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

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          <p>
            <s xml:id="echoid-s18778" xml:space="preserve">
              <pb o="510" file="522" n="522" rhead=""/>
            _& </s>
            <s xml:id="echoid-s18779" xml:space="preserve">arcu_
              <emph style="sc">BD</emph>
            , _inuento indagetur angulus oppoſitus_ BA:</s>
            <s xml:id="echoid-s18780" xml:space="preserve">D _qui duplicatus offeres_
              <lb/>
            _totum_
              <emph style="sc">BA</emph>
            C, _quæſitum._</s>
            <s xml:id="echoid-s18781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18782" xml:space="preserve">IN hoc porro caſu non poteſt datus arcus AB, eſſe quadrans.</s>
            <s xml:id="echoid-s18783" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18784" xml:space="preserve">22. </s>
            <s xml:id="echoid-s18785" xml:space="preserve">DATIS duobus arcubus trianguli non
              <lb/>
              <note position="left" xlink:label="note-522-01" xlink:href="note-522-01a" xml:space="preserve">Quætũtur
                <lb/>
              luo angu-
                <lb/>
              li cum vno
                <lb/>
              ercu.</note>
            rectanguli, cum angulo, qui alteri eorum
              <lb/>
            opponitur, reliquos angulos, cum reliquo
              <lb/>
            arcu ſcrutari: </s>
            <s xml:id="echoid-s18786" xml:space="preserve">ſi modo conſter, num angu-
              <lb/>
            lus alteri arcui dato oppoſitus acutus ſit, aut
              <lb/>
            obtuſus.</s>
            <s xml:id="echoid-s18787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18788" xml:space="preserve">SINT in triangulo ABC, dati duo arcus AB, AC, cum angulo B, qui
              <lb/>
              <note position="left" xlink:label="note-522-02" xlink:href="note-522-02a" xml:space="preserve">Quãdo da-
                <lb/>
              ti duo ar-
                <lb/>
              cus sũt inę
                <lb/>
              quales, &
                <lb/>
              neuter eo-
                <lb/>
              rum qua-
                <lb/>
              drans.</note>
            arcui AC, opponitur: </s>
            <s xml:id="echoid-s18789" xml:space="preserve">ſint autem primum illi arcus inæquales, & </s>
            <s xml:id="echoid-s18790" xml:space="preserve">neuter qua-
              <lb/>
            drans, conſtetq́; </s>
            <s xml:id="echoid-s18791" xml:space="preserve">præterea ſpecies anguli C, alteri arcui dato AB, oppoſiti.
              <lb/>
            </s>
            <s xml:id="echoid-s18792" xml:space="preserve">Ducatur ex angulo A, à datis arcubus comprehenſo ad arcum BC, arcus per-
              <lb/>
              <figure xlink:label="fig-522-01" xlink:href="fig-522-01a" number="370">
                <image file="522-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/522-01"/>
              </figure>
            pendicularis, qui intra triangulum cadet, ſi
              <lb/>
            vterque angulus B, C, ſit acutus, vel obtu-
              <lb/>
            ſus; </s>
            <s xml:id="echoid-s18793" xml:space="preserve">extra vero, ſi vnus acutus ſit, & </s>
            <s xml:id="echoid-s18794" xml:space="preserve">alter ob-
              <lb/>
              <note position="left" xlink:label="note-522-03" xlink:href="note-522-03a" xml:space="preserve">Propoſ. 67.
