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

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            <s xml:id="echoid-s16254" xml:space="preserve">
              <pb o="459" file="471" n="471" rhead=""/>
            lo D, intriangulo ABD, oppoſitus, quam arcus AC, angulo recto D, in
              <lb/>
            triangulo ACD, oppoſitus inueniatur. </s>
            <s xml:id="echoid-s16255" xml:space="preserve">Poſtremo adducenda est praxis
              <lb/>
            problematis 2. </s>
            <s xml:id="echoid-s16256" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16257" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16258" xml:space="preserve">vel problematis 1. </s>
            <s xml:id="echoid-s16259" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16260" xml:space="preserve">42.
              <lb/>
            </s>
            <s xml:id="echoid-s16261" xml:space="preserve">vel certe praxis ſcholij propoſ. </s>
            <s xml:id="echoid-s16262" xml:space="preserve">52. </s>
            <s xml:id="echoid-s16263" xml:space="preserve">ad eruendum tam arcum BD, angulo
              <lb/>
            non recto BAD, in triangulo ABD, oppoſitum, quam arcum CD, an-
              <lb/>
            gulo non recto CAD, oppoſitum in triangulo ACD.</s>
            <s xml:id="echoid-s16264" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16265" xml:space="preserve">QVOD ſi in hoc problemate enodando ſolis ſinubus vti libeat, inue-
              <lb/>
              <note position="right" xlink:label="note-471-01" xlink:href="note-471-01a" xml:space="preserve">Praxis per
                <lb/>
              ſolos ſinus,
                <lb/>
              quãdo om-
                <lb/>
              nes tres an
                <lb/>
              guli dati
                <lb/>
              ſunt inæ-
                <lb/>
              quales.</note>
            niendus erit vterque angulus BAD, CAD, per praxim tertiam propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s16266" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16267" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s16268" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s16269" xml:space="preserve">non autem per primam, vel ſecundam. </s>
            <s xml:id="echoid-s16270" xml:space="preserve">Deinde cx praxi
              <lb/>
            problematis 1. </s>
            <s xml:id="echoid-s16271" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16272" xml:space="preserve">42, huius, eliciendus tam arcus BD, angu-
              <lb/>
            lo non recto BAD, oppoſitus in triangulo ABD, quam arcus CD, an-
              <lb/>
            gulo nonrecto CAD, in triangulo ACD, oppoſitus. </s>
            <s xml:id="echoid-s16273" xml:space="preserve">Ad extremum, per
              <lb/>
            praxim problematis 3. </s>
            <s xml:id="echoid-s16274" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16275" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16276" xml:space="preserve">inuestigandus tam arcus AB,
              <lb/>
            quam arcus AC, recto angulo D, quilibet in ſuo triangulo oppoſitus: </s>
            <s xml:id="echoid-s16277" xml:space="preserve">quia
              <lb/>
            præter inuentum arcum BD, & </s>
            <s xml:id="echoid-s16278" xml:space="preserve">oppoſitum angulum BAD; </s>
            <s xml:id="echoid-s16279" xml:space="preserve">necnon præ-
              <lb/>
            ter arcum inuentum CD, & </s>
            <s xml:id="echoid-s16280" xml:space="preserve">angulum CAD, oppoſitum, conſtat etiam
              <lb/>
              <note position="right" xlink:label="note-471-02" xlink:href="note-471-02a" xml:space="preserve">Quãdo oẽs
                <lb/>
              tres anguli
                <lb/>
              dati@, vel
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              duo ſalté,
                <lb/>
              sũc ęquales.</note>
            ſpecies tam anguli B, quam anguli C, cum vterque datus ſit.</s>
            <s xml:id="echoid-s16281" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16282" xml:space="preserve">LONGE facilius fit hoc problema, quando omnes tres anguli dati, vel
              <lb/>
            duo ſaltem, ſunt æquales. </s>
            <s xml:id="echoid-s16283" xml:space="preserve">Nam ſi ſint duo v. </s>
            <s xml:id="echoid-s16284" xml:space="preserve">g. </s>
            <s xml:id="echoid-s16285" xml:space="preserve">anguli B, C, æquales, quic-
              <lb/>
            quid ſit de reliquo A; </s>
            <s xml:id="echoid-s16286" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s16287" xml:space="preserve">arcus AB, AC, æquales. </s>
            <s xml:id="echoid-s16288" xml:space="preserve">Et quoniam trian-
              <lb/>
