Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div866" type="section" level="1" n="302">
          <pb o="303" file="333" n="333" rhead="LIBER SEPTIMVS."/>
        </div>
        <div xml:id="echoid-div868" type="section" level="1" n="303">
          <head xml:id="echoid-head330" xml:space="preserve">THEOR. 10. PROPOS. 12.</head>
          <note position="right" xml:space="preserve">Inter Iſoperi-
            <lb/>
          metr{as} figur{as}
            <lb/>
          æqualia nu-
            <lb/>
          mero habent{es}
            <lb/>
          latera maxi-
            <lb/>
          ma, & æqui-
            <lb/>
          latera eſt, &
            <lb/>
          æquiangula.</note>
          <p>
            <s xml:id="echoid-s14254" xml:space="preserve">ISOPERIMETRARVM figurarum latera numero æqualia haben-
              <lb/>
            tium maxima & </s>
            <s xml:id="echoid-s14255" xml:space="preserve">æquilatera eſt, & </s>
            <s xml:id="echoid-s14256" xml:space="preserve">æquiangula.</s>
            <s xml:id="echoid-s14257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14258" xml:space="preserve">
              <emph style="sc">Esto</emph>
            figura quotcunque laterum A B C D E F, maxima inter omnes toti-
              <lb/>
            dem laterum ſibi Iſoperimetras, ita vt maior dari non poſsit. </s>
            <s xml:id="echoid-s14259" xml:space="preserve">Dico eam eſſe æ-
              <lb/>
            quilateram, & </s>
            <s xml:id="echoid-s14260" xml:space="preserve">æquiangulam. </s>
            <s xml:id="echoid-s14261" xml:space="preserve">Sit enim ſi fieri poteſt, primum non æquilatera,
              <lb/>
            ſed ſint latera AB, BC, proximain æqualia. </s>
            <s xml:id="echoid-s14262" xml:space="preserve">Ducta igitur recta AC, ſi
              <note symbol="a" position="right" xlink:label="note-333-02" xlink:href="note-333-02a" xml:space="preserve">7. hui{us}.</note>
            tur ſuper AC, triangulũ Iſoſceles AGC, quod
              <lb/>
              <figure xlink:label="fig-333-01" xlink:href="fig-333-01a" number="226">
                <image file="333-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/333-01"/>
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            ſit iſoperimetrum triangulo ABC; </s>
            <s xml:id="echoid-s14263" xml:space="preserve">erit tota fi-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-333-03" xlink:href="note-333-03a" xml:space="preserve">8. hui{us}.</note>
            gura AGCDEF. </s>
            <s xml:id="echoid-s14264" xml:space="preserve">Iſoperimetra figurę ABCD-
              <lb/>
            EF. </s>
            <s xml:id="echoid-s14265" xml:space="preserve"> Et quia triangulum AGC, maius eſt tri- angulo ABC; </s>
            <s xml:id="echoid-s14266" xml:space="preserve">ſi addatur commune polygo-
              <lb/>
            num ACDEF, erit ſigura AGCDEF, maior
              <lb/>
            quam figura ABCDEF. </s>
            <s xml:id="echoid-s14267" xml:space="preserve">quod eſt contrarium
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            hypotheſi. </s>
            <s xml:id="echoid-s14268" xml:space="preserve">Non ergo inæqualia ſunt latera
              <lb/>
            AB, BC, ſed æqualia. </s>
            <s xml:id="echoid-s14269" xml:space="preserve">Eademq; </s>
            <s xml:id="echoid-s14270" xml:space="preserve">ratione oſten-
              <lb/>
            demus, latera proxima BC, CD; </s>
            <s xml:id="echoid-s14271" xml:space="preserve">Item proxima
              <lb/>
            deinceps æqualia eſſe. </s>
            <s xml:id="echoid-s14272" xml:space="preserve">Maxima igitur figura
              <lb/>
            inter ſibi iſoperimetras æqualia numero late-
