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

Table of Notes

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            <s xml:id="echoid-s18616" xml:space="preserve">
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            inuenti erunt reliqui duo arcus. </s>
            <s xml:id="echoid-s18617" xml:space="preserve">Rurſus, per problema 5. </s>
            <s xml:id="echoid-s18618" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18619" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18620" xml:space="preserve">ex
              <lb/>
            eodem arcu BD, dimidio dati arcus BC, & </s>
            <s xml:id="echoid-s18621" xml:space="preserve">dato angulo B, adiacente reperia-
              <lb/>
            tur alter angulus non rectus BAD. </s>
            <s xml:id="echoid-s18622" xml:space="preserve">Hic namque duplicatus totum quæſi-
              <lb/>
            tum angulum BAC, dabit.</s>
            <s xml:id="echoid-s18623" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18624" xml:space="preserve">_PER_ ſolos ſinus ita operabimur. </s>
            <s xml:id="echoid-s18625" xml:space="preserve">_P_er problema _5._ </s>
            <s xml:id="echoid-s18626" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18627" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18628" xml:space="preserve">inueniatur ex
              <lb/>
              <note position="left" xlink:label="note-520-01" xlink:href="note-520-01a" xml:space="preserve">Per ſolos ſi-
                <lb/>
              nus, quãdo
                <lb/>
              duo anguli
                <lb/>
              dati sũt æ-
                <lb/>
              quales.</note>
            arcu _BD,_ dimidio dati arcus _BD,_ & </s>
            <s xml:id="echoid-s18629" xml:space="preserve">dato angulo _B,_ adiacente angulus _BAD:_ </s>
            <s xml:id="echoid-s18630" xml:space="preserve">qui
              <lb/>
            duplicatus dabit totum _
              <emph style="sc">BAc</emph>
            ,_ quæſitum. </s>
            <s xml:id="echoid-s18631" xml:space="preserve">_D_einde per _1._ </s>
            <s xml:id="echoid-s18632" xml:space="preserve">praxim problematis _3._ </s>
            <s xml:id="echoid-s18633" xml:space="preserve">triang.
              <lb/>
            </s>
            <s xml:id="echoid-s18634" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18635" xml:space="preserve">ex arcu _BD,_ dimidio dati arcus _BC,_ & </s>
            <s xml:id="echoid-s18636" xml:space="preserve">inuento angulo _BAD,_ oppoſito re-
              <lb/>
            periatur (cum præterea conſtet ſpecies alterius anguli _B,_ qui datus eſt) arcus _AB,_
              <lb/>
            recto angulo _D,_ oppoſitus: </s>
            <s xml:id="echoid-s18637" xml:space="preserve">cui æqualis eſt _AC._</s>
            <s xml:id="echoid-s18638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18639" xml:space="preserve">21. </s>
            <s xml:id="echoid-s18640" xml:space="preserve">DATIS duobus angulis trianguli non re-
              <lb/>
              <note position="left" xlink:label="note-520-02" xlink:href="note-520-02a" xml:space="preserve">Quærũtur
                <lb/>
              duo arcus,
                <lb/>
              cũ vno an-
                <lb/>
              gulo.</note>
            ctanguli, cum arcu qui alteri illorum oppo-
              <lb/>
            nitur, reliquos arcus, cum reliquo angulo in-
              <lb/>
            ueſtigare: </s>
            <s xml:id="echoid-s18641" xml:space="preserve">ſi modo conſtet, num arcus alteri
              <lb/>
            angulo dato oppoſitus quadrante maior ſit,
              <lb/>
            aut minor, aut certe quadrans.</s>
            <s xml:id="echoid-s18642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18643" xml:space="preserve">SINT in triangulo ABC, dati duo anguli B, C, primum inæquales, cum
              <lb/>
              <note position="left" xlink:label="note-520-03" xlink:href="note-520-03a" xml:space="preserve">Quãdo da-
                <lb/>
              ti duo an-
                <lb/>
              guli inęqua
                <lb/>
              les ſunt, &
                <lb/>
              arcus datus
                <lb/>
              non qua-
                <lb/>
              drans.</note>
            arcu AB, qui angulo C, opponitur, non quadrante, conſtetq́; </s>
            <s xml:id="echoid-s18644" xml:space="preserve">præterea ſpe-
              <lb/>
              <figure xlink:label="fig-520-01" xlink:href="fig-520-01a" number="368">
