Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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              <pb o="95" file="131" n="132" rhead="Ioan. de Sacro Boſco."/>
            @o æqualia habentium maxima & </s>
            <s xml:id="echoid-s4602" xml:space="preserve">æquilatera eſt, & </s>
            <s xml:id="echoid-s4603" xml:space="preserve">æquiangula. </s>
            <s xml:id="echoid-s4604" xml:space="preserve">quod demon-
              <lb/>
            ſtrandum erat.</s>
            <s xml:id="echoid-s4605" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div250" type="section" level="1" n="86">
          <head xml:id="echoid-head90" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4606" xml:space="preserve">
              <emph style="sc">Circa</emph>
            demonſtrationem prioris partis huius propoſ. </s>
            <s xml:id="echoid-s4607" xml:space="preserve">obſeruandum efl, acci-
              <lb/>
              <note position="right" xlink:label="note-131-01" xlink:href="note-131-01a" xml:space="preserve">Quæ obſer-
                <lb/>
              uanda ſint
                <lb/>
              in demon-
                <lb/>
              ſtratiõe hu-
                <lb/>
              ius propoſ.</note>
            pienda eſſe duo latrea inęqualia proxima inter ſe, ita vt angulum conſtituant, nul-
              <lb/>
            lumq́ue aliud inter ea interponatur, qualia ſunt latera accepta A B, B C, angulum
              <lb/>
            B, efficientia. </s>
            <s xml:id="echoid-s4608" xml:space="preserve">Hac enim ratione, ducta recta A C, factum erit triangulum A B C,
              <lb/>
            cuius duo latera A B, B C, inæquælia ſunt, vt in demonſtratione aſſumebatur. </s>
            <s xml:id="echoid-s4609" xml:space="preserve">Ne
              <lb/>
            que vero dubitare quis poterit, in figuranon æquilatera, qualis ponitur A B C
              <lb/>
            D E F, accipi poſſe duo latera proxima inæqualia. </s>
            <s xml:id="echoid-s4610" xml:space="preserve">Nam ſi quis dicat latera A
              <emph style="sc">B</emph>
            ,
              <lb/>
            B C, eſſe æqualia, ſumemus latera A B, A F, quæ ſi dicantur etiam æqualia eſſe,
              <lb/>
            accipiemus A F, F E: </s>
            <s xml:id="echoid-s4611" xml:space="preserve">Et ſi hęc adhuc æqualia eſſe dicantur, capiemus E F, E D: </s>
            <s xml:id="echoid-s4612" xml:space="preserve">& </s>
            <s xml:id="echoid-s4613" xml:space="preserve">ſic de-
              <lb/>
            inceps progrediemur, donec ad duo latera proxima inæqualia ueniamus, quæ angulum
              <lb/>
            Conſtituant. </s>
            <s xml:id="echoid-s4614" xml:space="preserve">Neceſſarium autem ad duo huiuſmodi latera perueniemus: </s>
            <s xml:id="echoid-s4615" xml:space="preserve">aliàs figura eſ-
              <lb/>
            ſet æquilatera, quod non conceditur.</s>
            <s xml:id="echoid-s4616" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4617" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            vero ad poſterioris partis demonſtrationem attinet, aduertendum eſt,
              <lb/>
            in figuris multilateris accipiendos eſſe duos angulos inæquales non proximos inter ſe
              <lb/>
            ita vt inter ipſos vnus vel plures anguli interponantur, quales ſunt anguli accepti
              <lb/>
            B, D, inter quos ponitur angulus C. </s>
            <s xml:id="echoid-s4618" xml:space="preserve">Hac enim ratione duæ rectæ A C, C E, dictos
              <lb/>
            augulos ſubtendentes ſe mutuo non interſecabunt, conſtituenturq́ue duæ figuræ A C-
              <lb/>
            C D E F, A G C H E F, ex additione communis figuræ A C E E, ad triangula ſu-
              <lb/>
            pra baſes AC, C E, conſiructa: </s>
            <s xml:id="echoid-s4619" xml:space="preserve">quod non contingeret, ſi duo anguli inæquales pro-
              <lb/>
            ximi inter ſe ſumerentur, vt conſtat. </s>
            <s xml:id="echoid-s4620" xml:space="preserve">Non eſt autem in dubinm vertendum, an ta-
              <lb/>
            les duo anguli poſſint accipi. </s>
            <s xml:id="echoid-s4621" xml:space="preserve">In omni enim figura multilatera non æquiangula ne-
              <lb/>
            ceſſario erunt aliqui duo anguli non proximi inter ſe inæquales. </s>
            <s xml:id="echoid-s4622" xml:space="preserve">Nam in propoſitæ
              <unsure/>
              <lb/>
            figura A B k D E F, comparabimus angulum B, cum omnibus non proximis angulis
              <lb/>
            D, E, F, qui neceſſario duo erunt in pentagono, in hexagono uero tres, & </s>
            <s xml:id="echoid-s4623" xml:space="preserve">ita dein-
              <lb/>
            ceps. </s>
            <s xml:id="echoid-s4624" xml:space="preserve">Quod ſi uni alicui eorum fuerit inæqualis, habebimus iam duos angulos non
              <lb/>
            proximos inter ſe inæquales, nempe angulum B, & </s>
            <s xml:id="echoid-s4625" xml:space="preserve">illum, cui inæqualis eſt: </s>
            <s xml:id="echoid-s4626" xml:space="preserve">Si vero
              <lb/>
            omnibus dicatur æqualis, erit tunc angulus B, ſaltem alteri proximorum inæqualis,
              <lb/>
            aliàs figura eßet æquiangula. </s>
            <s xml:id="echoid-s4627" xml:space="preserve">Si ergo inæqualis fuerit angulo A, erit angulus A,
              <lb/>
            tam angulo E, quàm angulo D, non proximo inæqualis, cum utriuis horum æqualis
              <lb/>
            ponatur angulus B: </s>
            <s xml:id="echoid-s4628" xml:space="preserve">Si uero inæqualis fuerit angulo C, erit angulus K, tam angule
              <unsure/>
              <lb/>
            E, quàm angulo F, non proximo inæqualis, quòd vtrius horum angulus B, ponatur
              <lb/>
            æqualis.</s>
            <s xml:id="echoid-s4629" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4630" xml:space="preserve">
              <emph style="sc">Sed</emph>
            quoniam propoſitio hæc demonſtrata tantum eſt in figuris multilateris, vt
              <lb/>
            ex ijsconſiat, quæ proxi-
              <lb/>
              <figure xlink:label="fig-131-01" xlink:href="fig-131-01a" number="33">
                <image file="131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/131-01"/>
              </figure>
            me de duobus angulis non
              <lb/>
            proximis inæqualibus di-
              <lb/>
            ximus: </s>
            <s xml:id="echoid-s4631" xml:space="preserve">In triangulis enim,
              <lb/>
            & </s>
            <s xml:id="echoid-s4632" xml:space="preserve">quadrilateris figuris
              <lb/>
            æquilateris anguli eiuſmo-
              <lb/>
            di reperiri non poſſunt,
              <lb/>
            cum in triangulis æquila-
              <lb/>
            teris omnes anguli ſint æ-
              <lb/>
            quales, vt ex coroll. </s>
            <s xml:id="echoid-s4633" xml:space="preserve">ꝓpoſ.</s>
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