Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres
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          <p>
            <s xml:id="echoid-s13028" xml:space="preserve">IN triangulo ſphærico ABC, ſint primum ſingula latera quadrante ma-
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            iora. </s>
            <s xml:id="echoid-s13029" xml:space="preserve">Dico tres angulos A, B, C, eſſe obtuſos. </s>
            <s xml:id="echoid-s13030" xml:space="preserve">Aut enim triangulum æquila-
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            terum eſt, aut Iſoſceles, aut Scalenum.</s>
            <s xml:id="echoid-s13031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13032" xml:space="preserve">SI æquilaterum, perſpicuum eſt, tres angulos eſſe obtuſos.</s>
            <s xml:id="echoid-s13033" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Corollar.
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          25. huius.</note>
          <p>
            <s xml:id="echoid-s13034" xml:space="preserve">SI vero eſt Iſoſceles, habens duo latera AB,
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              <figure xlink:label="fig-395-01" xlink:href="fig-395-01a" number="234">
                <image file="395-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/395-01"/>
              </figure>
              <note position="right" xlink:label="note-395-02" xlink:href="note-395-02a" xml:space="preserve">25. huius.</note>
            AC, æqualia, erunt duo anguli B, C, ad baſim ob-
              <lb/>
              <note position="right" xlink:label="note-395-03" xlink:href="note-395-03a" xml:space="preserve">20. 1. Theod.</note>
            tuſi. </s>
            <s xml:id="echoid-s13035" xml:space="preserve">Sint quadrantes BD, BE, & </s>
            <s xml:id="echoid-s13036" xml:space="preserve">per puncta
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            D, E, arcus circuli maximi ducatur ED, conue-
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            nienscum arcu CA, protracto in F. </s>
            <s xml:id="echoid-s13037" xml:space="preserve">Quoniam igi-
              <lb/>
            tur BD, BE, quadrantes ſunt, & </s>
            <s xml:id="echoid-s13038" xml:space="preserve">angulus B, oſten
              <lb/>
              <note position="left" xlink:label="note-395-04" xlink:href="note-395-04a" xml:space="preserve">26. huius</note>
            ſus eſt obtuſus, erit DE, arcus quadrante maior,
              <lb/>
              <note position="right" xlink:label="note-395-05" xlink:href="note-395-05a" xml:space="preserve">25. huius.</note>
            & </s>
            <s xml:id="echoid-s13039" xml:space="preserve">anguli BDE, BED, recti: </s>
            <s xml:id="echoid-s13040" xml:space="preserve">Ponitur autem & </s>
            <s xml:id="echoid-s13041" xml:space="preserve">
              <lb/>
            arcus AC, quadrante maior. </s>
            <s xml:id="echoid-s13042" xml:space="preserve">Igitur arcus DE,
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            AC, ſimul ſemicirculo maiores ſunt; </s>
            <s xml:id="echoid-s13043" xml:space="preserve">ac propte-
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            rea arcus FD, FA, ſimul minores ſemicirculo, cum
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            arcus FE, FC, integro circulo ſimul ſint mino-
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            res; </s>
            <s xml:id="echoid-s13044" xml:space="preserve">cum vterque arcus minor ſit ſemicirculo. </s>
            <s xml:id="echoid-s13045" xml:space="preserve">An-
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              <note position="right" xlink:label="note-395-06" xlink:href="note-395-06a" xml:space="preserve">2. huius.</note>
            gulus igitur FDB, maior eſt angulo FAD: </s>
            <s xml:id="echoid-s13046" xml:space="preserve">Eſt autem angulus FDB, rectus;
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            </s>
            <s xml:id="echoid-s13047" xml:space="preserve">
              <note position="right" xlink:label="note-395-07" xlink:href="note-395-07a" xml:space="preserve">14. huius.</note>
            quòd anguli FDB, BDE, duobus rectis æquales ſint, & </s>
            <s xml:id="echoid-s13048" xml:space="preserve">BDE, rectus oſten-
              <lb/>
              <note position="right" xlink:label="note-395-08" xlink:href="note-395-08a" xml:space="preserve">5 huius.</note>
            ſus. </s>
            <s xml:id="echoid-s13049" xml:space="preserve">Ergo FAD, acutus eſt; </s>
            <s xml:id="echoid-s13050" xml:space="preserve">ac proinde, cum FAD, DAC, æquales ſint duo-
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              <note position="right" xlink:label="note-395-09" xlink:href="note-395-09a" xml:space="preserve">5. huius.</note>
            bus rectis, angulus BAC, obtuſus erit: </s>
            <s xml:id="echoid-s13051" xml:space="preserve">oſtenſi ſunt autem & </s>
            <s xml:id="echoid-s13052" xml:space="preserve">anguli B, C,
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            obtuſi. </s>
            <s xml:id="echoid-s13053" xml:space="preserve">Omnes ergo tres anguli A, B, C, obtuſi ſunt.</s>
            <s xml:id="echoid-s13054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13055" xml:space="preserve">SI denique triangulum ABC, eſt Scalenum, ſit latus AC, latere AB,
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            maius, & </s>
            <s xml:id="echoid-s13056" xml:space="preserve">abſcindatur arcus AD, arcui AB, æqualis; </s>
            <s xml:id="echoid-s13057" xml:space="preserve">eritq́ue adhuc arcus AD,
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            quadrante maior, quòd & </s>
            <s xml:id="echoid-s13058" xml:space="preserve">arcus AB, cui æqualis eſt, maior ponatur quadran
              <lb/>
              <note position="left" xlink:label="note-395-10" xlink:href="note-395-10a" xml:space="preserve">1. huius.</note>
