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

Table of Notes

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            <s xml:id="echoid-s18342" xml:space="preserve">
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            bifariam. </s>
            <s xml:id="echoid-s18343" xml:space="preserve">Inueniatur ergo, per problema 1. </s>
            <s xml:id="echoid-s18344" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18345" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18346" xml:space="preserve">ex dato arcu AB,
              <lb/>
              <figure xlink:label="fig-516-01" xlink:href="fig-516-01a" number="363">
                <image file="516-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/516-01"/>
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            rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18347" xml:space="preserve">arcu BD, dimidio
              <lb/>
            dati arcus BC, angulus BAD, qui duplicatus totum
              <lb/>
            angulum BAC, dabit. </s>
            <s xml:id="echoid-s18348" xml:space="preserve">Deinde, per problema 13. </s>
            <s xml:id="echoid-s18349" xml:space="preserve">triang.
              <lb/>
            </s>
            <s xml:id="echoid-s18350" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18351" xml:space="preserve">ex eiſdem notis arcubus AB, BD, reperiatur an-
              <lb/>
            gulus B, cui æqualis eſt angulus C, (ob æquales arcus
              <lb/>
            AB, AC,) ac proinde cognitus quoque.</s>
            <s xml:id="echoid-s18352" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18353" xml:space="preserve">_PER_ ſolos ſinus ita agemus. </s>
            <s xml:id="echoid-s18354" xml:space="preserve">_P_er _1._ </s>
            <s xml:id="echoid-s18355" xml:space="preserve">praxim problematis
              <lb/>
              <note position="left" xlink:label="note-516-01" xlink:href="note-516-01a" xml:space="preserve">Per ſolos ſi
                <lb/>
              nus, quãdo
                <lb/>
              dati duo ar
                <lb/>
              cus æquales
                <lb/>
              ſunt.</note>
            _1._ </s>
            <s xml:id="echoid-s18356" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18357" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18358" xml:space="preserve">inueniatur ex dato arcu _
              <emph style="sc">Ab</emph>
            ,_ rectum angu
              <lb/>
            lum _D,_ ſubtendente, & </s>
            <s xml:id="echoid-s18359" xml:space="preserve">arcu _
              <emph style="sc">B</emph>
            D,_ dimidio arcus dati _
              <emph style="sc">B</emph>
            C,_ an-
              <lb/>
            gulus _
              <emph style="sc">B</emph>
            AD,_ qui duplicatus totum _
              <emph style="sc">BA</emph>
            C,_ notum efficiet.
              <lb/>
            </s>
            <s xml:id="echoid-s18360" xml:space="preserve">Deinde per _1._ </s>
            <s xml:id="echoid-s18361" xml:space="preserve">praxim problematis 6. </s>
            <s xml:id="echoid-s18362" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18363" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18364" xml:space="preserve">ex arcu _
              <emph style="sc">B</emph>
            D,_ dimidio arcus da-
              <lb/>
            ti _
              <emph style="sc">B</emph>
            C,_ & </s>
            <s xml:id="echoid-s18365" xml:space="preserve">angulo oppoſito _
              <emph style="sc">BA</emph>
            D,_ inuento, (cum ſpecies alterius anguli _B,_ conſtet. </s>
            <s xml:id="echoid-s18366" xml:space="preserve">
              <lb/>
            _N_am ſi datus arcus _
              <emph style="sc">AB</emph>
            ,_ recto angulo _D,_ oppoſitus eſt quadrante minor, angulus _
              <emph style="sc">B</emph>
            ,_
              <lb/>
            acutus erit, quemadmodum & </s>
            <s xml:id="echoid-s18367" xml:space="preserve">_
              <emph style="sc">BA</emph>
            D,_ acutus eſt: </s>
            <s xml:id="echoid-s18368" xml:space="preserve">Si vero _
              <emph style="sc">Ab</emph>
            ,_ quadrante maior eſt,
              <lb/>
            erit angulus _
              <emph style="sc">B</emph>
            ,_ obtuſus, cum _
              <emph style="sc">BA</emph>
            D,_ acutus ſit.) </s>
            <s xml:id="echoid-s18369" xml:space="preserve">reperiatur angulus _
              <emph style="sc">B</emph>
            ,_ cui æqualis
              <lb/>
            eſt angulus _C,_ ob æquales arcus _
              <emph style="sc">Ab, ac</emph>
            ._</s>
            <s xml:id="echoid-s18370" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18371" xml:space="preserve">NEQVE vero duo duo æquales arcus eſſe poſſunt quadrãtes. </s>
