Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s14332" xml:space="preserve">
              <pb o="305" file="335" n="335" rhead="LIBER SEPTIMVS."/>
            lio propoſ. </s>
            <s xml:id="echoid-s14333" xml:space="preserve">34. </s>
            <s xml:id="echoid-s14334" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14335" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14336" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s14337" xml:space="preserve">oſtendimus) ſinguli oppoſiti inter ſeſint
              <note symbol="a" position="right" xlink:label="note-335-01" xlink:href="note-335-01a" xml:space="preserve">34. primi.</note>
            les: </s>
            <s xml:id="echoid-s14338" xml:space="preserve">Idcirco totam hanc propoſitionem in triangulis, & </s>
            <s xml:id="echoid-s14339" xml:space="preserve">quadrilateris figuris ita
              <lb/>
              <figure xlink:label="fig-335-01" xlink:href="fig-335-01a" number="227">
                <image file="335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/335-01"/>
              </figure>
            demonſtrabimus. </s>
            <s xml:id="echoid-s14340" xml:space="preserve">Sit primum triangulum ABC, inter ſibi Iſoperimetra triangu-
              <lb/>
            la maximum. </s>
            <s xml:id="echoid-s14341" xml:space="preserve">Dico illud æquilaterum eſſe & </s>
            <s xml:id="echoid-s14342" xml:space="preserve">æquiangulum. </s>
            <s xml:id="echoid-s14343" xml:space="preserve">Si enim non eſt
              <lb/>
              <note symbol="b" position="right" xlink:label="note-335-02" xlink:href="note-335-02a" xml:space="preserve">7. hui{us}.</note>
            æquilaterum, ſed latera AB, BC, ſuntinæqualia, ſi ſuper baſem AC, conſtitua- tur triangulum Iſoſceles ADC, ita vt latera AD, DC, ſimul æqualia ſint lateri-
              <lb/>
            bus AB, BC, ſimul; </s>
            <s xml:id="echoid-s14344" xml:space="preserve">erunt triangula ABC, ADC, Iſoperimetra; </s>
            <s xml:id="echoid-s14345" xml:space="preserve"> atque
              <note symbol="c" position="right" xlink:label="note-335-03" xlink:href="note-335-03a" xml:space="preserve">8. hui{us}.</note>
            ADC, maius, quam ABC, quod eſt contra hypotheſim. </s>
            <s xml:id="echoid-s14346" xml:space="preserve">Non ergo inæqualia
              <lb/>
            ſunt latera AB, BC, ſed æqualia. </s>
            <s xml:id="echoid-s14347" xml:space="preserve">Eademque ratio eſt de cæteris. </s>
            <s xml:id="echoid-s14348" xml:space="preserve">Æquilaterum
              <lb/>
            ergo eſt triangulum ABC. </s>
            <s xml:id="echoid-s14349" xml:space="preserve">Igitur, ex coroll. </s>
            <s xml:id="echoid-s14350" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14351" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14352" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14353" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14354" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s14355" xml:space="preserve">& </s>
            <s xml:id="echoid-s14356" xml:space="preserve">æquian-
              <lb/>
            gulum eſt. </s>
            <s xml:id="echoid-s14357" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s14358" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14359" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            ſit quadrilaterum ABCD, inter omnia ſibi Iſoperimetra maxi-
              <lb/>
            mum. </s>
            <s xml:id="echoid-s14360" xml:space="preserve">Dico illud eſſe, & </s>
            <s xml:id="echoid-s14361" xml:space="preserve">æquilaterum, & </s>
            <s xml:id="echoid-s14362" xml:space="preserve">æquiangulum. </s>
            <s xml:id="echoid-s14363" xml:space="preserve">Si enim non eſt æqui-
              <lb/>
            laterum, ſint latera AB, BC, ſi fieri poteſt, inæqualia, ducaturq; </s>
            <s xml:id="echoid-s14364" xml:space="preserve">recta AC. </s>
            <s xml:id="echoid-s14365" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-335-04" xlink:href="note-335-04a" xml:space="preserve">7. hui{us}.</note>
            igitur ſuper AC, conſtituatur triangulum Iſoſceles, AEC, Iſoperimetrum trian-
              <lb/>
            gulo ABC; </s>
            <s xml:id="echoid-s14366" xml:space="preserve">erit triangulum AEC, maius triangulo ABC. </s>
            <s xml:id="echoid-s14367" xml:space="preserve">Addito ergo com-
              <lb/>
            muni triangulo ACD, erit quadrilaterum AECD, maius quadrilatero ABCD.</s>
            <s xml:id="echoid-s14368" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-335-05" xlink:href="note-335-05a" xml:space="preserve">8. hui{us}.</note>
