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

Table of figures

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            <s xml:id="echoid-s18531" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s18532" xml:space="preserve">angulo adiacente CAD, inuento, eruatur arcus AC, recto angulo D, op-
              <lb/>
            poſitus; </s>
            <s xml:id="echoid-s18533" xml:space="preserve">qui quidem eſt vnus ex quæſitis.</s>
            <s xml:id="echoid-s18534" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18535" xml:space="preserve">DEINDE, per problema 8. </s>
            <s xml:id="echoid-s18536" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18537" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18538" xml:space="preserve">tam ex dato arcu AB, rectum
              <lb/>
            angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18539" xml:space="preserve">inuento arcu AD, indagetur arcus BD; </s>
            <s xml:id="echoid-s18540" xml:space="preserve">quam
              <lb/>
            ex inuento arcu AC, rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18541" xml:space="preserve">arcu inuento AD,
              <lb/>
            arcus CD: </s>
            <s xml:id="echoid-s18542" xml:space="preserve">qui adiectus ad inuentum arcum BD, cadente arcu AD, intra
              <lb/>
            triangulum, vel ſubductus ex eodem arcu BD, cadente arcu AD, extra trian
              <lb/>
            gulum, notum dabit alterum arcum BC, quæſitum.</s>
            <s xml:id="echoid-s18543" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18544" xml:space="preserve">AD extremum, per problema 15. </s>
            <s xml:id="echoid-s18545" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18546" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18547" xml:space="preserve">inueſtigetur ex inuento
              <lb/>
            arcu AC, rectum angulum D, ſubtendente, & </s>
            <s xml:id="echoid-s18548" xml:space="preserve">angulo inuento CAD, angulus
              <lb/>
            ACD: </s>
            <s xml:id="echoid-s18549" xml:space="preserve">qui in priori triangulo eſt is, qui quæritur; </s>
            <s xml:id="echoid-s18550" xml:space="preserve">in poſteriori autem ſubdu-
              <lb/>
            ctus ex duobus rectis reliquum facit ACB, quæſitum.</s>
            <s xml:id="echoid-s18551" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18552" xml:space="preserve">_PER_ ſolos ſinus ſic negotium abſoluetur. </s>
            <s xml:id="echoid-s18553" xml:space="preserve">_P_er problema _2._ </s>
            <s xml:id="echoid-s18554" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18555" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18556" xml:space="preserve">inue-
              <lb/>
              <note position="right" xlink:label="note-519-01" xlink:href="note-519-01a" xml:space="preserve">Per ſolos ſi
                <lb/>
              nus, quãdo
                <lb/>
              dati anguli
                <lb/>
              sũt inęqua-
                <lb/>
              les, & arcus
                <lb/>
              adiacẽs nõ
                <lb/>
              quadrans.</note>
            niatur ex dato arcu _AB,_ rectum angulum _D,_ ſubtendente, & </s>
            <s xml:id="echoid-s18557" xml:space="preserve">angulo dato _B,_ arcus
              <lb/>
            oppoſitus _AD:_ </s>
            <s xml:id="echoid-s18558" xml:space="preserve">_E_tper _1._ </s>
            <s xml:id="echoid-s18559" xml:space="preserve">praxim problematis _8._ </s>
            <s xml:id="echoid-s18560" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18561" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18562" xml:space="preserve">reperiatur ex dato ar-
              <lb/>
            cu _AB,_ rectum angulum _D,_ ſubtendente, & </s>
            <s xml:id="echoid-s18563" xml:space="preserve">inuento arcu _AD,_ tertius arcus _BD._
              <lb/>
            </s>
            <s xml:id="echoid-s18564" xml:space="preserve">_I_tem per _1._ </s>
            <s xml:id="echoid-s18565" xml:space="preserve">praxim problematis _1._ </s>
            <s xml:id="echoid-s18566" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18567" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18568" xml:space="preserve">inquiratur ex dato arcu _
              <emph style="sc">Ab</emph>
            ,_ an-
              <lb/>
            gulum rectum _D,_ ſubtendente, & </s>
            <s xml:id="echoid-s18569" xml:space="preserve">inuento arcu _BD,_ angulus oppoſitus _
              <emph style="sc">B</emph>
            AD:_ </s>
            <s xml:id="echoid-s18570" xml:space="preserve">qui
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            ablatus ex dato _BAC,_ (ſi ille hoc minor eſt) vel ex eo datus _BAC,_ detractus, (ſi hic
              <lb/>
            illo minor eſt) notũ relinquet angulum _
              <emph style="sc">Ca</emph>
            D. </s>
            <s xml:id="echoid-s18571" xml:space="preserve">R_urſus per problema _5._ </s>
            <s xml:id="echoid-s18572" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18573" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18574" xml:space="preserve">
              <lb/>
            ex inuento arcu _AD,_ & </s>
            <s xml:id="echoid-s18575" xml:space="preserve">angulo adiacẽte _CAD,_ eruatur angulus _
              <emph style="sc">A</emph>
            CD;_ </s>
            <s xml:id="echoid-s18576" xml:space="preserve">qui in priori
              <lb/>
            triangulo eſt quæſitus, in poſteriori vero reliquus duorũ rectorum _
              <emph style="sc">Ac</emph>
            B,_ quæſitus eſt.</s>
