Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1081" type="section" level="1" n="389">
          <pb o="370" file="398" n="398" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div1083" type="section" level="1" n="390">
          <head xml:id="echoid-head417" xml:space="preserve">PROBL. 25. PROPOS. 39.</head>
          <p>
            <s xml:id="echoid-s17488" xml:space="preserve">DATO cubo æquale parallelepipedum rectangulum ſub data altitu-
              <lb/>
            dine, vel ſupra datam baſem conſtruere.</s>
            <s xml:id="echoid-s17489" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17490" xml:space="preserve">
              <emph style="sc">Sit</emph>
            in præcedenti figura datus cubus E F G, & </s>
            <s xml:id="echoid-s17491" xml:space="preserve">primum data altitudo A B,
              <lb/>
              <note symbol="a" position="left" xlink:label="note-398-01" xlink:href="note-398-01a" xml:space="preserve">11. ſexti.</note>
            ſub qua conſtruendum ſit parallelepipedum rectangulum cubo æquale. </s>
            <s xml:id="echoid-s17492" xml:space="preserve"> Alti- tudini AB, & </s>
            <s xml:id="echoid-s17493" xml:space="preserve">lateri cubi E F, reperiatur tertia proportionalis BC. </s>
            <s xml:id="echoid-s17494" xml:space="preserve">Et fiat rectan-
              <lb/>
            gulum BD, comprehenſum ſub tertia proportionali BC, & </s>
            <s xml:id="echoid-s17495" xml:space="preserve">recta CD, lateri cu-
              <lb/>
            bi E F, æquali; </s>
            <s xml:id="echoid-s17496" xml:space="preserve">erigatur que ſupra B D, parallelepipedum rectangulum ſub data
              <lb/>
            altitudine AB. </s>
            <s xml:id="echoid-s17497" xml:space="preserve">quod dico cubo eſſe æquale. </s>
            <s xml:id="echoid-s17498" xml:space="preserve">Quoniam enim parallelepipedum
              <lb/>
            rectangulum A B D, continetur ſub tribus rectis AB, CD, BC, hoc eſt, ſub A B,
              <lb/>
            E F, B C, continuè proportionalibus; </s>
            <s xml:id="echoid-s17499" xml:space="preserve"> erit parallelepipedum æquale cubo
              <note symbol="b" position="left" xlink:label="note-398-02" xlink:href="note-398-02a" xml:space="preserve">36. vndec.</note>
            media E F, deſcripto. </s>
            <s xml:id="echoid-s17500" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17502" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde data baſis BD, quæ ſi non eſt parallelogrammum, r@uocetur
              <note symbol="c" position="left" xlink:label="note-398-03" xlink:href="note-398-03a" xml:space="preserve">45. primi.</note>
            parallelogrammum æquale. </s>
            <s xml:id="echoid-s17503" xml:space="preserve">Et quam proportio-
              <lb/>
              <figure xlink:label="fig-398-01" xlink:href="fig-398-01a" number="290">
                <image file="398-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/398-01"/>
              </figure>
            nem habeat baſis data BD, ad baſem cubi dati, eam
              <lb/>
            habet latus cubi E F, ad rectam A B. </s>
            <s xml:id="echoid-s17504" xml:space="preserve">(quod fiet, ſi
              <lb/>
            ſupra latus cubi E F, fiat rectangulum æquale baſi
              <lb/>
            B D, & </s>
            <s xml:id="echoid-s17505" xml:space="preserve">ſuper alterum latus huius rectangulialiud
              <lb/>
            rectangulum æquale quadrato lateris cubi E F. </s>
            <s xml:id="echoid-s17506" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-398-04" xlink:href="note-398-04a" xml:space="preserve">1. ſexti.</note>
            Namtunc erit, vt primum rectangulum, id eſt, ba-
              <lb/>
            ſis BD, ad ſecundum rectangulum, id eſt, ad quadratum, vel baſem cubi, ita primi
              <lb/>
            rectanguli baſis, videlicet EF, ad baſem ſecundirectanguli.) </s>
            <s xml:id="echoid-s17507" xml:space="preserve">Nam ſi ſupra baſem
              <lb/>
            BD, erigatur parallelepipedum in altitu dine inuenta AB, erunt
              <note symbol="e" position="left" xlink:label="note-398-05" xlink:href="note-398-05a" xml:space="preserve">34. vndec.</note>
            dum, & </s>
            <s xml:id="echoid-s17508" xml:space="preserve">cubus æqualia: </s>
            <s xml:id="echoid-s17509" xml:space="preserve">quippe cum baſes, & </s>
            <s xml:id="echoid-s17510" xml:space="preserve">altitudines ſint reciprocæ, ex con-
              <lb/>
            ſtructione. </s>
            <s xml:id="echoid-s17511" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17512" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1086" type="section" level="1" n="391">
          <head xml:id="echoid-head418" xml:space="preserve">COR OLLARIVM.</head>
          <p>
            <s xml:id="echoid-s17513" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            igitur cuilibet cylindro, priſmati, cono, ac pyramidi
              <note symbol="f" position="left" xlink:label="note-398-06" xlink:href="note-398-06a" xml:space="preserve">coroll. 38.
