Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < (25) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="85">
          <pb o="25" file="0161" n="161" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:space="preserve">Sint duo priſmata a e, a f, quorum eadem baſis quadri-
              <lb/>
            latera a b c d: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">priſmatis a e altitudo e g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſmatis
              <lb/>
            a f altitudo f h. </s>
            <s xml:space="preserve">Dico priſma a e ad priſma a f eam habere
              <lb/>
            proportionem, quam e g ad f h. </s>
            <s xml:space="preserve">iungatur enim a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in
              <lb/>
            unoquoque priſmate duo priſmata intelligantur, quorum
              <lb/>
            baſes ſint triangu
              <lb/>
              <anchor type="figure" xlink:label="fig-0161-01a" xlink:href="fig-0161-01"/>
            la a b c, a c d. </s>
            <s xml:space="preserve">habe
              <lb/>
            bunt duo priſma-
              <lb/>
            te in eadem baſi
              <lb/>
            a b c conſtituta,
              <lb/>
            proportionem eã
              <lb/>
            dem, quam ipſo-
              <lb/>
            rum altitudines e
              <lb/>
            g, f h, exiam de-
              <lb/>
            monſtratis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi-
              <lb/>
            militer alia duo,
              <lb/>
            quæ ſunt in baſi a
              <lb/>
            c d. </s>
            <s xml:space="preserve">quare totum priſma a e ad priſma a f eandem propor
              <lb/>
              <anchor type="note" xlink:label="note-0161-01a" xlink:href="note-0161-01"/>
            tionem habebit, quam altitudo e g ad f h altitudinem.
              <lb/>
            </s>
            <s xml:space="preserve">Quòd cum priſmata ſint pyramidum tripla, & </s>
            <s xml:space="preserve">ipſæ pyrami
              <lb/>
            des, quarum eadem eſt baſis quadrilatera, & </s>
            <s xml:space="preserve">altitudo priſ-
              <lb/>
            matum altitudini æqualis, eam inter ſe proportionem ha-
              <lb/>
            bebunt, quam altitudines.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0161-01" xlink:href="fig-0161-01a">
              <image file="0161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0161-01"/>
            </figure>
            <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">12. quinti</note>
          </div>
          <p>
            <s xml:space="preserve">Si uero priſmata baſes æquales habeant, nõ eaſdem, ſint
              <lb/>
            duo eiuſmodi priſmata a e, f l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit baſis priſmatis a e qua
              <lb/>
            drilaterum a b c d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſmatis f l quadrilaterum f g h k.
              <lb/>
            </s>
            <s xml:space="preserve">Dico priſma a e ad priſma f l ita eſſe, ut altitudo illius ad
              <lb/>
            huius altitudinem. </s>
            <s xml:space="preserve">nam ſi altitudo ſit eadem, intelligãtur
              <lb/>
            duæ pyramides a b c d e, f g h k l. </s>
            <s xml:space="preserve">quæ ĩter ſe æquales erũt,
              <lb/>
              <anchor type="note" xlink:label="note-0161-02a" xlink:href="note-0161-02"/>
            cum æ quales baſes, & </s>
            <s xml:space="preserve">altitudinem eandem habeant. </s>
            <s xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:space="preserve">priſmata a e, f l, quæ ſunt harù pyramidum tripla, æqua-
              <lb/>
              <anchor type="note" xlink:label="note-0161-03a" xlink:href="note-0161-03"/>
            lia ſint neceſſe eſt. </s>
            <s xml:space="preserve">ex quibus perſpicue conſtat propoſitũ.
              <lb/>
            </s>
            <s xml:space="preserve">Si uero altitudo priſmatis f l ſit maior, à priſmate f l ab-
              <lb/>
            ſcindatur priſma fm, quod æque altum ſit, atq; </s>
            <s xml:space="preserve">ipſum a e.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>