                <lb/>
              triãg. ſphęr.</note>
            tuſus. </s>
            <s xml:id="echoid-s18795" xml:space="preserve">Conſtat autem, an vterque angulus
              <lb/>
            acutus ſit, obtuſusve, an non; </s>
            <s xml:id="echoid-s18796" xml:space="preserve">quia angulus
              <lb/>
            B, datus eſt, cum ſpecie anguli C. </s>
            <s xml:id="echoid-s18797" xml:space="preserve">inquiratur
              <lb/>
            ergo, per problema 2. </s>
            <s xml:id="echoid-s18798" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18799" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18800" xml:space="preserve">ex dato
              <lb/>
            arcu AB, angulum rectum D, ſubtendente, & </s>
            <s xml:id="echoid-s18801" xml:space="preserve">
              <lb/>
            angulo dato B, arcus oppoſitus AD. </s>
            <s xml:id="echoid-s18802" xml:space="preserve">Et hinc,
              <lb/>
            per problema 8. </s>
            <s xml:id="echoid-s18803" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18804" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18805" xml:space="preserve">ex eodem ar-
              <lb/>
            cu dato AB, & </s>
            <s xml:id="echoid-s18806" xml:space="preserve">arcu inuento AD, eliciatur
              <lb/>
            tertius arcus BD. </s>
            <s xml:id="echoid-s18807" xml:space="preserve">Hinc rurſus, per proble-
              <lb/>
            ma 1. </s>
            <s xml:id="echoid-s18808" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18809" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18810" xml:space="preserve">ex dato arcu AB, rectum
              <lb/>
            angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18811" xml:space="preserve">arcu BD, inuen-
              <lb/>
            to reperiatur angulus BAD, arcui BD, oppoſitus: </s>
            <s xml:id="echoid-s18812" xml:space="preserve">Et per problema 13. </s>
            <s xml:id="echoid-s18813" xml:space="preserve">triãg.
              <lb/>
            </s>
            <s xml:id="echoid-s18814" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18815" xml:space="preserve">ex dato arcu AC, rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18816" xml:space="preserve">arcu AD, in-
              <lb/>
            uento eruatur angulus CAD, à dictis arcubus comprehenſus. </s>
            <s xml:id="echoid-s18817" xml:space="preserve">Nam hic an-
              <lb/>
            gulus adiectus ad inuentum angulum BAD, vel ab eodem ſubtractus, (prout
              <lb/>
            arcus AD, cadit intra, vel extra triangulum) dabit quæſitum angulum BAC. </s>
            <s xml:id="echoid-s18818" xml:space="preserve">
              <lb/>
            Inueniatur præterea, per problema 15. </s>
            <s xml:id="echoid-s18819" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18820" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18821" xml:space="preserve">ex dato arcu AC, re-
              <lb/>
            ctum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18822" xml:space="preserve">inuento angulo CAD, angulus ACD: </s>
            <s xml:id="echoid-s18823" xml:space="preserve">qui
              <lb/>
            erit is, quem quærimus, ſi arcus AD, intra triangulum cadit, ſi vero extra,
              <lb/>
            ablatus ex duobus rectis dabit angulum ACB, quæſitum: </s>
            <s xml:id="echoid-s18824" xml:space="preserve">ſicq́; </s>
            <s xml:id="echoid-s18825" xml:space="preserve">duo reliqui
              <lb/>
            anguli BAC, ACB, erunt cogniti.</s>
            <s xml:id="echoid-s18826" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18827" xml:space="preserve">DEINDE, per problema 8. </s>
            <s xml:id="echoid-s18828" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18829" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18830" xml:space="preserve">ex dato arcu AC, angulum
              <lb/>
            rectum D, ſubtendente, & </s>
            <s xml:id="echoid-s18831" xml:space="preserve">inuento arcu AD, inquira tur arcus CD. </s>
            <s xml:id="echoid-s18832" xml:space="preserve">Hic enim
              <lb/>
            additus arcui inuento BD, vel ab eodem ſubductus (prout arcus AD, intra
              <lb/>
            triangulum cadit, vel extra) notum offeret quæſitum arcum BC.</s>
            <s xml:id="echoid-s18833" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18834" xml:space="preserve">IN hoc porro caſu, nullus arcuum AD, BD, CD; </s>
            <s xml:id="echoid-s18835" xml:space="preserve">quadrans eſſe poteſt.</s>
            <s xml:id="echoid-s18836" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18837" xml:space="preserve">PER _ſolos ſinus ita erit agendum. </s>
            <s xml:id="echoid-s18838" xml:space="preserve">Per problema_ 2. </s>
            <s xml:id="echoid-s18839" xml:space="preserve">_triang. </s>
            <s xml:id="echoid-s18840" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18841" xml:space="preserve">ex dato </s>
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