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

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          <p>
            <s xml:id="echoid-s12944" xml:space="preserve">
              <pb o="381" file="393" n="393" rhead=""/>
            duo latera æqualia ſint quadrantes, ſi angulus ſub
              <lb/>
            ipſis comprehenſus fuerit rectus, erit baſis qua-
              <lb/>
            drans: </s>
            <s xml:id="echoid-s12945" xml:space="preserve">Si verò acutus, quadrante minor: </s>
            <s xml:id="echoid-s12946" xml:space="preserve">Si deni-
              <lb/>
            que obtuſus, quadrante maior. </s>
            <s xml:id="echoid-s12947" xml:space="preserve">Et ſi baſis fuerit
              <lb/>
            quadrans, eritangulus ſub lateribus comprehen-
              <lb/>
            ſus, rectus: </s>
            <s xml:id="echoid-s12948" xml:space="preserve">Si verò minor quadrante, acutus: </s>
            <s xml:id="echoid-s12949" xml:space="preserve">Si de-
              <lb/>
            nique maior quadrãte, obtuſus. </s>
            <s xml:id="echoid-s12950" xml:space="preserve">Semper autem po-
              <lb/>
            lus baſis erit in angulo ſub lateribus cõprehenſo.</s>
            <s xml:id="echoid-s12951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12952" xml:space="preserve">IN triangulo ſphærico Iſoſcele ABC, ſint latera AB, AC, quadrantes,
              <lb/>
            & </s>
            <s xml:id="echoid-s12953" xml:space="preserve">primum angulus A, ſit rectus, vt in prima figura. </s>
            <s xml:id="echoid-s12954" xml:space="preserve">Dico baſim BC, quadran
              <lb/>
            tem eſſe. </s>
            <s xml:id="echoid-s12955" xml:space="preserve">Cum enim AB,
              <lb/>
              <figure xlink:label="fig-393-01" xlink:href="fig-393-01a" number="232">
                <image file="393-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/393-01"/>
              </figure>
            AC, ſint quadrãtes, erunt
              <lb/>
            anguli B, C, recti. </s>
            <s xml:id="echoid-s12956" xml:space="preserve">Quare
              <lb/>
              <note position="right" xlink:label="note-393-01" xlink:href="note-393-01a" xml:space="preserve">25. huius
                <lb/>
              omnes arcus erunt qua-
                <lb/>
              Corollar.
                <lb/>
              25. huius.</note>
            drantes. </s>
            <s xml:id="echoid-s12957" xml:space="preserve">Quadrans ergo
              <lb/>
            eſt BC. </s>
            <s xml:id="echoid-s12958" xml:space="preserve">Quod eſt propo-
              <lb/>
            ſitum.</s>
            <s xml:id="echoid-s12959" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12960" xml:space="preserve">SIT deinde angulus
              <lb/>
            A, acutus, vt in ſecunda
              <lb/>
            figura. </s>
            <s xml:id="echoid-s12961" xml:space="preserve">Dico baſim BC,
              <lb/>
            minorem eſſe quadrante.
