Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1088" type="section" level="1" n="392">
          <p>
            <s xml:id="echoid-s17531" xml:space="preserve">
              <pb o="371" file="399" n="399" rhead="LIBER OCTAVVS."/>
            cylindrus ſphæræ æqualis. </s>
            <s xml:id="echoid-s17532" xml:space="preserve">Si igitur huic cylindro fiat cubus æqualis; </s>
            <s xml:id="echoid-s17533" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-399-01" xlink:href="note-399-01a" xml:space="preserve">coroll. 38.
                <lb/>
              hui{us}.</note>
            hic cubus datæ ſphæræ æqualis. </s>
            <s xml:id="echoid-s17534" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17535" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17536" xml:space="preserve">
              <emph style="sc">Vel</emph>
            quia per eandẽ propoſ. </s>
            <s xml:id="echoid-s17537" xml:space="preserve">32. </s>
            <s xml:id="echoid-s17538" xml:space="preserve">Archimedis, ſphæra quadrupla eſt coni, cu-
              <lb/>
            ius baſis eſt maximus ſphærę circulus, & </s>
            <s xml:id="echoid-s17539" xml:space="preserve">altitudo ſemidiameter ſphæræ æqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s17540" xml:space="preserve"> Eſt autem eiuſdem coni quadruplus etiam conus eiuſdem altitudinis,
              <note symbol="b" position="right" xlink:label="note-399-02" xlink:href="note-399-02a" xml:space="preserve">11. duodec.</note>
            habens circuli maximi in ſphæra quadruplam, hoc eſt, baſem habens circulum,
              <lb/>
            cuius ſemidiameter æqualis diametro maximi circuli; </s>
            <s xml:id="echoid-s17541" xml:space="preserve"> erit poſterior hic
              <note symbol="c" position="right" xlink:label="note-399-03" xlink:href="note-399-03a" xml:space="preserve">9. quinti.</note>
            ſphæræ æqualis. </s>
            <s xml:id="echoid-s17542" xml:space="preserve"> Si igitur huic cono fiat cubus æqualis, erit hic idem
              <note symbol="d" position="right" xlink:label="note-399-04" xlink:href="note-399-04a" xml:space="preserve">coroll. 38.
                <lb/>
              hui{us}.</note>
            ſphæræ datæ æqualis. </s>
            <s xml:id="echoid-s17543" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17544" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17545" xml:space="preserve">
              <emph style="sc">Sit</emph>
            viciſsim dato cubo fabricanda ſphæra æqualis. </s>
            <s xml:id="echoid-s17546" xml:space="preserve"> Fiat cubo,
              <note symbol="e" position="right" xlink:label="note-399-05" xlink:href="note-399-05a" xml:space="preserve">35. hui{us}.</note>
            Priſmati, cylindrus æqualis. </s>
            <s xml:id="echoid-s17547" xml:space="preserve">Deinde ſphæra fabricetur, habens diametrum ſeſ-
              <lb/>
            quialteram aititu dinis cylindri. </s>
            <s xml:id="echoid-s17548" xml:space="preserve"> Hæc enim ſphæra cylindro, ac proinde
              <note symbol="f" position="right" xlink:label="note-399-06" xlink:href="note-399-06a" xml:space="preserve">9. quinti.</note>
            dato æqualis erit: </s>
            <s xml:id="echoid-s17549" xml:space="preserve">propterea quod cylindrus eiuſdem baſis altitudinem habens
              <lb/>
            æqualem diametro ſphæræ, ſeſquialter eſt tam prioris cylindri, quam
              <note symbol="g" position="right" xlink:label="note-399-07" xlink:href="note-399-07a" xml:space="preserve">14. duodec.</note>
              <note symbol="h" position="right" xlink:label="note-399-08" xlink:href="note-399-08a" xml:space="preserve">32. lib. 1. de
                <lb/>
              ſph. & cyl.</note>
            ſphæræ. </s>
            <s xml:id="echoid-s17550" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17551" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1092" type="section" level="1" n="393">
          <head xml:id="echoid-head420" xml:space="preserve">COROLLARIVM I.</head>
          <p>
            <s xml:id="echoid-s17552" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            verò ſi baſi cubi fiat æqualis figura quotcunq; </s>
            <s xml:id="echoid-s17553" xml:space="preserve">laterum, ſiue
              <note symbol="i" position="right" xlink:label="note-399-09" xlink:href="note-399-09a" xml:space="preserve">25. ſexti.</note>
            gularis ſit, ſiue non; </s>
            <s xml:id="echoid-s17554" xml:space="preserve">& </s>
            <s xml:id="echoid-s17555" xml:space="preserve">ſupra hanc figuram erigatur ſolidum rectangulum ad al-
              <lb/>
              <note symbol="k" position="right" xlink:label="note-399-10" xlink:href="note-399-10a" xml:space="preserve">2. eoroll. 7.
