Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1072" type="section" level="1" n="385">
          <pb o="369" file="397" n="397" rhead="LIBER OCTAVVS."/>
        </div>
        <div xml:id="echoid-div1074" type="section" level="1" n="386">
          <head xml:id="echoid-head413" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s17452" xml:space="preserve">Ex his etiam manifeſtè colligitur, omnem cylindrum, ac priſma; </s>
            <s xml:id="echoid-s17453" xml:space="preserve">ſimiliter & </s>
            <s xml:id="echoid-s17454" xml:space="preserve">
              <lb/>
            conum, ac pyramidem conuerti poſſe in parallelepipedum rectangulum, cuius
              <lb/>
            baſis ſit quadrata. </s>
            <s xml:id="echoid-s17455" xml:space="preserve"> Nam conuerſo cylindro, aut cono, vel pyramidein
              <note symbol="a" position="right" xlink:label="note-397-01" xlink:href="note-397-01a" xml:space="preserve">35. & 36.
                <lb/>
              hui{us}.</note>
            qualecunque, ſi baſi priſmatis fiat quadratum æquale, & </s>
            <s xml:id="echoid-s17456" xml:space="preserve">ſupra illud erigatur pa-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-397-02" xlink:href="note-397-02a" xml:space="preserve">2. coroll. 7.
                <lb/>
              duodec.</note>
            rallelepipedum eiuſdem altitudinis; </s>
            <s xml:id="echoid-s17457" xml:space="preserve"> erit hoc parallelepipedum priori æquale, ac proinde & </s>
            <s xml:id="echoid-s17458" xml:space="preserve">propoſito cylindro, vel cono, aut pyramidi.</s>
            <s xml:id="echoid-s17459" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1076" type="section" level="1" n="387">
          <head xml:id="echoid-head414" xml:space="preserve">PROBL. 23. PROPOS. 37.</head>
          <p>
            <s xml:id="echoid-s17460" xml:space="preserve">DATVM cylindrum, vel priſma: </s>
            <s xml:id="echoid-s17461" xml:space="preserve">ſimiliter datum conum, vel pyrami-
              <lb/>
            dem cuiuſcunque altitudinis, in æqualem ſub data qualibet alia altitu-
              <lb/>
            dine, & </s>
            <s xml:id="echoid-s17462" xml:space="preserve">ſupra baſem quotcunque angulorum, reuocare.</s>
            <s xml:id="echoid-s17463" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17464" xml:space="preserve">
              <emph style="sc">In</emph>
            proportione, quam data altitudo ad altitudinem propoſiti ſolidi habet,
              <lb/>
            augeatur vel minuatur baſis eiuſdem ſolidi dati. </s>
            <s xml:id="echoid-s17465" xml:space="preserve">Nam ſolidum ſupra hanc
              <note symbol="c" position="right" xlink:label="note-397-03" xlink:href="note-397-03a" xml:space="preserve">16. ſexti.
                <lb/>
              hui{us}.</note>
            ſem auctam, vel diminutam ſecundum datam altitudinem conſtructum, erit id,
              <lb/>
            quod quæritur. </s>
            <s xml:id="echoid-s17466" xml:space="preserve"> Erit enim æquale dato ſolido: </s>
            <s xml:id="echoid-s17467" xml:space="preserve">quippe cum altitudines
              <note symbol="d" position="right" xlink:label="note-397-04" xlink:href="note-397-04a" xml:space="preserve">15. & 9.
                <lb/>
              duodec.</note>
            baſibus reciprocæ ſint. </s>
            <s xml:id="echoid-s17468" xml:space="preserve">Quod ſi baſi conſtructi ſolidi fiat æqualis baſis quot-
              <lb/>
            cunque angulorum & </s>
            <s xml:id="echoid-s17469" xml:space="preserve">ſupra eam conſtituatur ſolidum ſub data altitudine; </s>
            <s xml:id="echoid-s17470" xml:space="preserve">erit
              <lb/>
            hoc etiam ſolidum ſolido propoſito æquale.</s>
            <s xml:id="echoid-s17471" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1078" type="section" level="1" n="388">
          <head xml:id="echoid-head415" xml:space="preserve">PROBL. 24. PROPOS. 38.</head>
          <p>
            <s xml:id="echoid-s17472" xml:space="preserve">DATO parallelepipedo rectangulo cubum æqualem deſcribere.</s>
            <s xml:id="echoid-s17473" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17474" xml:space="preserve">
              <emph style="sc">Si</emph>
            parallelepipedum non habet baſem quadratam, fiat eius baſi
              <note symbol="e" position="right" xlink:label="note-397-05" xlink:href="note-397-05a" xml:space="preserve">14. ſecundi.</note>
              <figure xlink:label="fig-397-01" xlink:href="fig-397-01a" number="289">
                <image file="397-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/397-01"/>
              </figure>
            tum æquale BCD, ſupra quod erigatur parallelepi-
              <lb/>
            pedum rectangulum eiuſdem altitudinis A B, cum
              <lb/>
            parallelepipedo dato, quod æquale erit dato
              <note symbol="f" position="right" xlink:label="note-397-06" xlink:href="note-397-06a" xml:space="preserve">2. coroll. 7.
                <lb/>
              duodec.</note>
            rallelepipedo. </s>
            <s xml:id="echoid-s17475" xml:space="preserve">Huic ergo cubum æqualem con-
              <lb/>
            ſtruemus hacarte. </s>
            <s xml:id="echoid-s17476" xml:space="preserve">Inter BC, latus quadrati BD, & </s>
            <s xml:id="echoid-s17477" xml:space="preserve">
              <lb/>
            A B, altitudinem parallelepipedi, inueniantur duæ
              <lb/>
            med@æ prop@rtionales EF, H: </s>
            <s xml:id="echoid-s17478" xml:space="preserve">ita vt ſit BC, ad EF,
              <lb/>
            quemadmodum EF, ad H, & </s>
            <s xml:id="echoid-s17479" xml:space="preserve">H, ad A B. </s>
            <s xml:id="echoid-s17480" xml:space="preserve">Et ſuper
              <lb/>
            EF, propinquiorem lateri B C, conſtruatur cubus EFG. </s>
            <s xml:id="echoid-s17481" xml:space="preserve"> qui
              <note symbol="g" position="right" xlink:label="note-397-07" xlink:href="note-397-07a" xml:space="preserve">Lemma 18.
                <lb/>
              ſexti hui{us}.</note>
            ABCD, æqualis erit.</s>
            <s xml:id="echoid-s17482" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17483" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi fortè accidat, tres dimenſiones parallelepipedi dati, cuius baſis
              <lb/>
            quadrata non ſit eſſe continuè proportionales; </s>
            <s xml:id="echoid-s17484" xml:space="preserve"> erit cubus ex media
              <note symbol="h" position="right" xlink:label="note-397-08" xlink:href="note-397-08a" xml:space="preserve">36. vndec.</note>
            parallelepipedo æqualis.</s>
            <s xml:id="echoid-s17485" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1081" type="section" level="1" n="389">
          <head xml:id="echoid-head416" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s17486" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            igitur omnis cylindrus, omne priſma, conus ac pyramis in
              <note symbol="i" position="right" xlink:label="note-397-09" xlink:href="note-397-09a" xml:space="preserve">2. coroll.
                <lb/>
              36. hui{us}.</note>
            lum parallelepipedum poſsit commutari, liquidò conſtat, cuilibet ſolido eiuſ-
              <lb/>
            modi, cubum poſſe conſtrui æqualem.</s>
            <s xml:id="echoid-s17487" xml:space="preserve"/>
          </p>
        </div>
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