            <s xml:id="echoid-s18577" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18578" xml:space="preserve">_POST_ hæc, per _1._ </s>
            <s xml:id="echoid-s18579" xml:space="preserve">praxim problematis _4._ </s>
            <s xml:id="echoid-s18580" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18581" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18582" xml:space="preserve">ex vtroque angulo
              <lb/>
            _CAD, ACD,_ inuento reperiatur arcus _CD:_ </s>
            <s xml:id="echoid-s18583" xml:space="preserve">qui in priori triangulo additus iam-
              <lb/>
            dudum inuento arcui _
              <emph style="sc">B</emph>
            D,_ vel in poſteriori ab eo ablatus, notum faciet arcum _BC,_
              <lb/>
            quæſitum.</s>
            <s xml:id="echoid-s18584" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18585" xml:space="preserve">_DENIQVE,_ per problema _7._ </s>
            <s xml:id="echoid-s18586" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18587" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18588" xml:space="preserve">inueniatur exinuentis arcubus
              <lb/>
            _
              <emph style="sc">A</emph>
            D, CD,_ circa angulum rectum _D,_ arcus tertius _
              <emph style="sc">A</emph>
            C,_ recto angulo _D,_ oppoſitus,
              <lb/>
            qui quæritur. </s>
            <s xml:id="echoid-s18589" xml:space="preserve">_
              <emph style="sc">A</emph>
            _tqueita inuenti erunt duo reliqui arcus _
              <emph style="sc">B</emph>
            C,
              <emph style="sc">Ac</emph>
            ,_ cum reliquo an-
              <lb/>
            gulo _ACB._</s>
            <s xml:id="echoid-s18590" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18591" xml:space="preserve">QVOD ſi quando angulus inuentus CAD, fuerit rectus, (BAD, nun-
              <lb/>
            quam poteſt eſſe rectus, poſito AB, non quadrante) erunt AC, CD, qua-
              <lb/>
            drantes; </s>
            <s xml:id="echoid-s18592" xml:space="preserve">& </s>
            <s xml:id="echoid-s18593" xml:space="preserve">AD, arcus anguli C; </s>
            <s xml:id="echoid-s18594" xml:space="preserve">ac proinde angulus C, notus fiet ex inuento
              <lb/>
            arcu AD. </s>
            <s xml:id="echoid-s18595" xml:space="preserve">Reliquus autem arcus BC, cognoſcetur ex inuento arcu BD, & </s>
            <s xml:id="echoid-s18596" xml:space="preserve">
              <lb/>
            quadrante CD, veluti prius.</s>
            <s xml:id="echoid-s18597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18598" xml:space="preserve">IAM vero ſi datus arcus AB, ſit quadrans, exiſten tibus adhuc angulis B,
              <lb/>
              <note position="right" xlink:label="note-519-02" xlink:href="note-519-02a" xml:space="preserve">Quãdo da-
                <lb/>
              tus arcus eſt
                <lb/>
              quadrans.</note>
            BAC, datis inæqualibus, erit angulus BAD, rectus, & </s>
            <s xml:id="echoid-s18599" xml:space="preserve">arcus quoque BD,
              <lb/>
            quadrans. </s>
            <s xml:id="echoid-s18600" xml:space="preserve">Item B, erit polus arcus AD; </s>
            <s xml:id="echoid-s18601" xml:space="preserve">proptereaq́; </s>
            <s xml:id="echoid-s18602" xml:space="preserve">arcus ipſe AD, ex dato
              <lb/>
            angulo B, cognitus erit. </s>
            <s xml:id="echoid-s18603" xml:space="preserve">Inuentis autem tunc tanta facilitate arcubus AD,
              <lb/>
            BD, & </s>
            <s xml:id="echoid-s18604" xml:space="preserve">angulo recto BAD, reperiemus cætera, vt prius.</s>
            <s xml:id="echoid-s18605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18606" xml:space="preserve">SINT deinde in triangulo ABC, dati duo anguli B,
              <lb/>
              <note position="right" xlink:label="note-519-03" xlink:href="note-519-03a" xml:space="preserve">Quãdo da-
                <lb/>
              ti duo an -
                <lb/>
              guli sũt æ-
                <lb/>
              quales.</note>
              <figure xlink:label="fig-519-01" xlink:href="fig-519-01a" number="367">
                <image file="519-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/519-01"/>
              </figure>
            C, æquales, cum arcu BC, adiacente, ſiue quadrans is ſit,
              <lb/>
            ſiue non. </s>
            <s xml:id="echoid-s18607" xml:space="preserve">Erunt arcus AB, AC, æquales, & </s>
            <s xml:id="echoid-s18608" xml:space="preserve">arcus per-
              <lb/>
            pendicularis AD, ex tertio angulo A, ad BC, demiſſus
              <lb/>
            ſecabit & </s>
            <s xml:id="echoid-s18609" xml:space="preserve">arcum BC, & </s>
            <s xml:id="echoid-s18610" xml:space="preserve">angulum A, bifariam. </s>
            <s xml:id="echoid-s18611" xml:space="preserve">Inuenia-
              <lb/>
            tur ergo, per problema 12. </s>
            <s xml:id="echoid-s18612" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s18613" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s18614" xml:space="preserve">ex arcu BD, di-
              <lb/>
            midio dati arcus BC, & </s>
            <s xml:id="echoid-s18615" xml:space="preserve">dato angulo B, adiacente, arcus
              <lb/>
            AB, recto angulo D, oppoſitus; </s>
            <s xml:id="echoid-s18616" xml:space="preserve">cui cum æqualis ſit </s>
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