Clavius, Christoph, Geometria practica

Table of figures

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            <s xml:id="echoid-s15264" xml:space="preserve">
              <pb o="326" file="356" n="356" rhead="GEOMETR. PRACT."/>
            AE. </s>
            <s xml:id="echoid-s15265" xml:space="preserve"> Quare tertia illa proportionalis arcui Quadrantis B D, æqualis erit: </s>
            <s xml:id="echoid-s15266" xml:space="preserve">Et
              <note symbol="a" position="left" xlink:label="note-356-01" xlink:href="note-356-01a" xml:space="preserve">9. quinti.</note>
            duplicetur, fiet recta æqualis ſemicircumferentiæ eiuſdem circuli: </s>
            <s xml:id="echoid-s15267" xml:space="preserve">Si verò qua-
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            druplicetur, fiet recta toti circumferentiæ æqualis.</s>
            <s xml:id="echoid-s15268" xml:space="preserve"/>
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        <div xml:id="echoid-div931" type="section" level="1" n="325">
          <head xml:id="echoid-head352" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s15269" xml:space="preserve">SEQVITVR quoque exhis, ſi baſis Quadratricis AE, ſtatuatur ſemi-
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            diameter alicuius circuli, eius latus A D, quartæ parti circumferentię
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            illius circuli eſſe æquale: </s>
            <s xml:id="echoid-s15270" xml:space="preserve">Et lineam lateris A D, duplam æqualem eſſe
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            ſemicircumferentiæ eiuſdem circuli: </s>
            <s xml:id="echoid-s15271" xml:space="preserve">Et lineam quadruplam lateris
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            toti circumferentiæ eſſe æqualem.</s>
            <s xml:id="echoid-s15272" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15273" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim, vt lib. </s>
            <s xml:id="echoid-s15274" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15275" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s15276" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15277" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15278" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15279" xml:space="preserve">oſtendimus, diametri circulorum cir-
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            cumferentijs ſint proportionales, erunt quo que ſemidiametri
              <note symbol="b" position="left" xlink:label="note-356-02" xlink:href="note-356-02a" xml:space="preserve">15. quinti.</note>
              <figure xlink:label="fig-356-01" xlink:href="fig-356-01a" number="245">
                <image file="356-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/356-01"/>
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            rentijs, & </s>
            <s xml:id="echoid-s15280" xml:space="preserve">quadrantibus proportionales. </s>
            <s xml:id="echoid-s15281" xml:space="preserve">Igitur erit, vt A D, ad A E, hoc eſt, vt
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            ſupradicta tertia proportionalis ad AD, ita Quadrans BD, ſemidiametri AD, ad
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            Quadrantem ſemidiametri A E. </s>
            <s xml:id="echoid-s15282" xml:space="preserve">Cum ergo tertia illa proportionalis æqualis ſit
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              <note symbol="c" position="left" xlink:label="note-356-03" xlink:href="note-356-03a" xml:space="preserve">14. quinti.</note>
            oſtenſa Quadranti BD; </s>
            <s xml:id="echoid-s15283" xml:space="preserve"> erit quo que recta A D, quadranti ſemidiametri A E, æ- qualis. </s>
            <s xml:id="echoid-s15284" xml:space="preserve">Dupla ergo linea ipſius AD, ſemicircumferentiæ circuli, cuius ſemidia-
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            meter AE; </s>
            <s xml:id="echoid-s15285" xml:space="preserve">& </s>
            <s xml:id="echoid-s15286" xml:space="preserve">quadrupla toti circumferentiæ erit ęqualis.</s>
            <s xml:id="echoid-s15287" xml:space="preserve"/>
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        <div xml:id="echoid-div933" type="section" level="1" n="326">
          <head xml:id="echoid-head353" xml:space="preserve">COROLLARIVM III.</head>
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            <s xml:id="echoid-s15288" xml:space="preserve">EX his quoque infertur, ſi duæ rectę N, O, in præcedenti figura eandem
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            proportionem habeant, quam AD, AE, minor autem O, ſtatuatur ſe-
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            midiameter circuli alicuius, maiorem N, æqualem eſſe arcui Quadrã-
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            tis illius circuli.</s>
            <s xml:id="echoid-s15289" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15290" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            enim ſit AD, ad AE, vt N, ad O; </s>
            <s xml:id="echoid-s15291" xml:space="preserve">erit permutando AD, ad N, vt AE, ad
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            O. </s>
            <s xml:id="echoid-s15292" xml:space="preserve">Vt autem AE, ad O, ita eſt Quadrans ſemidiametri A E, ad Quadrantem ſe-
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            midiametri O, vt lib. </s>
            <s xml:id="echoid-s15293" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15294" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s15295" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15296" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15297" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15298" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s15299" xml:space="preserve"> Igitur @rit
              <note symbol="d" position="left" xlink:label="note-356-04" xlink:href="note-356-04a" xml:space="preserve">11. quinti.</note>
            AD, ad N, vt Quadrans ſemidiametri AE, ad Quadrantem ſemidiametri O. </s>
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