Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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          <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>
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            <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"/>
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            <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"/>
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