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

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            <s xml:id="echoid-s16775" xml:space="preserve">
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            tus ſit arcus AC, angulo recto oppoſitus, & </s>
            <s xml:id="echoid-s16776" xml:space="preserve">angulus CAD, iam inuentus:
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            </s>
            <s xml:id="echoid-s16777" xml:space="preserve">VEL cum ſit cognitus arcus CD, circa angulum. </s>
            <s xml:id="echoid-s16778" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-481-01" xlink:href="note-481-01a" xml:space="preserve">Schol. 56.
                <lb/>
              vel 42. huiꝰ.</note>
            rectum, ac præterea angulus CAD; </s>
            <s xml:id="echoid-s16779" xml:space="preserve">conſtetq́; </s>
            <s xml:id="echoid-s16780" xml:space="preserve">de re-
              <lb/>
            liquo arcu AD, circa rectum angulum noto iam facto,
              <lb/>
            an minor quadrante ſit, an maior:
              <lb/>
            </s>
            <s xml:id="echoid-s16781" xml:space="preserve">AVT, cum datus ſit arcus AC, angulo recto oppo-
              <lb/>
              <note position="right" xlink:label="note-481-02" xlink:href="note-481-02a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            ſitus, cum arcu CD, circa angulum rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s16782" xml:space="preserve">VEL denique, quoniam notus eſt arcus AC, recto
              <lb/>
              <note position="right" xlink:label="note-481-03" xlink:href="note-481-03a" xml:space="preserve">Schol. 55.
                <lb/>
              vel 41. hui ꝰ.</note>
            angulo oppoſitus, vnà cum arcu AD, circa angu-
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            lum rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s16783" xml:space="preserve">cognitus quoque fiet, per ſcholia in margine adducta, angulus ACD; </s>
            <s xml:id="echoid-s16784" xml:space="preserve">qui qui-
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            dem in priori triangulo, vbi arcus AD, intra triangulum cadit, quærebatur: </s>
            <s xml:id="echoid-s16785" xml:space="preserve">
              <lb/>
            in poſterioriautem, vbi arcus AD, extra triangulum cadit, idem angulus
              <lb/>
            ACD, ex duobus rectis ablatus, notum relinquit quæſitum angulum ACB. </s>
            <s xml:id="echoid-s16786" xml:space="preserve">
              <lb/>
            Atque ita inuentus eſt & </s>
            <s xml:id="echoid-s16787" xml:space="preserve">arcus reliquus AC, & </s>
            <s xml:id="echoid-s16788" xml:space="preserve">reliqui anguli BAC, ACB.</s>
            <s xml:id="echoid-s16789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16790" xml:space="preserve">NVLLA porro ratione alteruter arcuum AD, BD, eſſe poteſt quadrans:
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            </s>
            <s xml:id="echoid-s16791" xml:space="preserve">quia alias & </s>
            <s xml:id="echoid-s16792" xml:space="preserve">arcus AB, recto angulo oppoſitus quadrans foret: </s>
            <s xml:id="echoid-s16793" xml:space="preserve">quod eſt con
              <lb/>
              <note position="right" xlink:label="note-481-04" xlink:href="note-481-04a" xml:space="preserve">35. huius.</note>
            tra hypotheſim.</s>
            <s xml:id="echoid-s16794" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16795" xml:space="preserve">QVOD ſi quando arcus CD, deprehenſus fuerit quadrans; </s>
            <s xml:id="echoid-s16796" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s16797" xml:space="preserve">arcus
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            AC, quæſitus, & </s>
            <s xml:id="echoid-s16798" xml:space="preserve">recto angulo oppoſitus, quadrans; </s>
            <s xml:id="echoid-s16799" xml:space="preserve">& </s>
            <s xml:id="echoid-s16800" xml:space="preserve">angulus CAD, rectus.
