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

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        <div xml:id="echoid-div1366" type="section" level="1" n="615">
          <head xml:id="echoid-head650" xml:space="preserve">PROBL. 8. PROP. 67.</head>
          <p>
            <s xml:id="echoid-s17363" xml:space="preserve">DATIS duobus arcubus trianguli ſphærici
              <lb/>
            non rectanguli, cum angulo, qui alteri eorum op-
              <lb/>
            ponitur; </s>
            <s xml:id="echoid-s17364" xml:space="preserve">reliquos angulos, cum reliquo arcu inue-
              <lb/>
            nire. </s>
            <s xml:id="echoid-s17365" xml:space="preserve">Oportet autem conſtare, num angulus alte-
              <lb/>
            ri arcui dato oppoſitus acutus ſit, an obtuſus.</s>
            <s xml:id="echoid-s17366" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17367" xml:space="preserve">IN triangulo ſphærico non rectangulo ABC, dati ſint duo arcus AB, AC,
              <lb/>
            cum angulo B, qui arcui AC, opponitur,
              <lb/>
              <note position="left" xlink:label="note-492-01" xlink:href="note-492-01a" xml:space="preserve">Quando
                <lb/>
              aeuter da-
                <lb/>
              torũ arcuũ
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              inæqualiũ
                <lb/>
              oſt quadrás.</note>
              <figure xlink:label="fig-492-01" xlink:href="fig-492-01a" number="354">
                <image file="492-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/492-01"/>
              </figure>
            conſtetq́;</s>
            <s xml:id="echoid-s17368" xml:space="preserve">, an angulus C, acutus ſit, an obtu-
              <lb/>
            ſus. </s>
            <s xml:id="echoid-s17369" xml:space="preserve">Oportet ex his & </s>
            <s xml:id="echoid-s17370" xml:space="preserve">reliquos angulos C,
              <lb/>
            BAC, & </s>
            <s xml:id="echoid-s17371" xml:space="preserve">reliquum arcum BC, ſcrutari. </s>
            <s xml:id="echoid-s17372" xml:space="preserve">Sint
              <lb/>
            primum dati duo arcus AB, AC, inæquales, & </s>
            <s xml:id="echoid-s17373" xml:space="preserve">
              <lb/>
            neuter eorum quadrans. </s>
            <s xml:id="echoid-s17374" xml:space="preserve">Ducantur ab angulo
              <lb/>
            A, tertio arcui oppoſito ad ipſum arcum ter-
              <lb/>
            tium BC, arcus perpendicularis AD: </s>
            <s xml:id="echoid-s17375" xml:space="preserve">qui in-
              <lb/>
            tra triangulum cadet, ſi vterque angulus B,
              <lb/>
              <note position="left" xlink:label="note-492-02" xlink:href="note-492-02a" xml:space="preserve">57. huius.</note>
            C, acutus eſt, vel obtuſus; </s>
            <s xml:id="echoid-s17376" xml:space="preserve">extra vero, ſi vnus
              <lb/>
            acutus, & </s>
            <s xml:id="echoid-s17377" xml:space="preserve">alter obtuſus fuerit: </s>
            <s xml:id="echoid-s17378" xml:space="preserve">conſtat autem
              <lb/>
            ex datis, an vterque angulus acutus ſit, obtu-
              <lb/>
            ſusve, an vnus acutus, & </s>
            <s xml:id="echoid-s17379" xml:space="preserve">obtuſus alter; </s>
            <s xml:id="echoid-s17380" xml:space="preserve">cum
              <lb/>
            datus ſit angulus B, cum ſpecie anguli C. </s>
            <s xml:id="echoid-s17381" xml:space="preserve">Ita-
              <lb/>
            que quoniam in triangulo ABD, rectum habente angulum D, datus eſt arcus
              <lb/>
              <note position="left" xlink:label="note-492-03" xlink:href="note-492-03a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            AB, angulo recto oppoſitus, cum angulo B; </s>
            <s xml:id="echoid-s17382" xml:space="preserve">datus etiam erit arcus AD, circa
              <lb/>
            rectum angulum dato angulo B, oppoſitus. </s>
            <s xml:id="echoid-s17383" xml:space="preserve">Hinc in eodem triangulo ABD,
              <lb/>
            quia datus eſt arcus AB, recto angulo oppoſitus, & </s>
            <s xml:id="echoid-s17384" xml:space="preserve">inſuper arcus AD, circa
              <lb/>
              <note position="left" xlink:label="note-492-04" xlink:href="note-492-04a" xml:space="preserve">Schol. 43.