              <note position="right" xlink:label="note-471-03" xlink:href="note-471-03a" xml:space="preserve">9. huius.</note>
            gulum ABC, ponitur non rectangulum, erit vterque an-
              <lb/>
            gulorum æqualium B, C, vel acutus, vel obtuſus. </s>
            <s xml:id="echoid-s16289" xml:space="preserve">Quare
              <lb/>
              <figure xlink:label="fig-471-01" xlink:href="fig-471-01a" number="340">
                <image file="471-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/471-01"/>
              </figure>
            arcus perpendicularis AD, ex tertio angulo A, ad arcum
              <lb/>
            BC, demiſſus intra triangulum cadet. </s>
            <s xml:id="echoid-s16290" xml:space="preserve">Quia ergo triangu-
              <lb/>
              <note position="right" xlink:label="note-471-04" xlink:href="note-471-04a" xml:space="preserve">57. huius.</note>
            la ABD, ACD, angulos ad D, rectos habent, & </s>
            <s xml:id="echoid-s16291" xml:space="preserve">angulos
              <lb/>
            B, C, non rectos, æquales; </s>
            <s xml:id="echoid-s16292" xml:space="preserve">necnon & </s>
            <s xml:id="echoid-s16293" xml:space="preserve">arcus AB, AC, rectis
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            angulis oppoſitos, æquales, vt oſtendimus; </s>
            <s xml:id="echoid-s16294" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s16295" xml:space="preserve">arcus
              <lb/>
            BD, CD, & </s>
            <s xml:id="echoid-s16296" xml:space="preserve">anguli BAD, CAD, æquales; </s>
            <s xml:id="echoid-s16297" xml:space="preserve">ac proinde
              <lb/>
              <note position="right" xlink:label="note-471-05" xlink:href="note-471-05a" xml:space="preserve">21. huius.</note>
            vterque angulus BAD, CAD, cum dimidium ſit dati an-
              <lb/>
            guli BAC, notus erit. </s>
            <s xml:id="echoid-s16298" xml:space="preserve">Poſt hæc, quoniam in triangulo
              <lb/>
            ABD, rectum habente angulum D, datus eſt vterque an-
              <lb/>
            gulus non rectus B, & </s>
            <s xml:id="echoid-s16299" xml:space="preserve">BAD; </s>
            <s xml:id="echoid-s16300" xml:space="preserve">dabitur quoque arcus AB, recto angulo oppo-
              <lb/>
              <note position="right" xlink:label="note-471-06" xlink:href="note-471-06a" xml:space="preserve">Schol. 50.
                <lb/>
              huius.</note>
            ſitus; </s>
            <s xml:id="echoid-s16301" xml:space="preserve">proptereaque & </s>
            <s xml:id="echoid-s16302" xml:space="preserve">illi æqualis AC, notus erit. </s>
            <s xml:id="echoid-s16303" xml:space="preserve">Atque ita iam duo arcus
              <lb/>
              <note position="right" xlink:label="note-471-07" xlink:href="note-471-07a" xml:space="preserve">Schol. 42.
                <lb/>
              vel 52. huiꝰ.</note>
            AB, AC, noti facti ſunt. </s>
            <s xml:id="echoid-s16304" xml:space="preserve">Rurſus quia in eodem triangulo ABD, dati ſunt
              <lb/>
            duo anguli non recti B, & </s>
            <s xml:id="echoid-s16305" xml:space="preserve">BAD:
              <lb/>
            </s>
            <s xml:id="echoid-s16306" xml:space="preserve">VEL, quoniam datus eſt arcus AB, angulo recto op-
              <lb/>
              <note position="right" xlink:label="note-471-08" xlink:href="note-471-08a" xml:space="preserve">Schol. 45.
                <lb/>
              huius.</note>
            poſitus, & </s>
            <s xml:id="echoid-s16307" xml:space="preserve">angulus non rectus B:
              <lb/>
            </s>
            <s xml:id="echoid-s16308" xml:space="preserve">VEL denique, quia datus eſt arcus AB, recto angulo
              <lb/>
              <note position="right" xlink:label="note-471-09" xlink:href="note-471-09a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            oppoſitus, cum angulo non recto BAD;
              <lb/>
            </s>
            <s xml:id="echoid-s16309" xml:space="preserve">cognitus etiam erit arcus BD, circa angulum rectum: </s>
            <s xml:id="echoid-s16310" xml:space="preserve">qui duplicatus totum
              <lb/>
            tertium arcum BC, notum exhibebit. </s>
            <s xml:id="echoid-s16311" xml:space="preserve">Omnes ergo tres arcus, qui quæruntur,
              <lb/>
            noti effecti ſunt.</s>
            <s xml:id="echoid-s16312" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16313" xml:space="preserve">NON est obſcura praxis huius rei. </s>
            <s xml:id="echoid-s16314" xml:space="preserve">Pendet enim ex ſcholijs in </s>
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