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

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            <s xml:id="echoid-s8696" xml:space="preserve">
              <pb o="298" file="310" n="310" rhead=""/>
            centro B, conſtituentes inter cipere arcum quadrante AC, minorem, li-
              <lb/>
            neas vero rectas continẽtes angulum obtuſum abſcindere arcum quadran
              <lb/>
            te AC, maiorem.</s>
            <s xml:id="echoid-s8697" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8698" xml:space="preserve">SED auferant iam rectæ BA, BC, ex centro B, egredientes qua-
              <lb/>
            àrantem AC. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">Dico angulum ABC, eſſe rectum, &</s>
            <s xml:id="echoid-s8700" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">Quoniam enim
              <lb/>
            eſt, vt arcus AC, ad totam circunferentiam, ita angulus ABC, in cen-
              <lb/>
              <note position="left" xlink:label="note-310-01" xlink:href="note-310-01a" xml:space="preserve">Coroll. 2.
                <lb/>
              33. ſexti.</note>
            tro ad quatuor rectos; </s>
            <s xml:id="echoid-s8702" xml:space="preserve">eſt autem arcus AC, quadrans, id eſt, quarta pars
              <lb/>
            circunferentiæ totius: </s>
            <s xml:id="echoid-s8703" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s8704" xml:space="preserve">angulus ABC, quarta pars quatuor
              <lb/>
            rectorum, atq; </s>
            <s xml:id="echoid-s8705" xml:space="preserve">adeo rectus. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">Quia vero rectæ ex centro B, emiſſæ, atque
              <lb/>
            arcum quadrante AC, minorem auferentes angulum conſtituunt mino-
              <lb/>
            rem angulo recto ABC, auferentes vero arcum quadrantc AC, maio-
              <lb/>
            rem conſtituunt angulum recto angulo ABC, maiorem; </s>
            <s xml:id="echoid-s8707" xml:space="preserve">perſpicuum eſt,
              <lb/>
            rectas lineas arcum quadrante AC, minorem intercipientes conſtituere
              <lb/>
            in centro B, angulum acutum, lineas vero rectas arcum quadrante AC,
              <lb/>
            maiorem includentes continere in centro B, angulum obtuſum. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">Quod est
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s8709" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s8710" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s8711" xml:space="preserve">Contineant rurſum rectæ AB, CB, angulum rectum
              <lb/>
              <figure xlink:label="fig-310-01" xlink:href="fig-310-01a" number="159">
                <image file="310-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/310-01"/>
              </figure>
            ABC, et ex B, circulus deſcribatur ACDE.
              <lb/>
            </s>
            <s xml:id="echoid-s8712" xml:space="preserve">Dico arcum AC, eſſe quadrantem, &</s>
            <s xml:id="echoid-s8713" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">
              <lb/>
            Productis enim rectis AB, CB, ad D, E,
              <lb/>
            erunt & </s>
            <s xml:id="echoid-s8715" xml:space="preserve">anguli ABE, CBD, cum ſint an-
              <lb/>
            gulo ABC, deinceps, recti, ex definitione; </s>
            <s xml:id="echoid-s8716" xml:space="preserve">
              <lb/>
            necnõ & </s>
            <s xml:id="echoid-s8717" xml:space="preserve">angulus DBE, quòd angulo ABC,
              <lb/>
              <note position="left" xlink:label="note-310-02" xlink:href="note-310-02a" xml:space="preserve">23. primi.</note>
            ſit ad verticem æqualis, rectus. </s>
            <s xml:id="echoid-s8718" xml:space="preserve">Quare cum
              <lb/>
            omnes quatuor anguli ad B, centrum ſint re-
              <lb/>
              <note position="left" xlink:label="note-310-03" xlink:href="note-310-03a" xml:space="preserve">26. tertij.</note>
            cti, id eſt, æquales, æquales quoq; </s>
            <s xml:id="echoid-s8719" xml:space="preserve">erunt qua-
              <lb/>
            tuor arcus AC, CD, DE, EA; </s>
            <s xml:id="echoid-s8720" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s8721" xml:space="preserve">adeo
              <lb/>
            quilibet eorum quadrans erit. </s>
            <s xml:id="echoid-s8722" xml:space="preserve">Reliqua demonſtrabuntur, vt prius.</s>
            <s xml:id="echoid-s8723" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8724" xml:space="preserve">VERVM rectæ BA, BC, ex centro B, emiſſæ auferant iam qua-
              <lb/>
            drantem AC. </s>
            <s xml:id="echoid-s8725" xml:space="preserve">Dico angulum ABC, rectum eſſe, &</s>
            <s xml:id="echoid-s8726" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">Pro tuctis enim
              <lb/>
            rectis AB, CB, ad D, E, cum angulus DBE, angulo ABC, ad verti-
              <lb/>
              <note position="left" xlink:label="note-310-04" xlink:href="note-310-04a" xml:space="preserve">23. primi.</note>
            cem ſit æqualis, erit & </s>
            <s xml:id="echoid-s8728" xml:space="preserve">arcus DE, arcui AC, æqualis, & </s>
            <s xml:id="echoid-s8729" xml:space="preserve">proinde qua-
              <lb/>
              <note position="left" xlink:label="note-310-05" xlink:href="note-310-05a" xml:space="preserve">26. tertij.</note>
            drans. </s>
            <s xml:id="echoid-s8730" xml:space="preserve">Semicir culum ergo conficiunt duo quadrantes AC, DE; </s>
            <s xml:id="echoid-s8731" xml:space="preserve">atque
              <lb/>
            adeo reliqui duo arcus AE, DC, alterum ſemicir culum conſtituent. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">Cum
              <lb/>
              <note position="left" xlink:label="note-310-06" xlink:href="note-310-06a" xml:space="preserve">26. tertij.</note>
            ergo duo arcus AE, DC, æquales ſint, quòd anguli ABE, CBD, ad
              <lb/>
            verticem ſint æquales; </s>
            <s xml:id="echoid-s8733" xml:space="preserve">erit vterq; </s>
            <s xml:id="echoid-s8734" xml:space="preserve">eorum quadrans: </s>
            <s xml:id="echoid-s8735" xml:space="preserve">ac propterea qua-
              <lb/>
              <note position="left" xlink:label="note-310-07" xlink:href="note-310-07a" xml:space="preserve">15. primi.</note>
            tuor arcus AC, CD, DE, EA, cum ſint quadrantes, æquales erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s8736" xml:space="preserve">Quatuor ergo anguli ad centrum B, æquales quoq; </s>
            <s xml:id="echoid-s8737" xml:space="preserve">erunt; </s>
            <s xml:id="echoid-s8738" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s8739" xml:space="preserve">adeo eorum
              <lb/>
              <note position="left" xlink:label="note-310-08" xlink:href="note-310-08a" xml:space="preserve">27. tertij.</note>
            quilibet erit rectus. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">Vel breuius. </s>
            <s xml:id="echoid-s8741" xml:space="preserve">Cum AC, ſit quadrans, erit </s>
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