            <s xml:id="echoid-s18372" xml:space="preserve">Nam alias
              <lb/>
            duo anguli ſupra baſim eſſent recti; </s>
            <s xml:id="echoid-s18373" xml:space="preserve">atque adeo triangulum eſſet rectangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s18374" xml:space="preserve">quod eſt contra hypotheſin.</s>
            <s xml:id="echoid-s18375" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          arcus, cum
            <lb/>
          duobus an
            <lb/>
          gulis adia-
            <lb/>
          centibus.</note>
          <p>
            <s xml:id="echoid-s18376" xml:space="preserve">19. </s>
            <s xml:id="echoid-s18377" xml:space="preserve">DATIS duobus arcubus trianguli non re-
              <lb/>
            ctanguli cum angulo ab ipſis comprehen ſo,
              <lb/>
            inueſtigare reliquum arcum, cum reliquis
              <lb/>
            duobus angulis.</s>
            <s xml:id="echoid-s18378" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18379" xml:space="preserve">SINT in triangulo ABC, duo arcus AB, BC, dati, cum angulo B: </s>
            <s xml:id="echoid-s18380" xml:space="preserve">ſintq́;
              <lb/>
            </s>
            <s xml:id="echoid-s18381" xml:space="preserve">
              <note position="left" xlink:label="note-516-03" xlink:href="note-516-03a" xml:space="preserve">Quãdoduo
                <lb/>
              arcus dati
                <lb/>
              ſunt inæ-
                <lb/>
              quales, &
                <lb/>
              neuter eo-
                <lb/>
              rum qua-
                <lb/>
              drans.</note>
            primum inæquales, & </s>
            <s xml:id="echoid-s18382" xml:space="preserve">neuter eorum quadrans. </s>
            <s xml:id="echoid-s18383" xml:space="preserve">Ex A, termino vnius eorum ad
              <lb/>
            alterum demittatur arcus perpendicularis AD, qui an intra triangulum, an
              <lb/>
            vero extra cadat, ex operatione ipſa diſcemus. </s>
            <s xml:id="echoid-s18384" xml:space="preserve">Nam inueniatur, per proble-
              <lb/>
              <figure xlink:label="fig-516-02" xlink:href="fig-516-02a" number="364">
                <image file="516-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/516-02"/>
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            ma 2. </s>
            <s xml:id="echoid-s18385" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18386" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18387" xml:space="preserve">ex arcu dato AB, rectum
              <lb/>
            angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18388" xml:space="preserve">dato angulo B,
              <lb/>
            arcus AD, angulo B, oppoſitus. </s>
            <s xml:id="echoid-s18389" xml:space="preserve">Rurſus ex da-
              <lb/>
              <note position="left" xlink:label="note-516-04" xlink:href="note-516-04a" xml:space="preserve">Proproſ. 64.
                <lb/>
              @riãg. ſphęr.</note>
            to arcu AB, rectum angulum D, ſubtenden-
              <lb/>
            te, & </s>
            <s xml:id="echoid-s18390" xml:space="preserve">inuento arcu AD, reperiatur, per pro-
              <lb/>
            blema 8. </s>
            <s xml:id="echoid-s18391" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18392" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18393" xml:space="preserve">tertius arcus BD. </s>
            <s xml:id="echoid-s18394" xml:space="preserve">Si
              <lb/>
            igitur arcus hic BD, inuentus fuerit minor
              <lb/>
            dato arcu BC, cadet arcus AD, intra trian-
              <lb/>
            gulum, extra vero, ſi maior. </s>
            <s xml:id="echoid-s18395" xml:space="preserve">Sublato autem
              <lb/>
            inuento arcu BD, ex dato arcu BC, (ſi ille
              <lb/>
            hoc minor eſt) vel dempto arcu BC, dato ex
              <lb/>
            inuento arcu BD, (ſi hic illo maior eſt) no-
              <lb/>
            tus relinquetur arcus CD. </s>
            <s xml:id="echoid-s18396" xml:space="preserve">Ex arcubus deni-
              <lb/>
            que AD, CD, circa angulum rectum D, inueniatur, per problema 7. </s>
            <s xml:id="echoid-s18397" xml:space="preserve">triang.
              <lb/>
            </s>
            <s xml:id="echoid-s18398" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18399" xml:space="preserve">tertius arcus AC, qui quæritur.</s>
            <s xml:id="echoid-s18400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18401" xml:space="preserve">DEINDE, per problema 13. </s>
            <s xml:id="echoid-s18402" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18403" xml:space="preserve">ſphær, ex dato arcu AB, </s>
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