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

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          <p>
            <s xml:id="echoid-s13377" xml:space="preserve">
              <pb o="390" file="402" n="402" rhead=""/>
            qui illi ad verticem æqualis eſt, maior erit angulo ACE: </s>
            <s xml:id="echoid-s13378" xml:space="preserve">Sed angulus ACE,
              <lb/>
              <note position="left" xlink:label="note-402-01" xlink:href="note-402-01a" xml:space="preserve">@4. huius.</note>
            & </s>
            <s xml:id="echoid-s13379" xml:space="preserve">anguli ACB, & </s>
            <s xml:id="echoid-s13380" xml:space="preserve">B, duobus rectis ſuntæquales. </s>
            <s xml:id="echoid-s13381" xml:space="preserve">Igitur anguli BAC, ACB,
              <lb/>
              <note position="left" xlink:label="note-402-02" xlink:href="note-402-02a" xml:space="preserve">16. huius.</note>
            & </s>
            <s xml:id="echoid-s13382" xml:space="preserve">B, maiores erunt duobus rectis. </s>
            <s xml:id="echoid-s13383" xml:space="preserve">Semper ergo tres anguli ſimul duobus re-
              <lb/>
            ctis ſunt maiores.</s>
            <s xml:id="echoid-s13384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13385" xml:space="preserve">QVIA verò omnis angulus ſphæricus, etiam obtuſus, minor eſt duobus
              <lb/>
            rectis; </s>
            <s xml:id="echoid-s13386" xml:space="preserve">perſpicuum eſt, tres angulos cuiusuis trianguli ſphærici ſimul minores
              <lb/>
            eſſe ſex rectis. </s>
            <s xml:id="echoid-s13387" xml:space="preserve">Cuiuſcunque ergo trianguli ſphærici tres anguli, &</s>
            <s xml:id="echoid-s13388" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13389" xml:space="preserve">Quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s13390" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1058" type="section" level="1" n="529">
          <head xml:id="echoid-head564" xml:space="preserve">THEOR. 30. PROPOS. 32.</head>
          <p>
            <s xml:id="echoid-s13391" xml:space="preserve">IN omni triangulo ſphærico, cuius vnus an-
              <lb/>
            gulus rectus ſit, & </s>
            <s xml:id="echoid-s13392" xml:space="preserve">alter reliquorum acutus, ſi qui-
              <lb/>
            dem arcus illis angulis adiacẽs fuerit quadians, erit
              <lb/>
            & </s>
            <s xml:id="echoid-s13393" xml:space="preserve">arcus rectum ſubtendens angulum quadrans; </s>
            <s xml:id="echoid-s13394" xml:space="preserve">ſi
              <lb/>
            verò minor fuerit quadrante, quadrante quoque
              <lb/>
            minor erit: </s>
            <s xml:id="echoid-s13395" xml:space="preserve">ſi deniq; </s>
            <s xml:id="echoid-s13396" xml:space="preserve">quadrante fuerit maior, qua-
              <lb/>
            drante quoq; </s>
            <s xml:id="echoid-s13397" xml:space="preserve">maior erit: </s>
            <s xml:id="echoid-s13398" xml:space="preserve">Sem per autem arcus acu-
              <lb/>
            tum angulum ſubtendens minor erit quadrante.</s>
            <s xml:id="echoid-s13399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13400" xml:space="preserve">IN triangulo ABC, angulus C, rectus ſit, & </s>
            <s xml:id="echoid-s13401" xml:space="preserve">B, acutus, ſitque primum ar-
              <lb/>
            cus BC, quadrans, Dico & </s>
            <s xml:id="echoid-s13402" xml:space="preserve">AB, quadrantem eſſe. </s>
            <s xml:id="echoid-s13403" xml:space="preserve">Fiat enim angulus CBD,
              <lb/>
              <figure xlink:label="fig-402-01" xlink:href="fig-402-01a" number="248">
                <image file="402-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/402-01"/>
              </figure>
            rectus, coëatq́ue arcus BD, cum arcu CA,