                <lb/>
              vel 53. huiꝰ.</note>
            eundem angulum rectum:</s>
            <s xml:id="echoid-s17385" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17386" xml:space="preserve">VEL, quia datus eſt arcus AB, recto angulo op-
              <lb/>
              <note position="left" xlink:label="note-492-05" xlink:href="note-492-05a" xml:space="preserve">Schol. 45.
                <lb/>
              huius.</note>
            poſitus, & </s>
            <s xml:id="echoid-s17387" xml:space="preserve">præterea angulus non rectus B:</s>
            <s xml:id="echoid-s17388" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17389" xml:space="preserve">VEL denique, quia datus eſt arcus AD, circa an-
              <lb/>
              <note position="left" xlink:label="note-492-06" xlink:href="note-492-06a" xml:space="preserve">Schol 49.
                <lb/>
              vel 44. huiꝰ.</note>
            gulum rectum, cum angulo B, oppoſito; </s>
            <s xml:id="echoid-s17390" xml:space="preserve">conſtatq́; </s>
            <s xml:id="echoid-s17391" xml:space="preserve">ſpe-
              <lb/>
            cies præterea arcus BD. </s>
            <s xml:id="echoid-s17392" xml:space="preserve">Nam ſi AB, datus fuerit mi-
              <lb/>
            nor quadrante; </s>
            <s xml:id="echoid-s17393" xml:space="preserve">ſi quidem & </s>
            <s xml:id="echoid-s17394" xml:space="preserve">AD, inuentus minor ſit,
              <lb/>
            erit quoque BD, minor; </s>
            <s xml:id="echoid-s17395" xml:space="preserve">ſi autem maior, maior. </s>
            <s xml:id="echoid-s17396" xml:space="preserve">At ſi
              <lb/>
              <note position="left" xlink:label="note-492-07" xlink:href="note-492-07a" xml:space="preserve">36. huius.</note>
            AB, datus fuerit maior quadrante; </s>
            <s xml:id="echoid-s17397" xml:space="preserve">ſi quidem & </s>
            <s xml:id="echoid-s17398" xml:space="preserve">AD,
              <lb/>
            inuentus maior ſit, erit BD, minor; </s>
            <s xml:id="echoid-s17399" xml:space="preserve">ſi autem AD, mi-
              <lb/>
            nor ſit, erit BD, maior;</s>
            <s xml:id="echoid-s17400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17401" xml:space="preserve">cognitus etiam erit, ex adductis ſcholijs in margine, alter arcus BD, circa an-
              <lb/>
            gulum rectum. </s>
            <s xml:id="echoid-s17402" xml:space="preserve">Hinc rurſus in eodem triangulo ABD, quia datus eſt arcus
              <lb/>
              <note position="left" xlink:label="note-492-08" xlink:href="note-492-08a" xml:space="preserve">Schol. 41.
                <lb/>
              vel 55. huiꝰ.</note>
            AB, angulo recto oppoſitus, cum arcu BD, circa eundem rectum angulum:</s>
            <s xml:id="echoid-s17403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17404" xml:space="preserve">VEL, quia datus eſt vterque arcus AD, BD, cir-
              <lb/>
              <note position="left" xlink:label="note-492-09" xlink:href="note-492-09a" xml:space="preserve">Schol 44.
                <lb/>
              vel 48. huiꝰ.</note>
            ca angulum rectum:</s>
            <s xml:id="echoid-s17405" xml:space="preserve"/>
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