Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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          <p>
            <s xml:id="echoid-s17085" xml:space="preserve">
              <pb o="475" file="487" n="487" rhead=""/>
            cus reliqui iam noti facti ſunt. </s>
            <s xml:id="echoid-s17086" xml:space="preserve">Rurſus quia in eodem triangulo datus eſt, per
              <lb/>
              <note position="right" xlink:label="note-487-01" xlink:href="note-487-01a" xml:space="preserve">Schol. 41.
                <lb/>
              vel 55. huiꝰ.</note>
            inuentionem, arcus AB, recto angulo oppoſitus, cum arcu BD, circa re-
              <lb/>
            ctum angulum:
              <lb/>
            </s>
            <s xml:id="echoid-s17087" xml:space="preserve">VEL, quia datus eſt arcus BD, circa angulum re-
              <lb/>
              <note position="right" xlink:label="note-487-02" xlink:href="note-487-02a" xml:space="preserve">Schol. 42.
                <lb/>
              huius.</note>
            ctum, vnà cum angulo non recto B, ei adiacente:
              <lb/>
            </s>
            <s xml:id="echoid-s17088" xml:space="preserve">VEL certe, quia datus eſt arcus AB, angulo recto
              <lb/>
              <note position="right" xlink:label="note-487-03" xlink:href="note-487-03a" xml:space="preserve">Schol. 47.
                <lb/>
              huius.</note>
            oppoſitus, cum angulo non recto B;
              <lb/>
            </s>
            <s xml:id="echoid-s17089" xml:space="preserve">reperietur, per ſcholia in margine adducta, angulus quoque BAD: </s>
            <s xml:id="echoid-s17090" xml:space="preserve">qui du-
              <lb/>
            plicatus totum angulum BAC, quæſitum efficiet cognitum.</s>
            <s xml:id="echoid-s17091" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17092" xml:space="preserve">SED per ſolos ſinus ita praxis ſe habet. </s>
            <s xml:id="echoid-s17093" xml:space="preserve">Per praxim problematis 2.
              <lb/>
            </s>
            <s xml:id="echoid-s17094" xml:space="preserve">
              <note position="right" xlink:label="note-487-04" xlink:href="note-487-04a" xml:space="preserve">Praxis per
                <lb/>
              ſolos ſinus,
                <lb/>
              quãdo duo
                <lb/>
              anguli dati
                <lb/>
              ſunt æqua-
                <lb/>
              les.</note>
            ſcholij propoſ. </s>
            <s xml:id="echoid-s17095" xml:space="preserve">42. </s>
            <s xml:id="echoid-s17096" xml:space="preserve">ex arcu BD, circa angulum recturn dato, & </s>
            <s xml:id="echoid-s17097" xml:space="preserve">ex angu-
              <lb/>
            lo B, ei adiacente dato, inueniemus angulum BAD, qui duplicatus totum
              <lb/>
            angulum quæſitum BAC, dabit. </s>
            <s xml:id="echoid-s17098" xml:space="preserve">Deinde per praxim problematis 3. </s>
            <s xml:id="echoid-s17099" xml:space="preserve">ſcho
              <lb/>
            lij propoſ. </s>
            <s xml:id="echoid-s17100" xml:space="preserve">41, ex arcu BD, circa rectum angulum, & </s>
            <s xml:id="echoid-s17101" xml:space="preserve">angulo BAD, op-
              <lb/>
            poſito iam inuento, eruemus ar cum AB, recto angulo oppoſitum, ideo{quam}
              <lb/>
            & </s>
            <s xml:id="echoid-s17102" xml:space="preserve">arcum AC, illi æqualem. </s>
            <s xml:id="echoid-s17103" xml:space="preserve">Nam præter data conſiat etiam ſpecies re-
              <lb/>
            liqui anguli B, dati non recti.</s>
            <s xml:id="echoid-s17104" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17105" xml:space="preserve">DATIS igitur duobus angulis trianguli ſphærici non rectanguli, vnà
              <lb/>
            cum arcu ipſis adiacente; </s>
            <s xml:id="echoid-s17106" xml:space="preserve">reliquos arcus, cum reliquo angulo ſcrutati ſumus.
              <lb/>
            </s>
            <s xml:id="echoid-s17107" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s17108" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1351" type="section" level="1" n="612">
          <head xml:id="echoid-head647" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s17109" xml:space="preserve">IN triangulis rectilineis non rectãgulis problema huic ſimile propoſitum non fuit:
              <lb/>
            </s>
            <s xml:id="echoid-s17110" xml:space="preserve">propterea quod, datis duobus angulis, datur & </s>
            <s xml:id="echoid-s17111" xml:space="preserve">tertius: </s>
            <s xml:id="echoid-s17112" xml:space="preserve">qui nimirum relinquitur,
              <lb/>
              <note position="right" xlink:label="note-487-05" xlink:href="note-487-05a" xml:space="preserve">32. primi.</note>
            ſi duo illi ex duobus rectis tollantur. </s>
            <s xml:id="echoid-s17113" xml:space="preserve">Quare cum vnum etiam latus detur, duo reli-
              <lb/>
            qua latera per propoſ. </s>
            <s xml:id="echoid-s17114" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17115" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s17116" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s17117" xml:space="preserve">efficientur nota.</s>
            <s xml:id="echoid-s17118" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1353" type="section" level="1" n="613">
          <head xml:id="echoid-head648" xml:space="preserve">PROBL. 7. PROPOS. 66.</head>
          <p>
            <s xml:id="echoid-s17119" xml:space="preserve">DATIS duobus angulis triãguli ſphærici non
              <lb/>
            rectanguli, cum arcu, qui alteri illorum opponi-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s17120" xml:space="preserve">reliquos arcus, cum reliquo angulo indagare.
              <lb/>
            </s>
            <s xml:id="echoid-s17121" xml:space="preserve">Oporter autem conſtare, num arcus alteri angulo
              <lb/>
            dato oppoſitus maior ſit quadrante, an minor, aut
              <lb/>
            certe quadrans.</s>
            <s xml:id="echoid-s17122" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quãdoduo
            <lb/>
          anguli dati
            <lb/>
          inæquales
            <lb/>
          sũt, & arcns
            <lb/>
          datꝰ qui v-
            <lb/>
          ni eorũ op-
            <lb/>
          ponitur, nõ
            <lb/>
          quadrans.</note>
          <p>
            <s xml:id="echoid-s17123" xml:space="preserve">IN triangulo ABC, non rectangulo dati ſint duo anguli B, C, cum ar-
              <lb/>
            cu AB, qui angulo C, opponitur, conſtetq́ue, an arcus AC, maior quadrante
              <lb/>
            ſit, minorve, an quadrans. </s>
            <s xml:id="echoid-s17124" xml:space="preserve">Oportet ex his & </s>
            <s xml:id="echoid-s17125" xml:space="preserve">reliquos arcus AC, BC, & </s>
            <s xml:id="echoid-s17126" xml:space="preserve">reliquũ
              <lb/>
            angulum BAC, inuenire. </s>
            <s xml:id="echoid-s17127" xml:space="preserve">Sint primum dati duo anguli B, C, inæquales, &</s>
            <s xml:id="echoid-s17128" xml:space="preserve"/>
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