              <lb/>
            </s>
            <s xml:id="echoid-s12962" xml:space="preserve">Ductoenim per A, & </s>
            <s xml:id="echoid-s12963" xml:space="preserve">po-
              <lb/>
              <note position="right" xlink:label="note-393-02" xlink:href="note-393-02a" xml:space="preserve">20. 1. Theod.</note>
            lum arcus AB, arcu cir-
              <lb/>
            culi maximi AD, erit an-
              <lb/>
            gulus BAD, rectus, atque adeo maior acuto angulo BAC. </s>
            <s xml:id="echoid-s12964" xml:space="preserve">Occurret ergo
              <lb/>
              <note position="right" xlink:label="note-393-03" xlink:href="note-393-03a" xml:space="preserve">15. 1 Theod.</note>
            AD, arcus arcui BC, producto, nempe in puncto D. </s>
            <s xml:id="echoid-s12965" xml:space="preserve">Quoniam igitur in trian
              <lb/>
            gulo ABC, vterque angulus B, C, rectus eſt, erunt in triangulo ABD, duo
              <lb/>
              <note position="right" xlink:label="note-393-04" xlink:href="note-393-04a" xml:space="preserve">25. huius.</note>
            anguli recti B, & </s>
            <s xml:id="echoid-s12966" xml:space="preserve">DAB, ideoque æquales; </s>
            <s xml:id="echoid-s12967" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s12968" xml:space="preserve">arcus DA, DB,
              <lb/>
              <note position="right" xlink:label="note-393-05" xlink:href="note-393-05a" xml:space="preserve">9. huius.</note>
            æquales erunt. </s>
            <s xml:id="echoid-s12969" xml:space="preserve">Quare Iſoſceles eſt DAB, habens ad baſim AB, duos angu-
              <lb/>
              <note position="right" xlink:label="note-393-06" xlink:href="note-393-06a" xml:space="preserve">25. huius.</note>
            los rectos; </s>
            <s xml:id="echoid-s12970" xml:space="preserve">ac proinde vterque arcus AD, BD, quadrans eſt. </s>
            <s xml:id="echoid-s12971" xml:space="preserve">Igitur BC, qua-
              <lb/>
            drante erit minor. </s>
            <s xml:id="echoid-s12972" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12974" xml:space="preserve">TERTIO ſit angulus A, obtuſus, vt in tertia figura. </s>
            <s xml:id="echoid-s12975" xml:space="preserve">Dico baſim BC,
              <lb/>
            eſſe quadrante maiorem. </s>
            <s xml:id="echoid-s12976" xml:space="preserve">Ducto enim per A, & </s>
            <s xml:id="echoid-s12977" xml:space="preserve">polum arcus AB, arcu circuli
              <lb/>
              <note position="right" xlink:label="note-393-07" xlink:href="note-393-07a" xml:space="preserve">20. 1 Theod.</note>
            maximi AD, erit angulus DAB, rectus; </s>
            <s xml:id="echoid-s12978" xml:space="preserve">atque adeo minor obtuſo angulo
              <lb/>
              <note position="right" xlink:label="note-393-08" xlink:href="note-393-08a" xml:space="preserve">15. 1 Theod.</note>
            BAC. </s>
            <s xml:id="echoid-s12979" xml:space="preserve">Occurret ergo arcus AD, arcui BC, intra triangulum, nempe in pun
              <lb/>
            cto D. </s>
            <s xml:id="echoid-s12980" xml:space="preserve">Quoniam ergo in triangulo ABC, rectus eſt vterque angulus B, C,
              <lb/>
              <note position="right" xlink:label="note-393-09" xlink:href="note-393-09a" xml:space="preserve">25. huius.</note>
            erunt in triangulo DAB, duo anguli ad baſim AB, recti, & </s>
            <s xml:id="echoid-s12981" xml:space="preserve">propterea æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s12982" xml:space="preserve">atque idcirco & </s>
            <s xml:id="echoid-s12983" xml:space="preserve">arcus AD, BD, æquales. </s>
            <s xml:id="echoid-s12984" xml:space="preserve">Quare Iſoſceles eſt DAB, ha-
              <lb/>
              <note position="right" xlink:label="note-393-10" xlink:href="note-393-10a" xml:space="preserve">9. huius.</note>
            bens ad baſim AB, duos angulos rectos. </s>
            <s xml:id="echoid-s12985" xml:space="preserve">Vterque igitur arcus AD, BD, qua-
              <lb/>
              <note position="right" xlink:label="note-393-11" xlink:href="note-393-11a" xml:space="preserve">25. huius.</note>
            drans eſt, ideoque BC, quadrante maior. </s>
            <s xml:id="echoid-s12986" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12988" xml:space="preserve">SED iam baſis BC, quadrans ſit, vt in eadem prima figura. </s>
            <s xml:id="echoid-s12989" xml:space="preserve">Dico angu-
              <lb/>
            lum A, rectum eſſe. </s>
            <s xml:id="echoid-s12990" xml:space="preserve">Quoniam enim duo arcus CA, CB, quadrantes ſunt,
              <lb/>
              <note position="right" xlink:label="note-393-12" xlink:href="note-393-12a" xml:space="preserve">25. huius.</note>
            </s>
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