            te. </s>
            <s xml:id="echoid-s13059" xml:space="preserve">Si igitur per puncta B, D, ducatur arcus BD, circuli maximi, erit vterq;
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            </s>
            <s xml:id="echoid-s13060" xml:space="preserve">
              <note position="right" xlink:label="note-395-11" xlink:href="note-395-11a" xml:space="preserve">20. 1 Theod.</note>
            angulus ADB, ABD, obtuſus. </s>
            <s xml:id="echoid-s13061" xml:space="preserve">Multo ergo ma-
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              <note position="right" xlink:label="note-395-12" xlink:href="note-395-12a" xml:space="preserve">25. huius.</note>
              <figure xlink:label="fig-395-02" xlink:href="fig-395-02a" number="235">
                <image file="395-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/395-02"/>
              </figure>
            gis obtuſus erit angulus ABC. </s>
            <s xml:id="echoid-s13062" xml:space="preserve">Sint quadrantes
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            BE, BF, & </s>
            <s xml:id="echoid-s13063" xml:space="preserve">per puncta E, F, ducatur arcus EF,
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              <note position="right" xlink:label="note-395-13" xlink:href="note-395-13a" xml:space="preserve">20. 1 Theod.</note>
            circuli maximi, coiens cum arcu CA, producto in
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            G. </s>
            <s xml:id="echoid-s13064" xml:space="preserve">Quoniã igitur BE, BF, quadrantes ſunt, erunt
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            anguli ad E, & </s>
            <s xml:id="echoid-s13065" xml:space="preserve">F, recti; </s>
            <s xml:id="echoid-s13066" xml:space="preserve">& </s>
            <s xml:id="echoid-s13067" xml:space="preserve">cum angulus EBF, oſten
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              <note position="right" xlink:label="note-395-14" xlink:href="note-395-14a" xml:space="preserve">25. huius.</note>
            ſus ſit obtuſus, erit arcus EF, quadrante maior:
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            </s>
            <s xml:id="echoid-s13068" xml:space="preserve">
              <note position="right" xlink:label="note-395-15" xlink:href="note-395-15a" xml:space="preserve">26. huius.</note>
            Ponitur autem & </s>
            <s xml:id="echoid-s13069" xml:space="preserve">arcus AC, quadrante maior.
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            </s>
            <s xml:id="echoid-s13070" xml:space="preserve">Igitur arcus EF, AC, ſimul ſemicirculo ſunt ma-
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            iores; </s>
            <s xml:id="echoid-s13071" xml:space="preserve">& </s>
            <s xml:id="echoid-s13072" xml:space="preserve">idcirco multo magis FG, CG, maiores
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            erũt ſemicirculo. </s>
            <s xml:id="echoid-s13073" xml:space="preserve">Angulus ergo BFG, quem oſten
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            dimus eſſe rectum, min or eſt angulo BCG; </s>
            <s xml:id="echoid-s13074" xml:space="preserve">ac pro-
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              <note position="right" xlink:label="note-395-16" xlink:href="note-395-16a" xml:space="preserve">14. huius.</note>
            pterea angulus C, obtuſus erit. </s>
            <s xml:id="echoid-s13075" xml:space="preserve">Et quoniam arcus
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            FG, CG, ſimul integro ſunt circulo minores;
              <lb/>
            </s>
            <s xml:id="echoid-s13076" xml:space="preserve">quòd vterque ſemicirculo min or ſit; </s>
            <s xml:id="echoid-s13077" xml:space="preserve">& </s>
            <s xml:id="echoid-s13078" xml:space="preserve">EF, AC,
              <lb/>
              <note position="right" xlink:label="note-395-17" xlink:href="note-395-17a" xml:space="preserve">2. huius.</note>
            ſimul ſemicirculo maiores; </s>
            <s xml:id="echoid-s13079" xml:space="preserve">eruntarcus GE, GA, ſimul ſemicirculo mino-
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            res; </s>
            <s xml:id="echoid-s13080" xml:space="preserve">ac proinde angulus GEB, maior erit angulo GAB. </s>
            <s xml:id="echoid-s13081" xml:space="preserve">Cum ergo angu-
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              <note position="right" xlink:label="note-395-18" xlink:href="note-395-18a" xml:space="preserve">14. huius.</note>
            lus GEB, rectus ſit, quòd duo anguli ad E, duobus ſint rectis æquales, & </s>
            <s xml:id="echoid-s13082" xml:space="preserve">an-
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              <note position="right" xlink:label="note-395-19" xlink:href="note-395-19a" xml:space="preserve">5. huius.</note>
            gulus BEF, oſtenſus ſit rectus; </s>
            <s xml:id="echoid-s13083" xml:space="preserve">erit angulus GAB, acutus. </s>
            <s xml:id="echoid-s13084" xml:space="preserve">Quapropter cum
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            GAB, BAC, ęquales ſint duobus rectis, erit BAC, obtuſus. </s>
            <s xml:id="echoid-s13085" xml:space="preserve">Suntautem duo
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              <note position="right" xlink:label="note-395-20" xlink:href="note-395-20a" xml:space="preserve">5. huius.</note>
            etiam anguli ABC, & </s>
            <s xml:id="echoid-s13086" xml:space="preserve">C, oſtenſi obtuſi. </s>
            <s xml:id="echoid-s13087" xml:space="preserve">Tres ergo anguli A, B, C, trianguli
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            ABC, obtuſi ſunt. </s>
            <s xml:id="echoid-s13088" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s13089" xml:space="preserve"/>
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