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            </s>
            <s xml:id="echoid-s16801" xml:space="preserve">
              <note position="right" xlink:label="note-481-05" xlink:href="note-481-05a" xml:space="preserve">35. huius.</note>
            Atque ita ſine vllo labore inuentus erit & </s>
            <s xml:id="echoid-s16802" xml:space="preserve">arcus AC, qui quæritur, & </s>
            <s xml:id="echoid-s16803" xml:space="preserve">angulus
              <lb/>
              <note position="right" xlink:label="note-481-06" xlink:href="note-481-06a" xml:space="preserve">34. huius.</note>
            CAD. </s>
            <s xml:id="echoid-s16804" xml:space="preserve">Reliqua reperientur, vt prius.</s>
            <s xml:id="echoid-s16805" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16806" xml:space="preserve">PRAXIS ad enodandum hoc problema petenda eſt ex ſcholijs in
              <lb/>
            margine citatis.</s>
            <s xml:id="echoid-s16807" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16808" xml:space="preserve">VERVM per ſolos ſinus ita progrediendum erit. </s>
            <s xml:id="echoid-s16809" xml:space="preserve">Ex praxi proble-
              <lb/>
              <note position="right" xlink:label="note-481-07" xlink:href="note-481-07a" xml:space="preserve">Praxis per
                <lb/>
              ſolos ſinus,
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              quãdo duo
                <lb/>
              dati arcus
                <lb/>
              ſunt inæ-
                <lb/>
              quales, &
                <lb/>
              neuter qua
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              drans.</note>
            matis 2. </s>
            <s xml:id="echoid-s16810" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16811" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16812" xml:space="preserve">inquirendus erit arcus AD.</s>
            <s xml:id="echoid-s16813" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16814" xml:space="preserve">DEINDE ex praxi ſcholij 1. </s>
            <s xml:id="echoid-s16815" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16816" xml:space="preserve">43. </s>
            <s xml:id="echoid-s16817" xml:space="preserve">arcus BD; </s>
            <s xml:id="echoid-s16818" xml:space="preserve">ex quo arcus CD,
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            notus efficietur, auferendo inuentum arcum BD, ex dato arcu BC, vel
              <lb/>
            datum arcum BC, ex ipſo inuento arcu BD, prout minor inuentus fuerit,
              <lb/>
            quam datus arcus BC, aut maior.</s>
            <s xml:id="echoid-s16819" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16820" xml:space="preserve">AD hæc, in triãgulo BAD, explorãdus erit angulus BAD, per praxim
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            problematis 1. </s>
            <s xml:id="echoid-s16821" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16822" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16823" xml:space="preserve">vel per praxim problematis 2. </s>
            <s xml:id="echoid-s16824" xml:space="preserve">ſcholij propoſ.
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            </s>
            <s xml:id="echoid-s16825" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16826" xml:space="preserve">Similiter in triangulo ACD, eliciendus angulus CAD, ex praxi
              <lb/>
            problematis 1. </s>
            <s xml:id="echoid-s16827" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16828" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16829" xml:space="preserve">Ex duobus autem angulis BAD, CAD,
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            inuentis notus euadet angulus BAC, trianguli propoſiti; </s>
            <s xml:id="echoid-s16830" xml:space="preserve">addendo ſcili-
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            cet vnum alteri, vt in prioritriangulo, vel auferendo angulum CAD, ex
              <lb/>
            angulo BAD, vt in triangulo poſteriori.</s>
            <s xml:id="echoid-s16831" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16832" xml:space="preserve">PER praxim denique problematis 1. </s>
            <s xml:id="echoid-s16833" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16834" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16835" xml:space="preserve">vel problema-
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            tis 2. </s>
            <s xml:id="echoid-s16836" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16837" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16838" xml:space="preserve">in triangulo ACD, eodem indagandus angulus
              <lb/>
            ACD. </s>
            <s xml:id="echoid-s16839" xml:space="preserve">Hic enim in priori triangulo propoſito eſt quæſitus, in poſteriori
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            veroreliquus duorum rectorum eſt is, qui quæritur.</s>
            <s xml:id="echoid-s16840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16841" xml:space="preserve">ALITER, & </s>
            <s xml:id="echoid-s16842" xml:space="preserve">quidem magis expeditè. </s>
            <s xml:id="echoid-s16843" xml:space="preserve">Sint rurſus in triangulo ABC, dati
              <lb/>
              <note position="right" xlink:label="note-481-08" xlink:href="note-481-08a" xml:space="preserve">Alia demõ
                <lb/>
              ſtratio bre-
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              uior.</note>
            duo arcus inæquales AB, AC, cum angulo A. </s>
            <s xml:id="echoid-s16844" xml:space="preserve">Quoniam igitur eſt, vt </s>
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