                <lb/>
              duodec.</note>
            titudinẽ cubi ſolidum hoc cubo eſt æquale: </s>
            <s xml:id="echoid-s17556" xml:space="preserve">fit vt ſphæræ datæ conſtrui poſsit æquale ſolidum rectangulum ſupra baſem quotlibet angulorum; </s>
            <s xml:id="echoid-s17557" xml:space="preserve"> ſi
              <note symbol="l" position="right" xlink:label="note-399-11" xlink:href="note-399-11a" xml:space="preserve">40. hui{us}.</note>
            prius conſtruatur cubus æqualis: </s>
            <s xml:id="echoid-s17558" xml:space="preserve">deinde huic cubo ſolidum rectangulum æ-
              <lb/>
            quale, vt proximè dictum eſt. </s>
            <s xml:id="echoid-s17559" xml:space="preserve"> Item quia cuicunque priſmati pyramis
              <note symbol="m" position="right" xlink:label="note-399-12" xlink:href="note-399-12a" xml:space="preserve">36 hui{us}.</note>
            poteſt æqualis: </s>
            <s xml:id="echoid-s17560" xml:space="preserve">ſi cubo, qui ſphærę eſt æqualis, tanquam priſmati, fiat pyramis
              <lb/>
            æqualis; </s>
            <s xml:id="echoid-s17561" xml:space="preserve">erit quo que eadem pyramis ſp hærę æqualis. </s>
            <s xml:id="echoid-s17562" xml:space="preserve"> Immo quoniam
              <note symbol="n" position="right" xlink:label="note-399-13" xlink:href="note-399-13a" xml:space="preserve">36. hui{us}.</note>
            bet cylindro conus fieri poteſt æqualis: </s>
            <s xml:id="echoid-s17563" xml:space="preserve">ſi cylindrus extruatur ſphærę æqualis,
              <lb/>
            ſupra baſem videlicet maximo circulo in ſphæra æqualẽ, & </s>
            <s xml:id="echoid-s17564" xml:space="preserve">cuius altitudo con-
              <lb/>
            tineat {2/3}. </s>
            <s xml:id="echoid-s17565" xml:space="preserve">diametri, vt ad initium huius propoſ. </s>
            <s xml:id="echoid-s17566" xml:space="preserve">oſtendimus: </s>
            <s xml:id="echoid-s17567" xml:space="preserve">Deinde huic cylin-
              <lb/>
            dro conus æqualis; </s>
            <s xml:id="echoid-s17568" xml:space="preserve">conſtitutus erit conus quo que datæ ſphærę æqualis.</s>
            <s xml:id="echoid-s17569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17570" xml:space="preserve">
              <emph style="sc">Vicissim</emph>
            quia cuilibet priſmati conſtrui poteſt cubus æqualis: </s>
            <s xml:id="echoid-s17571" xml:space="preserve"> Si
              <note symbol="o" position="right" xlink:label="note-399-14" xlink:href="note-399-14a" xml:space="preserve">37. hui{us}.</note>
            cubo fiat æqualis ſphæra, erit eadem hæc ſphæra conſtituta æqualis dato priſma-
              <lb/>
              <note symbol="p" position="right" xlink:label="note-399-15" xlink:href="note-399-15a" xml:space="preserve">40. hui{us}.</note>
            tiſupra baſem quotcunque angulorum.</s>
            <s xml:id="echoid-s17572" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1095" type="section" level="1" n="394">
          <head xml:id="echoid-head421" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s17573" xml:space="preserve">
              <emph style="sc">Qvin</emph>
            etiam colligitur, poſſe ſphęram conſtrui æqualem cuilibet corporire-
              <lb/>
            gulari. </s>
            <s xml:id="echoid-s17574" xml:space="preserve">Nam de cubo quidem oſtenſum eſt hac propoſ. </s>
            <s xml:id="echoid-s17575" xml:space="preserve">40. </s>
            <s xml:id="echoid-s17576" xml:space="preserve">De Tetraedro ve-
              <lb/>
            ro, ſiue Pyramide regulari patet. </s>
            <s xml:id="echoid-s17577" xml:space="preserve">Nam ſi Pyramidi fiat Parallelepipedum
              <note symbol="q" position="right" xlink:label="note-399-16" xlink:href="note-399-16a" xml:space="preserve">2. coroll. 36.
                <lb/>
              hui{us}.</note>
            le: </s>
            <s xml:id="echoid-s17578" xml:space="preserve"> Et huic parallelepipedo cubus æqualis; </s>
            <s xml:id="echoid-s17579" xml:space="preserve">Ac tandem huic cubo fabrice- tur ſphęra æqualis; </s>
            <s xml:id="echoid-s17580" xml:space="preserve">erit eadem hæc ſphæra Tetraedro, ſiue pyramidi regulariæ-
              <lb/>
              <note symbol="r" position="right" xlink:label="note-399-17" xlink:href="note-399-17a" xml:space="preserve">38. cui{us}.</note>
            qualis. </s>
            <s xml:id="echoid-s17581" xml:space="preserve">De Octaedro autem, Icoſaedro, & </s>
            <s xml:id="echoid-s17582" xml:space="preserve">Dodecaedro ita res peragetur. </s>
            <s xml:id="echoid-s17583" xml:space="preserve">Si o-
              <lb/>
            mnibus baſibus corporis regularis fiat quadratum æquale, per ea, quæ ad finem
              <lb/>
            lib. </s>
            <s xml:id="echoid-s17584" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17585" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s17586" xml:space="preserve">vel potius per ea, quę lib. </s>
            <s xml:id="echoid-s17587" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17588" xml:space="preserve">huius Geometrię cap. </s>
            <s xml:id="echoid-s17589" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17590" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s17591" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17592" xml:space="preserve">tra-
              <lb/>
            didimus; </s>
            <s xml:id="echoid-s17593" xml:space="preserve">& </s>
            <s xml:id="echoid-s17594" xml:space="preserve">ſuper hoc quadratum fiat pyramis habens altitudinem æqualem
              <lb/>
            perpendiculari è centro corporis ad quamlibet baſem ductę, hoc eſt, altitudini
              <lb/>
            vnius pyramidis ex iis, in quas corpus diuiditur è centro: </s>
            <s xml:id="echoid-s17595" xml:space="preserve"> Erit hæc
              <note symbol="s" position="right" xlink:label="note-399-18" xlink:href="note-399-18a" xml:space="preserve">9. quinti.</note>
            </s>
          </p>
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