Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div864" type="section" level="1" n="301">
          <p>
            <s xml:id="echoid-s14159" xml:space="preserve">
              <pb o="300" file="330" n="330" rhead="GEOMETR. PRACT."/>
            rectis AB, GL, LK, triangulum ANB, quod erit Iſoſceles, cadetque punctum N,
              <lb/>
            extra triangulum AEB, cum AE, EB, ſimul dimidium conſtituant rectæ G, H; </s>
            <s xml:id="echoid-s14160" xml:space="preserve">at
              <lb/>
            verò A N, N@B, ſimul maius efficiant, quam dimidium rectæ G H. </s>
            <s xml:id="echoid-s14161" xml:space="preserve"> Rurſus
              <note symbol="a" position="left" xlink:label="note-330-01" xlink:href="note-330-01a" xml:space="preserve">22. primi.</note>
            tribus rectis CD, KM, MH, conſtituatur quoque triangulum C O D, quod Iſo-
              <lb/>
            ſceles erit, cadetque punctum O, intra triangulum CFD, eo quod CF, FD, ſimul
              <lb/>
            æquales ſint dimidio rectæ GH; </s>
            <s xml:id="echoid-s14162" xml:space="preserve">at CO, OD, ſimul minores ſint dimidio rectæ
              <lb/>
            GH. </s>
            <s xml:id="echoid-s14163" xml:space="preserve">Et quoniam quatuor latera AE, EB, CF, FD, ſimul; </s>
            <s xml:id="echoid-s14164" xml:space="preserve">Item AN, NB, C O,
              <lb/>
            O D, ſimul æqualia ſunt rectæ G H, erunt priora quatuor ſimul, poſterioribus
              <lb/>
            quatuor ſimul æqualia; </s>
            <s xml:id="echoid-s14165" xml:space="preserve">additis ergo communibus AB, CD, fient ſex latera AE,
              <lb/>
            EB, BA, CF, FD, DC, ſimul ęqualia ſex lateribus AN, NB, BA, CO, OD, DC, ſi-
              <lb/>
            mul; </s>
            <s xml:id="echoid-s14166" xml:space="preserve">ideo que triangula ANB, COD, ſimul Iſoperimetra erunt triangulis AEB,
              <lb/>
            CFD, ſimul. </s>
            <s xml:id="echoid-s14167" xml:space="preserve">Dico iam, quod & </s>
            <s xml:id="echoid-s14168" xml:space="preserve">ſimilia inter ſe ſunt triangula ANB, COD. </s>
            <s xml:id="echoid-s14169" xml:space="preserve">Nam
              <lb/>
            quoniam eſt, vt AB, ad CD, ita GK, ad KH, hoc eſt, ita GL, ad KM, hoc eſt
              <note symbol="b" position="left" xlink:label="note-330-02" xlink:href="note-330-02a" xml:space="preserve">15. quinti.</note>
            A N, ad C O, & </s>
            <s xml:id="echoid-s14170" xml:space="preserve">N B, ad O D; </s>
            <s xml:id="echoid-s14171" xml:space="preserve">erit permutando, vt A B, ad AN,
              <lb/>
            ita C D, ad C O; </s>
            <s xml:id="echoid-s14172" xml:space="preserve">& </s>
            <s xml:id="echoid-s14173" xml:space="preserve">vt A N, ad N B, ita C O, ad O D. </s>
            <s xml:id="echoid-s14174" xml:space="preserve">Proportionalia ergo
              <lb/>
            ſunt latera triangulorum ANB, COD; </s>
            <s xml:id="echoid-s14175" xml:space="preserve"> ac proinde æquiangula inter ſe erunt, &</s>
            <s xml:id="echoid-s14176" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-330-03" xlink:href="note-330-03a" xml:space="preserve">5. ſexti.</note>
            idcirco ſimilia. </s>
            <s xml:id="echoid-s14177" xml:space="preserve">Quare datis duobus triangulis Iſoſcelibus, quorum baſes inæ-
              <lb/>
            quales exiſtant &</s>
            <s xml:id="echoid-s14178" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14179" xml:space="preserve">conſtituimus. </s>
            <s xml:id="echoid-s14180" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s14181" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div866" type="section" level="1" n="302">
          <head xml:id="echoid-head329" xml:space="preserve">THEOR. 9. PROPOS. 11.</head>
          <note position="left" xml:space="preserve">Triangula
            <lb/>
          duo Iſoſcelia
            <lb/>
          ſimilia maio-
            <lb/>
          ra ſunt duo-
            <lb/>
          bus Iſoſcelib{us}
            <lb/>
          non ſi milib{us},
            <lb/>
          quæillis ſint
            <lb/>
          Iſoperimetr@,
            <lb/>
          baſeſque ha-
            <lb/>
          beant eaſdem.</note>
          <p>
            <s xml:id="echoid-s14182" xml:space="preserve">DVO triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtituta,
              <lb/>
            vtraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, vtriſque ſi-
              <lb/>
            mul, quæ habeant eaſdem baſes cum prioribus, ſintq; </s>
            <s xml:id="echoid-s14183" xml:space="preserve">diſſimilia qui-
              <lb/>
            dem inter ſe, at Iſoperimetra prioribus duobus, nec non quatuor la-
              <lb/>
            tera inter ſe habeant æqualia.</s>
            <s xml:id="echoid-s14184" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14185" xml:space="preserve">
              <emph style="sc">Svper</emph>
            baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia inter ſe
              <lb/>
            nonſimilia ABC, CDE, ita vt quatuor latera AB, BC, C D, D E, inter ſe ſint æ-
              <lb/>
            qualia. </s>
            <s xml:id="echoid-s14186" xml:space="preserve"> Atque ſuper eiſdem baſibus A C, C E, conſtituantur alia duo
              <note symbol="d" position="left" xlink:label="note-330-05" xlink:href="note-330-05a" xml:space="preserve">10. hui{us}.</note>
              <figure xlink:label="fig-330-01" xlink:href="fig-330-01a" number="223">
                <image file="330-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/330-01"/>
              </figure>
            la Iſoſcelia AFC, CGE, ſimilia inter ſe, & </s>
            <s xml:id="echoid-s14187" xml:space="preserve">Iſoperimetra ſimul prioribus triangulis
              <lb/>
            ſimul. </s>
            <s xml:id="echoid-s14188" xml:space="preserve">Dico duo triãgula AFC, CGE, ſimul maiora eſſe duobus triangulis ABC,
              <lb/>
            CDE, ſimul. </s>
            <s xml:id="echoid-s14189" xml:space="preserve">Ponantur enim A C, C E, ſecundum lineam rectam vnam; </s>
            <s xml:id="echoid-s14190" xml:space="preserve"/>
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