                <image file="520-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/520-01"/>
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            cies arcus AC, alteri angulo dato B, oppoſiti. </s>
            <s xml:id="echoid-s18645" xml:space="preserve">Du-
              <lb/>
            catur ex tertio angulo A, ad arcum BC, arcus per-
              <lb/>
            pendicularis AD; </s>
            <s xml:id="echoid-s18646" xml:space="preserve">qui intra triangulum cadet, ſi v-
              <lb/>
            terque angulus datus B, & </s>
            <s xml:id="echoid-s18647" xml:space="preserve">C, eſt acutus, vel obtu-
              <lb/>
            ſus; </s>
            <s xml:id="echoid-s18648" xml:space="preserve">extra vero, ſi vnus acutus, & </s>
            <s xml:id="echoid-s18649" xml:space="preserve">alter obtuſus eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s18650" xml:space="preserve">Inueſtigetur, per problema 2. </s>
            <s xml:id="echoid-s18651" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18652" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18653" xml:space="preserve">ex dato
              <lb/>
              <note position="left" xlink:label="note-520-04" xlink:href="note-520-04a" xml:space="preserve">Propoſ. 66.
                <lb/>
              triãg. ſphęr.</note>
            arcu AB, rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18654" xml:space="preserve">dato
              <lb/>
            angulo B, arcus oppofitus AD. </s>
            <s xml:id="echoid-s18655" xml:space="preserve">Item, per proble-
              <lb/>
            ma 14. </s>
            <s xml:id="echoid-s18656" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18657" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18658" xml:space="preserve">ex eodem dato arcu AB, an-
              <lb/>
            gulum rectum D, ſubtendente, & </s>
            <s xml:id="echoid-s18659" xml:space="preserve">dato angulo B, eli-
              <lb/>
            ciatur arcus BD. </s>
            <s xml:id="echoid-s18660" xml:space="preserve">Rurſus reperiatur, per problema
              <lb/>
            15. </s>
            <s xml:id="echoid-s18661" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18662" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18663" xml:space="preserve">ex eodem dato arcu AB, rectum
              <lb/>
            angulum D, fubtendente, & </s>
            <s xml:id="echoid-s18664" xml:space="preserve">dato angulo B, angu-
              <lb/>
            lus BAD. </s>
            <s xml:id="echoid-s18665" xml:space="preserve">Ad hæc, per problema 3. </s>
            <s xml:id="echoid-s18666" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18667" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18668" xml:space="preserve">inueniatur quoque ex in-
              <lb/>
            uento arcu AD, & </s>
            <s xml:id="echoid-s18669" xml:space="preserve">dato angulo C, oppoſito (Nam, cadente arcu AD, extra
              <lb/>
            triangulum, angulus ACD, arcui AD, oppoſitus relinquitur norus poſt ſub-
              <lb/>
            tractionem dati anguli ACB, ex duobus rectis) arcus AC, recto angulo D,
              <lb/>
            oppoſitus, cum eius ſpecies conſtare ponatur. </s>
            <s xml:id="echoid-s18670" xml:space="preserve">Atque ita inuentus erit arcus
              <lb/>
            AC, vnus ex quæſitis.</s>
            <s xml:id="echoid-s18671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18672" xml:space="preserve">DEINDE, per problema 14. </s>
            <s xml:id="echoid-s18673" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18674" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18675" xml:space="preserve">reperiatur ex inuento arcu
              <lb/>
            AC, rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18676" xml:space="preserve">dato angulo C, arcus CD: </s>
            <s xml:id="echoid-s18677" xml:space="preserve">quiad-
              <lb/>
            ditus arcui BD, ſupra inuento, vel ex eo detractus, (prout nimirũ arcus AD,
              <lb/>
            mtra triangulum cadit, aut extra) notum faciet arcum BC, qui eſt alter ex
              <lb/>
            quæſitis.</s>
            <s xml:id="echoid-s18678" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18679" xml:space="preserve">AD extremum, per problema 15. </s>
            <s xml:id="echoid-s18680" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18681" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18682" xml:space="preserve">ex inuento eodem </s>
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