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

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          <p>
            <s xml:id="echoid-s13473" xml:space="preserve">
              <pb o="392" file="404" n="404" rhead=""/>
            acutus, quadrante minor: </s>
            <s xml:id="echoid-s13474" xml:space="preserve">ſi denique obtuſus, ma-
              <lb/>
            ior quadrante. </s>
            <s xml:id="echoid-s13475" xml:space="preserve">Et ſi vteruis arcuum rectum angu-
              <lb/>
            lum continentium fuerit quadrans, erit angulus,
              <lb/>
            quem ſubtendit, rectus: </s>
            <s xml:id="echoid-s13476" xml:space="preserve">ſi verò minor quadrante,
              <lb/>
            acutus: </s>
            <s xml:id="echoid-s13477" xml:space="preserve">ſi denique quadrante maior, obtuſus.</s>
            <s xml:id="echoid-s13478" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13479" xml:space="preserve">SIT in triangulo ſphærico ABC, angulus C, rectus, ſitq́ue primum al-
              <lb/>
            ter reliquorum, nempe B, etiam rectus. </s>
            <s xml:id="echoid-s13480" xml:space="preserve">Dico arcum AC, qui eum ſubtendit,
              <lb/>
            quadrantem eſſe. </s>
            <s xml:id="echoid-s13481" xml:space="preserve">Cum enim vterque angulus B, C, rectus ſit, erit & </s>
            <s xml:id="echoid-s13482" xml:space="preserve">vterque
              <lb/>
            arcus AB, AC, quadrans.</s>
            <s xml:id="echoid-s13483" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">25. huius.</note>
          <p>
            <s xml:id="echoid-s13484" xml:space="preserve">SIT deinde B, angulus acutus. </s>
            <s xml:id="echoid-s13485" xml:space="preserve">Dieo arcum AC, eſſe quadrante mino-
              <lb/>
              <figure xlink:label="fig-404-01" xlink:href="fig-404-01a" number="250">
                <image file="404-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/404-01"/>
              </figure>
            rem. </s>
            <s xml:id="echoid-s13486" xml:space="preserve">Fiat enim angulus CBD, rectus, coëat-
              <lb/>
            que arcus BD, cum arcu CA, producto in
              <lb/>
            D. </s>
            <s xml:id="echoid-s13487" xml:space="preserve">Quoniam igitur vterq; </s>
            <s xml:id="echoid-s13488" xml:space="preserve">angulus C, CBD,
              <lb/>
            rectus eſt, erit & </s>
            <s xml:id="echoid-s13489" xml:space="preserve">vterque arcus BD, CD,
              <lb/>
              <note position="left" xlink:label="note-404-02" xlink:href="note-404-02a" xml:space="preserve">25. huius.</note>
            quadrans; </s>
            <s xml:id="echoid-s13490" xml:space="preserve">atque adeo arcus AC, minor erit
              <lb/>
            quadrante.</s>
            <s xml:id="echoid-s13491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13492" xml:space="preserve">SIT poſtremo angulus B, obtuſus. </s>
            <s xml:id="echoid-s13493" xml:space="preserve">Dico
              <lb/>
            arcum AC, quadrante maiorem eſſe. </s>
            <s xml:id="echoid-s13494" xml:space="preserve">Fiat
              <lb/>
            enim angulus CBE, rectus, ſecetq́ue arcus
              <lb/>
            BE, arcum AC, in E. </s>
            <s xml:id="echoid-s13495" xml:space="preserve">Quoniam igitur vter-
              <lb/>
            que angulus C, CBE, rectus eſt, erit & </s>
            <s xml:id="echoid-s13496" xml:space="preserve">v-
              <lb/>
            terque arcus BE, CE, quadrans; </s>
            <s xml:id="echoid-s13497" xml:space="preserve">atque adeo
              <lb/>
              <note position="left" xlink:label="note-404-03" xlink:href="note-404-03a" xml:space="preserve">25. huius.</note>
            arcus AC, quadrante maior erit.</s>
            <s xml:id="echoid-s13498" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13499" xml:space="preserve">RVRSVM ſit angulus C, rectus, & </s>
            <s xml:id="echoid-s13500" xml:space="preserve">ſit primum arcus AC, quadrans.
