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

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          <p>
            <s xml:id="echoid-s16207" xml:space="preserve">
              <pb o="458" file="470" n="470" rhead=""/>
            ſinum complementi anguli C: </s>
            <s xml:id="echoid-s16208" xml:space="preserve">proportio autem hæc poſterior data eſt in ſinu-
              <lb/>
            bus complementorum angulorum B, C, datorum; </s>
            <s xml:id="echoid-s16209" xml:space="preserve">erit quoque proportio ſi-
              <lb/>
            nus anguli BAD, ad ſinum anguli DAC, data, nempe in ſinubus complemen
              <lb/>
            torum angulorum B,C: </s>
            <s xml:id="echoid-s16210" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s16211" xml:space="preserve">aggregatum eorun-
              <lb/>
              <figure xlink:label="fig-470-01" xlink:href="fig-470-01a" number="339">
                <image file="470-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/470-01"/>
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            dem duorum angulorum BAD, DAC, datum eſt, & </s>
            <s xml:id="echoid-s16212" xml:space="preserve">
              <lb/>
            minus ſemicirculo, nempe totus angulus BAC, qui
              <lb/>
            duobus rectis minor eſt. </s>
            <s xml:id="echoid-s16213" xml:space="preserve">Sigillatim igitur vterque an-
              <lb/>
            gulorum BAD, DAC, cognitus erit. </s>
            <s xml:id="echoid-s16214" xml:space="preserve">Quoniam ergo
              <lb/>
              <note position="left" xlink:label="note-470-01" xlink:href="note-470-01a" xml:space="preserve">@. triang.
                <lb/>
              rectil.</note>
            in triangulo ABD, cuius angulus D, rectus, dati ſunt
              <lb/>
            duo anguli non recti B, & </s>
            <s xml:id="echoid-s16215" xml:space="preserve">BAD; </s>
            <s xml:id="echoid-s16216" xml:space="preserve">dabitur quoque ar-
              <lb/>
              <note position="left" xlink:label="note-470-02" xlink:href="note-470-02a" xml:space="preserve">Schol. 50.
                <lb/>
              huius.</note>
            cus AB, recto angulo oppoſitus. </s>
            <s xml:id="echoid-s16217" xml:space="preserve">Hinc, quia in eo-
              <lb/>
            dem triangulo ABD, angulum habente rectum D, co
              <lb/>
            gnitus eſt arcus AB, recto angulo oppoſitus, & </s>
            <s xml:id="echoid-s16218" xml:space="preserve">inſu-
              <lb/>
              <note position="left" xlink:label="note-470-03" xlink:href="note-470-03a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            per angulus non rectus BAD:
              <lb/>
            </s>
            <s xml:id="echoid-s16219" xml:space="preserve">VEL certe, quoniam dati ſunt duo anguli non
              <lb/>
              <note position="left" xlink:label="note-470-04" xlink:href="note-470-04a" xml:space="preserve">Schol. 42.
                <lb/>
              vel 52. huiꝰ.</note>
            recti B, & </s>
            <s xml:id="echoid-s16220" xml:space="preserve">BAD;
              <lb/>
            </s>
            <s xml:id="echoid-s16221" xml:space="preserve">notus quoque fiet, ex ſcholijs in margine citatis, arcus BD, circa angulum re-
              <lb/>
            ctum angulo BAD, oppoſitus. </s>
            <s xml:id="echoid-s16222" xml:space="preserve">Eadem ratione, quia in triangulo ACD, cu-
              <lb/>
            ius angulus D, rectus, dati ſunt duo anguli non recti C, & </s>
            <s xml:id="echoid-s16223" xml:space="preserve">CAD; </s>
            <s xml:id="echoid-s16224" xml:space="preserve">dabitur quo-
              <lb/>
              <note position="left" xlink:label="note-470-05" xlink:href="note-470-05a" xml:space="preserve">Schol. 50.
                <lb/>
              huius.</note>
            que arcus AC, angulo recto oppoſitus. </s>
            <s xml:id="echoid-s16225" xml:space="preserve">Hinc, quoniam in eodem triangulo
              <lb/>
            ACD, habente rectum angulum D, cognitus iam eſt arcus AC, recto angulo
              <lb/>
            oppoſitus, cum angulo non recto CAD:
              <lb/>
            </s>
            <s xml:id="echoid-s16226" xml:space="preserve">
              <note position="left" xlink:label="note-470-06" xlink:href="note-470-06a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            AVT certe, quia datiſunt duo anguli non re-
              <lb/>
              <note position="left" xlink:label="note-470-07" xlink:href="note-470-07a" xml:space="preserve">Schol. 42.