                <lb/>
              hui{us}.</note>
            pipedum rectangulum conſtrui poteſt æquale: </s>
            <s xml:id="echoid-s17514" xml:space="preserve"> ſi huic parallelepipedo fiat cu- bus æqualis; </s>
            <s xml:id="echoid-s17515" xml:space="preserve"> & </s>
            <s xml:id="echoid-s17516" xml:space="preserve">huic cubo parallelepipedum rectangulum ſub data
              <note symbol="g" position="left" xlink:label="note-398-07" xlink:href="note-398-07a" xml:space="preserve">38. hui{us}.</note>
            ne, vel baſe data æquale: </s>
            <s xml:id="echoid-s17517" xml:space="preserve">commutatus erit cylindrus, priſma, conus, ac pyramis
              <lb/>
              <note symbol="h" position="left" xlink:label="note-398-08" xlink:href="note-398-08a" xml:space="preserve">39. hui{us}.</note>
            in parallelepipedum rectangulum æquale datæ altitudinis, vel baſis.</s>
            <s xml:id="echoid-s17518" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1088" type="section" level="1" n="392">
          <head xml:id="echoid-head419" xml:space="preserve">PROBL. 26. PROPOS. 40.</head>
          <p>
            <s xml:id="echoid-s17519" xml:space="preserve">SPHÆRÆ datæ cubum æqualem: </s>
            <s xml:id="echoid-s17520" xml:space="preserve">Et dato cubo æqualem ſphæram
              <lb/>
            conſtituere.</s>
            <s xml:id="echoid-s17521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17522" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            per propoſ. </s>
            <s xml:id="echoid-s17523" xml:space="preserve">32. </s>
            <s xml:id="echoid-s17524" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17525" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17526" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s17527" xml:space="preserve">cylindro, Cylin-
              <lb/>
            drus rectus, cuius baſis eſt maximus ſphæræ circulus, & </s>
            <s xml:id="echoid-s17528" xml:space="preserve">altitudo diametro eiuſ-
              <lb/>
            dem ſphæræ æqualis, ſeſquialteram habet proportionem ad ſphæram: </s>
            <s xml:id="echoid-s17529" xml:space="preserve">
              <note symbol="i" position="left" xlink:label="note-398-09" xlink:href="note-398-09a" xml:space="preserve">14. vndec.</note>
            autem idem cylind@us ad cylindrum eiuſdem baſis, cuius altitudo contineat
              <lb/>
            {2/3}. </s>
            <s xml:id="echoid-s17530" xml:space="preserve">diametri ſphæræ, proportionem quo que ſeſquialteram; </s>
            <s xml:id="echoid-s17531" xml:space="preserve"> erit poſterior
              <note symbol="k" position="left" xlink:label="note-398-10" xlink:href="note-398-10a" xml:space="preserve">9. quinti.</note>
            </s>
          </p>
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