Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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            <s xml:id="echoid-s4562" xml:space="preserve">
              <pb o="94" file="130" n="131" rhead="Comment. in I. Cap. Sphæræ"/>
            A B, B C, proxima inæqualia. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">Ducta igitur recta A C, ſi conſtituatur ſuper
              <lb/>
            A C, (per 7. </s>
            <s xml:id="echoid-s4564" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">huius) triangulum Iſoſceles A G C, quod ſit iſoperime-
              <lb/>
              <figure xlink:label="fig-130-01" xlink:href="fig-130-01a" number="32">
                <image file="130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/130-01"/>
              </figure>
            trum triangulo A B C, erit to-
              <lb/>
            ta figura A G C D E F, iſoperime
              <lb/>
            tra figuræ A B C D E F. </s>
            <s xml:id="echoid-s4566" xml:space="preserve">Ft quia
              <lb/>
            triangulum A G C, maius eſt
              <lb/>
            (per 8. </s>
            <s xml:id="echoid-s4567" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4568" xml:space="preserve">huius) triangulo
              <lb/>
            A B C; </s>
            <s xml:id="echoid-s4569" xml:space="preserve">ſi addatur commune po-
              <lb/>
            lygonum A C D E F, erit figu-
              <lb/>
            ra A G C D E F, maior quàm
              <lb/>
            figura A B C D E F, quod eſt
              <lb/>
            contrarium hypotheſi. </s>
            <s xml:id="echoid-s4570" xml:space="preserve">Non er-
              <lb/>
            go inæqualia ſunt latera A B,
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            B C, ſed æqualia. </s>
            <s xml:id="echoid-s4571" xml:space="preserve">Eademq́ue ra-
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            tione oſtendemus, latera proxi-
              <lb/>
            ma B C, C D; </s>
            <s xml:id="echoid-s4572" xml:space="preserve">Itẽ proxima C D,
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            D E; </s>
            <s xml:id="echoid-s4573" xml:space="preserve">nec non & </s>
            <s xml:id="echoid-s4574" xml:space="preserve">reliqua proxi-
              <lb/>
            ma deinceps æqualia eſſe. </s>
            <s xml:id="echoid-s4575" xml:space="preserve">Ma-
              <lb/>
            xima igitur figura inter ſibi iſo-
              <lb/>
            perimetras æqualia numero lar
              <unsure/>
            e-
              <lb/>
            ra habentes æquilatera eſt, quod
              <lb/>
            eſt primum.</s>
            <s xml:id="echoid-s4576" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4577" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde, ſi fieri poteſt, figu
              <lb/>
            ra A B C D E F, æquilatera qui
              <lb/>
            dem, nt iam demonſtratum eſt,
              <lb/>
            at non æquiangula, ſed anguli
              <lb/>
            B, D, non proximi inæquales
              <lb/>
            ſint, maiorq́ue angulus B, quàm
              <lb/>
            angulus D. </s>
            <s xml:id="echoid-s4578" xml:space="preserve">Quoniã igitur demon
              <lb/>
            ſtratum eſt, figuram maximam eſ-
              <lb/>
            ſe æquilateram, erunt duo trian-
              <lb/>
            gula A B C, C D E, Iſoſcelia, ita ut duo latera A B, B C, æqualia ſint duo-
              <lb/>
            bus lateribus C D, D E; </s>
            <s xml:id="echoid-s4579" xml:space="preserve">Ponitur autem angulus B, maior angulo D, erit re-
              <lb/>
            cta A C, maior, quàm recta C E. </s>
            <s xml:id="echoid-s4580" xml:space="preserve">Si igitur conſtituantur ſuper baſes A C, C E,
              <lb/>
              <note position="left" xlink:label="note-130-01" xlink:href="note-130-01a" xml:space="preserve">24. primi.</note>
            (per 10. </s>
            <s xml:id="echoid-s4581" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4582" xml:space="preserve">huius) alia duo triangula Iſoſcelia A G C, C H E, ſimilia in
              <lb/>
            ter ſe, & </s>
            <s xml:id="echoid-s4583" xml:space="preserve">Iſoperimetra triangulis A B C, C D E, erunt triangula A G C, C H E,
              <lb/>
            utraq. </s>
            <s xml:id="echoid-s4584" xml:space="preserve">ſimnl (per præcedentẽ propoſ.) </s>
            <s xml:id="echoid-s4585" xml:space="preserve">maiora triangulis A B C, C D E, utriſq. </s>
            <s xml:id="echoid-s4586" xml:space="preserve">ſi
              <lb/>
            mul. </s>
            <s xml:id="echoid-s4587" xml:space="preserve">Si igitur addatur cõmune polygonũ A C EF, erit figura AGCHEF, maior
              <lb/>
            quàm figura ABCDEF, qđ cũ hypotheſi pugnat, quòd hæc omniũ maxima po-
              <lb/>
            natur. </s>
            <s xml:id="echoid-s4588" xml:space="preserve">Nõ ergo inæquales ſunt anguli B, D, ſed æquales. </s>
            <s xml:id="echoid-s4589" xml:space="preserve">Eadẽq́; </s>
            <s xml:id="echoid-s4590" xml:space="preserve">ratione oſten-
              <lb/>
            demus, angulos non proximos C, E, ęquales eſſe, & </s>
            <s xml:id="echoid-s4591" xml:space="preserve">binos alios quoſuis non
              <lb/>
            proximos. </s>
            <s xml:id="echoid-s4592" xml:space="preserve">Ex quo eſficitur, totam figutam æquiangulam eſſe, nempe proximos
              <lb/>
            etiam augulos inter ſe eſſe æquales. </s>
            <s xml:id="echoid-s4593" xml:space="preserve">Si enim v.</s>
            <s xml:id="echoid-s4594" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4595" xml:space="preserve">angulus B, non dicatur æqua-
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            lis angulo C; </s>
            <s xml:id="echoid-s4596" xml:space="preserve">cum angulus C, æqualis ſit non proximo angulo E; </s>
            <s xml:id="echoid-s4597" xml:space="preserve">erit quo-
              <lb/>
            que angulus B, angulo E, non æqualis, quod abſurdum eſt. </s>
            <s xml:id="echoid-s4598" xml:space="preserve">Bini enim anguli
              <lb/>
            non proximi inte ſe æquales ſunt, ut oſtendimus. </s>
            <s xml:id="echoid-s4599" xml:space="preserve">Maxima ergo figura inter ſi
              <lb/>
            bi Iſoperimetras ęqualia numero latera habentes non ſolum æquilatera,
              <lb/>
            ſed & </s>
            <s xml:id="echoid-s4600" xml:space="preserve">æquiangula eſt. </s>
            <s xml:id="echoid-s4601" xml:space="preserve">Quocirca Iſoperimetrarum figurarum latera </s>
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