Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div935" type="section" level="1" n="327">
          <p>
            <s xml:id="echoid-s15394" xml:space="preserve">
              <pb o="329" file="359" n="359" rhead="LIBER SEPTIMVS."/>
            cundum varias diametros deſcribantur circuli per A, tranſeuntes, abſcindent
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s15395" xml:space="preserve">ij circuli ex recta AB, latera quadratorum illis circulis æqualium. </s>
            <s xml:id="echoid-s15396" xml:space="preserve">Habes
              <lb/>
            ergo viam facilem inueniendi quadratum circulo dato æquale, ſiue quadratri-
              <lb/>
            cemn oſtram adhibeas, ſiue demonſtrata ab Archimede ſequaris.</s>
            <s xml:id="echoid-s15397" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div940" type="section" level="1" n="328">
          <head xml:id="echoid-head355" xml:space="preserve">IV.</head>
          <p>
            <s xml:id="echoid-s15398" xml:space="preserve">DATO quadrato circulum æqualem deſcribere.</s>
            <s xml:id="echoid-s15399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15400" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datum quadratum lateris AE, cui circulus æqualis eſt deſcribendus. </s>
            <s xml:id="echoid-s15401" xml:space="preserve">In
              <lb/>
            proxima figura ex recta AB, abſcindatur recta A E, dato lateri quadrati æqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s15402" xml:space="preserve">Et ex E, ducatur ad AB, perpendicularis E F, ſecans A C, in F. </s>
            <s xml:id="echoid-s15403" xml:space="preserve">Eritque circulus
              <lb/>
            diametri AF, quadrato lateris AE, æqualis, vt ex proximè demonſtratis liquet.</s>
            <s xml:id="echoid-s15404" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div941" type="section" level="1" n="329">
          <head xml:id="echoid-head356" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s15405" xml:space="preserve">
              <emph style="sc">Ex</emph>
            his, quæ demonſtrata ſunt, conſtruemus circulum cuicunq; </s>
            <s xml:id="echoid-s15406" xml:space="preserve">figuræ re-
              <lb/>
            ctilineæ æqualem. </s>
            <s xml:id="echoid-s15407" xml:space="preserve">Et contra cuicunque circulo figuram rectilineam æqualem
              <lb/>
            conſtituemus, quæ alteri datæ figuræ rectilineæ cuicunque ſimilis ſit. </s>
            <s xml:id="echoid-s15408" xml:space="preserve">Nam ſi da-
              <lb/>
            tæ figuræ rectilineæ deſcribamus quadratum æquale, & </s>
            <s xml:id="echoid-s15409" xml:space="preserve">huic quadrato
              <note symbol="a" position="right" xlink:label="note-359-01" xlink:href="note-359-01a" xml:space="preserve">14. ſecundi.</note>
            lum æqualem per hanc 4. </s>
            <s xml:id="echoid-s15410" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15411" xml:space="preserve">conſtituamus; </s>
            <s xml:id="echoid-s15412" xml:space="preserve">erit idem hic circulus datæ fi-
              <lb/>
            guræ rectilineæ æqualis.</s>
            <s xml:id="echoid-s15413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15414" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            ſi per propoſitionem 3. </s>
            <s xml:id="echoid-s15415" xml:space="preserve">dato circulo quadratum ęquale conſtru-
              <lb/>
            amus, huic autem quadrato conſtituamus figuram rectilineam æqualem, & </s>
            <s xml:id="echoid-s15416" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-359-02" xlink:href="note-359-02a" xml:space="preserve">25. ſexti.</note>
            milem alteri datę figuræ rectilineæ; </s>
            <s xml:id="echoid-s15417" xml:space="preserve">erit eadem hæc figura rectilinea conſtituta,
              <lb/>
            dato circulo æqualis. </s>
            <s xml:id="echoid-s15418" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s15419" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div944" type="section" level="1" n="330">
          <head xml:id="echoid-head357" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s15420" xml:space="preserve">DATÆ rectæ lineæ circumferentiam circuli reperire æqualem.</s>
            <s xml:id="echoid-s15421" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15422" xml:space="preserve">
              <emph style="sc">In</emph>
            ſecunda figura propoſ. </s>
            <s xml:id="echoid-s15423" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15424" xml:space="preserve">ſit rectæ O, exhibenda æqualis circumferentia.
              <lb/>
            </s>
            <s xml:id="echoid-s15425" xml:space="preserve">Eius quartæ parti capiatur in latere Quadratricis A D, recta æqualis A I, ac per I,
              <lb/>
            ipſi D E, agatur parallela I H. </s>
            <s xml:id="echoid-s15426" xml:space="preserve">Eritque circumferentia circuli ex diametro A H,
              <lb/>
            deſcripti æqualis datę rectæ O, propterea quod quarta pars eius circum-
              <lb/>
            ferentiæ æqualis eſt rectæ AI, vt oſtenſum eſt ac proinde tota circũ-
              <lb/>
            ferentia æqualis erit quadruplæ rectæ AI, hoc eſt, æqua-
              <lb/>
            lis rectæ O, cuius quarta pars poſita eſt recta
              <lb/>
            AI. </s>
            <s xml:id="echoid-s15427" xml:space="preserve">Datæ ergo rectæ circumfentiã æ-
              <lb/>
            qualem reperim
              <emph style="sub">9</emph>
            . </s>
            <s xml:id="echoid-s15428" xml:space="preserve">Quod faci-
              <lb/>
            endum erat.</s>
            <s xml:id="echoid-s15429" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div945" type="section" level="1" n="331">
          <head xml:id="echoid-head358" xml:space="preserve">FINIS LIBRI SEPTIMI.</head>
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