Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s14037" xml:space="preserve">
              <pb o="297" file="327" n="327" rhead="LIBER SEPTIMVS."/>
            Quamobrem rectangulum ſub GI, & </s>
            <s xml:id="echoid-s14038" xml:space="preserve">dimidio ambitu figuræ ABC, contentum,
              <lb/>
            maius erit rectangulo contento ſub HK, & </s>
            <s xml:id="echoid-s14039" xml:space="preserve">dimidio ambitu figuræ DEC, quiæ-
              <lb/>
            qualis ponitur dimidio ambitus figuræ A B C, Quocirca cumillud
              <note symbol="a" position="right" xlink:label="note-327-01" xlink:href="note-327-01a" xml:space="preserve">2. hui{us}.</note>
            oſtenſum ſit æquale figuræ ABC, hoc autem figuræ DEF, æquale; </s>
            <s xml:id="echoid-s14040" xml:space="preserve">maior quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s14041" xml:space="preserve">erit figura ABC, quàm figura DEF. </s>
            <s xml:id="echoid-s14042" xml:space="preserve">Iſoperimetrarum ergo figurarum regularium
              <lb/>
            maior eſt illa &</s>
            <s xml:id="echoid-s14043" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14044" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s14045" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Qua arte
            <lb/>
          triangulum
            <lb/>
          Iſoſcel{es} con-
            <lb/>
          ſtituatur Iſo-
            <lb/>
          perimetrum
            <lb/>
          cuiuis trian-
            <lb/>
          gulo non Iſo-
            <lb/>
          ſceli.</note>
        </div>
        <div xml:id="echoid-div856" type="section" level="1" n="297">
          <head xml:id="echoid-head324" xml:space="preserve">PROBL. 1. PROPOS. 7.</head>
          <p>
            <s xml:id="echoid-s14046" xml:space="preserve">PROPOSITO triangulo, cuius duo latera ſint inæqualia, ſupra re-
              <lb/>
            liquum latus triangulum priori Iſoperimetrum, ac duo habens latera
              <lb/>
            æqualia, deſcribere.</s>
            <s xml:id="echoid-s14047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14048" xml:space="preserve">
              <emph style="sc">Sit</emph>
            triangulum ABC, cuius duo latera AB, BC, ſintinæqualia, nempe AB,
              <lb/>
            maius, quam BC; </s>
            <s xml:id="echoid-s14049" xml:space="preserve">oporteat que ſupra AC, conſtruere triangulum Iſoſceles, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s14050" xml:space="preserve">Iſoperimetrum triangulo ABC. </s>
            <s xml:id="echoid-s14051" xml:space="preserve">Sumatur recta D E, æqualis duobus lateribus
              <lb/>
            AB, BC, ſimul, diuidaturque bifariam in F. </s>
            <s xml:id="echoid-s14052" xml:space="preserve">Et quoniam latera AB, BC, ſimul ma-
              <lb/>
            iora ſunt latere AC, erunt quoque DF, FE, ſimul, maiores quam linea A C. </s>
            <s xml:id="echoid-s14053" xml:space="preserve">At-
              <lb/>
              <note position="right" xlink:label="note-327-03" xlink:href="note-327-03a" xml:space="preserve">16. primi.</note>
            que ob id tres lineæ AC, DF, FE, ita ſeſe habebunt, vt quęlibet duæ ſintreliqua
              <lb/>
            maiores. </s>
            <s xml:id="echoid-s14054" xml:space="preserve">Si igitur ex ipſis conficiatur
              <note symbol="b" position="right" xlink:label="note-327-04" xlink:href="note-327-04a" xml:space="preserve">22. primi.</note>
              <figure xlink:label="fig-327-01" xlink:href="fig-327-01a" number="219">
                <image file="327-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/327-01"/>
              </figure>
            AGC, effectum erit, quod proponitur. </s>
            <s xml:id="echoid-s14055" xml:space="preserve">Erunt enim
              <lb/>
            latera A G, G C, & </s>
            <s xml:id="echoid-s14056" xml:space="preserve">inter ſe ęqualia, & </s>
            <s xml:id="echoid-s14057" xml:space="preserve">ſimul ſumpta
              <lb/>
            æqualia lateribus AB, BC, ſimul ſumptis: </s>
            <s xml:id="echoid-s14058" xml:space="preserve">Addito igi-
              <lb/>
            tur communi A C, erunt triangula ABC, AGC, Iſo-
              <lb/>
            perimetra. </s>
            <s xml:id="echoid-s14059" xml:space="preserve">Propoſito igitur triangulo, cuius duo la-
              <lb/>
            tera ſint inæqualia, ſupra reliquum latus triangulum,
              <lb/>
            &</s>
            <s xml:id="echoid-s14060" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14061" xml:space="preserve">deſcripſimus. </s>
            <s xml:id="echoid-s14062" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s14063" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div858" type="section" level="1" n="298">
          <head xml:id="echoid-head325" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s14064" xml:space="preserve">
              <emph style="sc">Cadet</emph>
            autem neceſſario punctum G, extra triangulum ABC: </s>
            <s xml:id="echoid-s14065" xml:space="preserve">Sinamque
              <lb/>
            caderet in latus AB, vtad punctum H, eſſet ducta recta HC, minor, quam
              <note symbol="c" position="right" xlink:label="note-327-05" xlink:href="note-327-05a" xml:space="preserve">20. primi.</note>
            BC, ſimul, & </s>
            <s xml:id="echoid-s14066" xml:space="preserve">obid triangulum AHC, non eſſet Iſoperimetrum triangulo ABC,
              <lb/>
            cuius contrarium ex conſtructione eſt demonſtratum. </s>
            <s xml:id="echoid-s14067" xml:space="preserve">Multo minus cadet pũ-
              <lb/>
            ctum G, intra triangulum ABC. </s>
            <s xml:id="echoid-s14068" xml:space="preserve">Quare extra cadet, quod eſt propoſitum.</s>
            <s xml:id="echoid-s14069" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div860" type="section" level="1" n="299">
          <head xml:id="echoid-head326" xml:space="preserve">THEOR. 7. PROPOS. 8.</head>
          <note position="right" xml:space="preserve">Iſoſcel{es} tri-
            <lb/>
          angulum ma-
            <lb/>
          i{us} eſt trian-
            <lb/>
          gulo ſibi Iſo-
            <lb/>
          perimetro non
            <lb/>
          Iſoſcele.</note>
          <p>
            <s xml:id="echoid-s14070" xml:space="preserve">DVORVM triangulorum Iſoperimetrorum eandem habentium ba-
              <lb/>
            ſim, quorum vnius duo latera ſint æqualia, alterius verò inæqualia;
              <lb/>
            </s>
            <s xml:id="echoid-s14071" xml:space="preserve">maius erit illud, cuius duo latera æqualia ſunt.</s>
            <s xml:id="echoid-s14072" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14073" xml:space="preserve">
              <emph style="sc">Esto</emph>
            triangulum ABC, cuius latus AB, maius ſit latere BC,
              <note symbol="d" position="right" xlink:label="note-327-07" xlink:href="note-327-07a" xml:space="preserve">7. hui{us}.</note>
            que ſuper baſim AC, triangulo ABC, triangulum Iſoperimetrum ADC, habens
              <lb/>
            latera AD, DC, æqualia & </s>
            <s xml:id="echoid-s14074" xml:space="preserve">inter ſe, & </s>
            <s xml:id="echoid-s14075" xml:space="preserve">lateribus AB, BC, ſimul ſumptis. </s>
            <s xml:id="echoid-s14076" xml:space="preserve">Dico </s>
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