Clavius, Christoph, Geometria practica

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          <pb o="220" file="250" n="250" rhead="GEOMETR. PRACT."/>
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          <head xml:id="echoid-head231" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s9916" xml:space="preserve">EADEM eſt proportio quadrati circumferentiæ circuli maximi in
              <lb/>
            ſphęra ad ſuperficiem ſphęræ, quę circumferentię circuli maximi ad
              <lb/>
            diametrum. </s>
            <s xml:id="echoid-s9917" xml:space="preserve">Item eadem eſt proportio quadrati diametri maximi cir-
              <lb/>
            culi in ſphęra ad ſuperficiem ſphęrę, quę diametri ad circumferenti-
              <lb/>
            am eiuſdem circuli maximi.</s>
            <s xml:id="echoid-s9918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9919" xml:space="preserve">
              <emph style="sc">Sit</emph>
            circulus ſphæræ maximus ABCD, eiuſque diameter AC. </s>
            <s xml:id="echoid-s9920" xml:space="preserve">Dico ita eſſe
              <lb/>
            quadratum ex circumferentia ABCD, deſcriptum ad ſuperficiem ſphęræ, cuius
              <lb/>
            diameter A C, vt eſt circumferentia ABCD, ad diametrum AC. </s>
            <s xml:id="echoid-s9921" xml:space="preserve">Itemita eſſe qua
              <lb/>
            dratum diametri AC, circulimaximi in ſphæra, ad ſuperficiem ſphęrę, vt eſt di-
              <lb/>
            ameter A C, ad circumferentiam A B C D. </s>
            <s xml:id="echoid-s9922" xml:space="preserve">Sit enim E F, diametro A C, & </s>
            <s xml:id="echoid-s9923" xml:space="preserve">recta
              <lb/>
            FG, circumferentię ABCD, æqualis, & </s>
            <s xml:id="echoid-s9924" xml:space="preserve">ſuper FG, conſtruatur quadratum GH,
              <lb/>
            capiaturque F I, ipſi E F, ęqualis, eritque E I, quadratum diametri E F, vel A C.
              <lb/>
            </s>
            <s xml:id="echoid-s9925" xml:space="preserve">
              <figure xlink:label="fig-250-01" xlink:href="fig-250-01a" number="163">
                <image file="250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/250-01"/>
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            Perfecta autem figura, vt vides, erit tam rectangulum G I, ſub ſemidiametro FI,
              <lb/>
            maximi circuli, & </s>
            <s xml:id="echoid-s9926" xml:space="preserve">circumfentia FG, quam rectangulum EH, ſub diametro EF,
              <lb/>
            eiuſdem circuli maximi, & </s>
            <s xml:id="echoid-s9927" xml:space="preserve">circumferentia FH, ęquale, per pręcedentem, ſuper-
              <lb/>
            ficiei conuexę ſphęrę. </s>
            <s xml:id="echoid-s9928" xml:space="preserve"> Cum ergo ſit, vt GH, quadratum ex circumferentia
              <note symbol="a" position="left" xlink:label="note-250-01" xlink:href="note-250-01a" xml:space="preserve">1. ſexti.</note>
            deſcriptum adrectangulum EH, ſuperficiei conuexę ſphęrę ęquale, ita GF, cir-
              <lb/>
            cumferentia ad EF, diametrum circulimaximi, conſtat primum.</s>
            <s xml:id="echoid-s9929" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9930" xml:space="preserve">
              <emph style="sc">Item</emph>
            cum ſit, vt E I, quadratum diametri EF, maximi circuli, ad I G,
              <note symbol="b" position="left" xlink:label="note-250-02" xlink:href="note-250-02a" xml:space="preserve">1. ſexti.</note>
            ctangulum ſuperficiei conuexæ ſphærę ęquale, ita E F, diameter maximi circuli
              <lb/>
            ad FG, circumferentiam, patetid, quod ſecundo loco proponitur.</s>
            <s xml:id="echoid-s9931" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div611" type="section" level="1" n="215">
          <head xml:id="echoid-head232" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s9932" xml:space="preserve">
              <emph style="sc">Hinc</emph>
            manifeſtum eſt (id quod lib. </s>
            <s xml:id="echoid-s9933" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9934" xml:space="preserve">capit. </s>
            <s xml:id="echoid-s9935" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9936" xml:space="preserve">Nume. </s>
            <s xml:id="echoid-s9937" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9938" xml:space="preserve">etiam demonſtra-
              <lb/>
              <note position="left" xlink:label="note-250-03" xlink:href="note-250-03a" xml:space="preserve">Area circuli.</note>
            uimus) circuli aream gignitam ex {1/4}. </s>
            <s xml:id="echoid-s9939" xml:space="preserve">diametri in totam circumferentiam, quam
              <lb/>
            ex {1/4}. </s>
            <s xml:id="echoid-s9940" xml:space="preserve">circumferentię in totam diametrum. </s>
            <s xml:id="echoid-s9941" xml:space="preserve">Cum enim circulus A B C D, ſit
              <lb/>
            quarta pars rectanguli GI, quòd hoc illius quadruplum ſit oſtenſum propoſ. </s>
            <s xml:id="echoid-s9942" xml:space="preserve">2.</s>
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