              <lb/>
            </s>
            <s xml:id="echoid-s13501" xml:space="preserve">Dico angulum ei ſubtenſum B, eſſe rectum. </s>
            <s xml:id="echoid-s13502" xml:space="preserve">Erit enim A, polus arcus BC,
              <lb/>
              <note position="left" xlink:label="note-404-04" xlink:href="note-404-04a" xml:space="preserve">Coroll 16.
                <lb/>
              1. Theod.
                <lb/>
              13. 1. Theod.
                <lb/>
              15. 1. Theod.</note>
            (cum arcus CA, per polum arcus BC, tranſeat, ob angulum rectum C;) </s>
            <s xml:id="echoid-s13503" xml:space="preserve">atque
              <lb/>
            adeo angulus ABC, rectus.</s>
            <s xml:id="echoid-s13504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13505" xml:space="preserve">DEINDE ſit arcus AC, quadrante minor. </s>
            <s xml:id="echoid-s13506" xml:space="preserve">Dico angulum ei ſubten-
              <lb/>
            ſum B, eſſe acutum. </s>
            <s xml:id="echoid-s13507" xml:space="preserve">Producto enim arcu CA, ad D, vt ſit CD, quadrans,
              <lb/>
              <note position="left" xlink:label="note-404-05" xlink:href="note-404-05a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. Theod.
                <lb/>
              13.1 Theod.
                <lb/>
              20.1 Theod.
                <lb/>
              15.1 Theod.</note>
            erit eodem modo D, polus arcus CB; </s>
            <s xml:id="echoid-s13508" xml:space="preserve">cum arcus CA, per polum arcus BC,
              <lb/>
            tranſeat. </s>
            <s xml:id="echoid-s13509" xml:space="preserve">Ducto ergo per puncta D, B, arcu DB, circuli maximi, erit angu-
              <lb/>
            lus DBC, rectus; </s>
            <s xml:id="echoid-s13510" xml:space="preserve">ac proinde ABC, acutus.</s>
            <s xml:id="echoid-s13511" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13512" xml:space="preserve">POSTREMO ſit arcus AC, maior quadrante. </s>
            <s xml:id="echoid-s13513" xml:space="preserve">Dico angulum B, ei
              <lb/>
              <note position="left" xlink:label="note-404-06" xlink:href="note-404-06a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. Theod.
                <lb/>
              13. 1. Theod.
                <lb/>
              20. 1 Theod.
                <lb/>
              25. 1. Theod.</note>
            ſubtenſum obtuſum eſſe. </s>
            <s xml:id="echoid-s13514" xml:space="preserve">Abſciſſo enim quadrante CE, erit rurſum E, polus
              <lb/>
            arcus BC; </s>
            <s xml:id="echoid-s13515" xml:space="preserve">propterea quod arcus CA, per plum arcus BC, tranſit. </s>
            <s xml:id="echoid-s13516" xml:space="preserve">Ducto
              <lb/>
            ergo per puncta E, B, arcu EB, circuli maximi, erit angulus EBC, rectus;
              <lb/>
            </s>
            <s xml:id="echoid-s13517" xml:space="preserve">atque adeò ABC, obtuſus. </s>
            <s xml:id="echoid-s13518" xml:space="preserve">Quapropter, in omni triangulo ſphærico, &</s>
            <s xml:id="echoid-s13519" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13520" xml:space="preserve">
              <lb/>
            Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s13521" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1072" type="section" level="1" n="532">
          <head xml:id="echoid-head567" xml:space="preserve">THEOR. 33. PROPOS. 35.</head>
          <p>
            <s xml:id="echoid-s13522" xml:space="preserve">IN omni triangulo ſphærico rectangulo, ſi v-
              <lb/>
            terque arcuum comprehendentium angulum </s>
          </p>
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