              <lb/>
            producto in D. </s>
            <s xml:id="echoid-s13404" xml:space="preserve">Erit igitur vterque arcus BD,
              <lb/>
              <note position="left" xlink:label="note-402-03" xlink:href="note-402-03a" xml:space="preserve">25. huius.</note>
            CD, quadrans: </s>
            <s xml:id="echoid-s13405" xml:space="preserve">Ponitur autem & </s>
            <s xml:id="echoid-s13406" xml:space="preserve">BC, qua-
              <lb/>
            drans. </s>
            <s xml:id="echoid-s13407" xml:space="preserve">Ergo B, polus eſt arcus CD; </s>
            <s xml:id="echoid-s13408" xml:space="preserve">atque
              <lb/>
              <note position="left" xlink:label="note-402-04" xlink:href="note-402-04a" xml:space="preserve">26. huius.</note>
            adeo rectus erit angulus ad A. </s>
            <s xml:id="echoid-s13409" xml:space="preserve">Quare vterque
              <lb/>
              <note position="left" xlink:label="note-402-05" xlink:href="note-402-05a" xml:space="preserve">15. 1 Theod.</note>
            arcus BC, BA, quadrans erit. </s>
            <s xml:id="echoid-s13410" xml:space="preserve">Quadrans igi-
              <lb/>
              <note position="left" xlink:label="note-402-06" xlink:href="note-402-06a" xml:space="preserve">25. huius.</note>
            tur eſt arcus AB, angulo recto C, oppoſitus.</s>
            <s xml:id="echoid-s13411" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13412" xml:space="preserve">SIT deinde arcus BC, quadrante minor.
              <lb/>
            </s>
            <s xml:id="echoid-s13413" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s13414" xml:space="preserve">arcum AB, quadrante eſſe minorem. </s>
            <s xml:id="echoid-s13415" xml:space="preserve">
              <lb/>
            Fiat enim rurſus angulus CBD, rectus, oc-
              <lb/>
            curratq́ue arcus BD, arcui CA, producto in
              <lb/>
            D; </s>
            <s xml:id="echoid-s13416" xml:space="preserve">eritque vt prius, vterque arcus BD, CD,
              <lb/>
              <note position="left" xlink:label="note-402-07" xlink:href="note-402-07a" xml:space="preserve">25. huius.</note>
            quadrans. </s>
            <s xml:id="echoid-s13417" xml:space="preserve">Producto autem BC, ad E, vt ſit
              <lb/>
            BE, quadrans, ducatur per puncta D, E, arcus circuli maximi DE, quem BA,
              <lb/>
              <note position="left" xlink:label="note-402-08" xlink:href="note-402-08a" xml:space="preserve">20. 1 Theod.</note>
            productus ſecet in F. </s>
            <s xml:id="echoid-s13418" xml:space="preserve">Quoniam igitur arcus BE, BD, quadrantes ſunt, erit
              <lb/>
            vterque angulus BDE, BED, rectus, & </s>
            <s xml:id="echoid-s13419" xml:space="preserve">B, polus arcus DE. </s>
            <s xml:id="echoid-s13420" xml:space="preserve">Rectus ergo
              <lb/>
              <note position="left" xlink:label="note-402-09" xlink:href="note-402-09a" xml:space="preserve">25. & 26.
                <lb/>
              huius.</note>
            erit angulus ad F; </s>
            <s xml:id="echoid-s13421" xml:space="preserve">atque adeò vterque arcus BE, BF, quadrans erit. </s>
            <s xml:id="echoid-s13422" xml:space="preserve">Igitur
              <lb/>
              <note position="left" xlink:label="note-402-10" xlink:href="note-402-10a" xml:space="preserve">15. 1 Theod.</note>
            arcus BA, quadrante erit minor.</s>
            <s xml:id="echoid-s13423" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">25. huius.</note>
          <p>
            <s xml:id="echoid-s13424" xml:space="preserve">SIT denique arcus BC, quadrante maior. </s>
            <s xml:id="echoid-s13425" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s13426" xml:space="preserve">arcum AB, </s>
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