                <lb/>
              vel 52. huiꝰ.</note>
            cti C, & </s>
            <s xml:id="echoid-s16227" xml:space="preserve">CAD;
              <lb/>
            </s>
            <s xml:id="echoid-s16228" xml:space="preserve">cognoſcetur etiam, ex eiſdem ſcholijs in margine adductis, arcus CD, circa
              <lb/>
            angulum rectum angulo CAD, oppoſitus. </s>
            <s xml:id="echoid-s16229" xml:space="preserve">Atque ita iam duo arcus AB, AC,
              <lb/>
            cogniti ſunt: </s>
            <s xml:id="echoid-s16230" xml:space="preserve">Aggregatum vero duorum arcuum BD, CD, inuentorum ter-
              <lb/>
            tium arcum BC, notum etiam efficiet.</s>
            <s xml:id="echoid-s16231" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16232" xml:space="preserve">QVOD ſi quando alter angulorum ad A, nempe BAD, inuentus fuerit
              <lb/>
            rectus, cum & </s>
            <s xml:id="echoid-s16233" xml:space="preserve">D, rectus ſit, erit vterque arcus AB, BD, quadrans: </s>
            <s xml:id="echoid-s16234" xml:space="preserve">atque ita
              <lb/>
              <note position="left" xlink:label="note-470-08" xlink:href="note-470-08a" xml:space="preserve">25. huius.</note>
            ſine vlla moleſtia inuenti erunt dicti arcus. </s>
            <s xml:id="echoid-s16235" xml:space="preserve">Pari ratione, ſi angulus CAD,
              <lb/>
            deprehenſus fuerit rectus, non autem BAD, (fieri enim non poteſt, vt vter-
              <lb/>
            que angulus ad A, rectus ſit, cum angulus BAD, duobus rectis ſit minor.)
              <lb/>
            </s>
            <s xml:id="echoid-s16236" xml:space="preserve">erunt arcus AC, CD, quadrantes; </s>
            <s xml:id="echoid-s16237" xml:space="preserve">atque adeo noti, ſine alio labore.</s>
            <s xml:id="echoid-s16238" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16239" xml:space="preserve">PRAXIS huius problematis, cum ex propoſ. </s>
            <s xml:id="echoid-s16240" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16241" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s16242" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s16243" xml:space="preserve">& </s>
            <s xml:id="echoid-s16244" xml:space="preserve">ex
              <lb/>
              <note position="left" xlink:label="note-470-09" xlink:href="note-470-09a" xml:space="preserve">Praxis, quã
                <lb/>
              do omnes
                <lb/>
              tres dati an
                <lb/>
              guli inæ-
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              quales sũt.</note>
            ſcholijs in margine ſcriptis petẽda ſit, nõ eſt, quòd hic pluribus explicetur.
              <lb/>
            </s>
            <s xml:id="echoid-s16245" xml:space="preserve">Nam ſi statuãtur duo ſinus complementorum angulorum B, C, acutorum,
              <lb/>
            vel obtuſorũ, pro terminis proportionis ſinus anguli BAD, ad ſinũ angu-
              <lb/>
            li CAD, inueniemus vtrumq; </s>
            <s xml:id="echoid-s16246" xml:space="preserve">angulũ BAD, CAD, per primã, vel ſecun
              <lb/>
            dam praxim propoſ. </s>
            <s xml:id="echoid-s16247" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16248" xml:space="preserve">triangulorum rectilineorum, quòd bæ expeditio-
              <lb/>
            res ſinò, quam tertia. </s>
            <s xml:id="echoid-s16249" xml:space="preserve">Nam licet propoſitio illa 6. </s>
            <s xml:id="echoid-s16250" xml:space="preserve">de arcubus, & </s>
            <s xml:id="echoid-s16251" xml:space="preserve">angulis
              <lb/>
              <note position="left" xlink:label="note-470-10" xlink:href="note-470-10a" xml:space="preserve">Pro@oſitio
                <lb/>
              6. triag. re-
                <lb/>
              ctil. intelli-
                <lb/>
              genda eti á
                <lb/>
              eſt de angu
                <lb/>
              lis ſphæri-
                <lb/>
              cis.</note>
            rectilineis antum propoſita ſit, intelligẽda tamen etiã eſt de angulis ſphæ
              <lb/>
            ricis, cumillorum ſinus à ſinubus arcuum eorũdem angulorum non diſcre-
              <lb/>
            pent. </s>
            <s xml:id="echoid-s16252" xml:space="preserve">Innento antem vtroque angulo BAD, CAD, adhibenda erit pra-
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            xis problematis ſcholy propoſ. </s>
            <s xml:id="echoid-s16253" xml:space="preserve">50. </s>
            <s xml:id="echoid-s16254" xml:space="preserve">huius, vt tam arcus AB, recto </s>
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