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            ra habentes æquilatera eſt, quod eſt primum.</s>
            <s xml:id="echoid-s14273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14274" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde, ſi fieri poteſt, figura ABCDEF,
              <lb/>
            æquilatera quidem, vt iam demonſtratum eſt,
              <lb/>
            at non æquiangula, ſed anguli B, D, non pro-
              <lb/>
            ximi inæquales ſint, maiorque angulus B,
              <lb/>
            quam angulus D. </s>
            <s xml:id="echoid-s14275" xml:space="preserve">Quo niamigitur demonſtra-
              <lb/>
            tum eſt, figuram maximam eſſe æquilateram,
              <lb/>
            erunt duo triangula ABC, CDE, Iſoſcelia, ita
              <lb/>
            vt duo latera AB, BC, æqualia ſint duobus la-
              <lb/>
            teribus CD, DE: </s>
            <s xml:id="echoid-s14276" xml:space="preserve">Ponitur autem angulus B,
              <lb/>
            maior angulo D; </s>
            <s xml:id="echoid-s14277" xml:space="preserve"> erit recta AC, maior
              <note symbol="c" position="right" xlink:label="note-333-04" xlink:href="note-333-04a" xml:space="preserve">24. prim.</note>
            recta CE. </s>
            <s xml:id="echoid-s14278" xml:space="preserve"> Si igitur conſtituantur ſuper
              <note symbol="d" position="right" xlink:label="note-333-05" xlink:href="note-333-05a" xml:space="preserve">10. hui{us}.</note>
            AC, CE, alia duo triangula Iſoſcelia AGC, CHE, ſimilia inter ſe, & </s>
            <s xml:id="echoid-s14279" xml:space="preserve">Iſoperime-
              <lb/>
            tra triangulis ABC, CDE; </s>
            <s xml:id="echoid-s14280" xml:space="preserve">erunt triangula AGC, CHE, vtra que ſimul maiora
              <lb/>
              <note symbol="e" position="right" xlink:label="note-333-06" xlink:href="note-333-06a" xml:space="preserve">11. hui{us}.</note>
            triangulis ABC, CDE, vtriſque ſimul. </s>
            <s xml:id="echoid-s14281" xml:space="preserve">Si igitur addatur commune polygonum
              <lb/>
            ACEF: </s>
            <s xml:id="echoid-s14282" xml:space="preserve">erit figura AGCHEF, maior, quam figura ABCDEF, quod cum hypo-
              <lb/>
            theſi pugnat, quod hæc omnium maxima ponatur. </s>
            <s xml:id="echoid-s14283" xml:space="preserve">Non ergo inæquales ſunt
              <lb/>
            anguli B, D, ſed æquales. </s>
            <s xml:id="echoid-s14284" xml:space="preserve">Eademque ratione oſtendemus, angulos non pro-
              <lb/>
            ximos C, E, æquales eſſe, & </s>
            <s xml:id="echoid-s14285" xml:space="preserve">binos alios quo ſuis non proximos. </s>
            <s xml:id="echoid-s14286" xml:space="preserve">Ex quo effici-
              <lb/>
            tur, totam figuram æquiangulam eſſe, nempe proximos etiam angulos inter
              <lb/>
            fe eſſe æquales. </s>
            <s xml:id="echoid-s14287" xml:space="preserve">Si enim verbi gratia angulus B, non dicatur æqualis eſſe an-
              <lb/>
            gulo C; </s>
            <s xml:id="echoid-s14288" xml:space="preserve">cum angulus C, æqualis ſit non proximo angulo E; </s>
            <s xml:id="echoid-s14289" xml:space="preserve">erit quo que an-
              <lb/>
            gulus B, angulo E, non æqualis, quod abſurdum eſt. </s>
            <s xml:id="echoid-s14290" xml:space="preserve">Bini enim anguli non pro-
              <lb/>
            ximi inter ſe æquales ſunt, vt oſtendimus. </s>
            <s xml:id="echoid-s14291" xml:space="preserve">Maxima ergo figura inter ſibi </s>
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