            quod eſt contra hypotheſim, cum ABCD, maximum ponatur. </s>
            <s xml:id="echoid-s14369" xml:space="preserve">Non ergo inæ-
              <lb/>
            qualia ſunt latera AB, BC, ſed æqualia. </s>
            <s xml:id="echoid-s14370" xml:space="preserve">Eademque ratio eſt de cæteris. </s>
            <s xml:id="echoid-s14371" xml:space="preserve">Æqui-
              <lb/>
            latera ergo eſt figura ABCD.</s>
            <s xml:id="echoid-s14372" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14373" xml:space="preserve">
              <emph style="sc">Sit</emph>
            iam quadrilatera figura ABCD, omnium iſoperimetrarum maxima, æ-
              <lb/>
            quilatera, vt oſtenſum eſt, at non æquiangula, ſed anguli BAD, CDA, inæqua-
              <lb/>
            les ſint. </s>
            <s xml:id="echoid-s14374" xml:space="preserve">Quoniam igitur figura ABCD, cum ſit æquilatera, parallelogrammum
              <lb/>
            eſt, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14375" xml:space="preserve">34. </s>
            <s xml:id="echoid-s14376" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14377" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14378" xml:space="preserve">demonſtrauimus; </s>
            <s xml:id="echoid-s14379" xml:space="preserve">neuter que angulorum A,
              <lb/>
            D, rectus eſt; </s>
            <s xml:id="echoid-s14380" xml:space="preserve">(alias, cum ambo duobus rectis ſint æquales, eſſent ambo
              <note symbol="f" position="right" xlink:label="note-335-06" xlink:href="note-335-06a" xml:space="preserve">29. primi.</note>
            ſed vnus acutus, & </s>
            <s xml:id="echoid-s14381" xml:space="preserve">obtuſus alter: </s>
            <s xml:id="echoid-s14382" xml:space="preserve">ſi educantur ex A, & </s>
            <s xml:id="echoid-s14383" xml:space="preserve">D, duæ lineæ perpen-
              <lb/>
            diculares AH, DG, occurrentes lateri BC, in H, & </s>
            <s xml:id="echoid-s14384" xml:space="preserve">G; </s>
            <s xml:id="echoid-s14385" xml:space="preserve">erit quo que AHGD, pa-
              <lb/>
            rallelogrammum. </s>
            <s xml:id="echoid-s14386" xml:space="preserve"> Quia verò latera AB, DC, maiora ſunt lateribus AH, DG;</s>
            <s xml:id="echoid-s14387" xml:space="preserve">
              <note symbol="g" position="right" xlink:label="note-335-07" xlink:href="note-335-07a" xml:space="preserve">19. primi.</note>
            producantur hæc, vt fiant rectæ AE, DF, lateribus AB, DC, æquales, iungatur-
              <lb/>
            que recta EF. </s>
            <s xml:id="echoid-s14388" xml:space="preserve">Quo facto, erit figura AEFD, iſoperimetra parallelogrammo
              <lb/>
            ABCD; </s>
            <s xml:id="echoid-s14389" xml:space="preserve">cum latera AE, DF, lateribus AB, DC, æqualia ſint, latus verò AD,
              <lb/>
            commune, & </s>
            <s xml:id="echoid-s14390" xml:space="preserve">latus EF, lateri B C, æquale, quod vtrumque æquale ſit
              <note symbol="h" position="right" xlink:label="note-335-08" xlink:href="note-335-08a" xml:space="preserve">34. primi.</note>
            oppoſito AD. </s>
            <s xml:id="echoid-s14391" xml:space="preserve">Cum ergo figura AEFD, maior ſit parallelogrammo AHGD;
              <lb/>
            </s>
            <s xml:id="echoid-s14392" xml:space="preserve">
              <note symbol="i" position="right" xlink:label="note-335-09" xlink:href="note-335-09a" xml:space="preserve">35. primi.</note>
            hoc autem æquale ſit parallelogrammo ABCD; </s>
            <s xml:id="echoid-s14393" xml:space="preserve">erit quoque figura AEFD, maior parallelogrammo ABCD. </s>
            <s xml:id="echoid-s14394" xml:space="preserve">Quare cum eidem ſit iſoperimetra, non erit
              <lb/>
            ABCD, figura quadrilatera inter ſibi Iſoperimetras maxima. </s>
            <s xml:id="echoid-s14395" xml:space="preserve">quod eſt contra
              <lb/>
            hypotheſim. </s>
            <s xml:id="echoid-s14396" xml:space="preserve">Non ergo inæquales ſunt anguli BAD, CDA, ſed æquales: </s>
            <s xml:id="echoid-s14397" xml:space="preserve">at-
              <lb/>
              <note symbol="k" position="right" xlink:label="note-335-10" xlink:href="note-335-10a" xml:space="preserve">34. primi.</note>
            que adeò cum ABCD, ſit parallelogrammum, erunt anguli oppoſiti B, C, angulis D, A, æquales, proptereaque tota figura æquiangula erit, quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s14398" xml:space="preserve"/>
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