.000526">Dico priſma ae ad priſma fl ita eſſe, ut altitudo illius ad
                <lb/>
              huius altitudinem. </s>
              <s id="s.000527">nam ſi altitudo ſit eadem,
                <expan abbr="intelligãtur">intelligantur</expan>
                <lb/>
                <arrow.to.target n="marg63"/>
                <lb/>
              duæ pyramides abcde, fghkl. </s>
              <s id="s.000528">quæ
                <expan abbr="ĩtcrſe">interſe</expan>
              æquales
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
              cum æquales baſes, & altitudinem eandem habeant. </s>
              <s id="s.000529">quare
                <lb/>
                <arrow.to.target n="marg64"/>
                <lb/>
              & priſmata ae, fl, quæ ſunt
                <expan abbr="harũ">harum</expan>
              pyramidum tripla, æqua­
                <lb/>
              lia ſint neceſſe eſt. </s>
              <s id="s.000530">ex quibus perſpicue conſtat
                <expan abbr="propoſitũ">propoſitum</expan>
              . </s>
              <lb/>
              <s id="s.000531">Si uero altitudo priſmatis fl ſit maior, à priſmate fl ab­
                <lb/>
              ſcindatur priſma fm, quod æque altum ſit,
                <expan abbr="atq;">atque</expan>
              ipſum ae. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum