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

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          <pb o="417" file="429" n="429" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s14506" xml:space="preserve">DATVS deinde ſit arcus AC, cum angulo B, ſibi oppoſito, conſtetq́; </s>
            <s xml:id="echoid-s14507" xml:space="preserve">de reliqu@
              <lb/>
            angulo A, num acutus ſit, an obtuſus: </s>
            <s xml:id="echoid-s14508" xml:space="preserve">vel de altero arcu B
              <emph style="sc">C</emph>
            , circa rectum angulum,
              <lb/>
            qualis ſit. </s>
            <s xml:id="echoid-s14509" xml:space="preserve">Dico rur ſum dari & </s>
            <s xml:id="echoid-s14510" xml:space="preserve">reliquum angulũ A, & </s>
            <s xml:id="echoid-s14511" xml:space="preserve">reliquos arcus
              <emph style="sc">Bc</emph>
            , AB. </s>
            <s xml:id="echoid-s14512" xml:space="preserve">Nam
              <lb/>
            cum ſit, vt ſinus anguli A, ad ſinum totum, ita ſinus complementi anguli B, ad ſinum
              <lb/>
              <note position="right" xlink:label="note-429-01" xlink:href="note-429-01a" xml:space="preserve">42. huius.</note>
            complementi arcus AC; </s>
            <s xml:id="echoid-s14513" xml:space="preserve">erit conuertendo, vt ſinus complementi arcus AC, dati ad
              <lb/>
            ſinum complementi anguli B, dati, ita ſinus totus ad ſinum anguli A, quæſiti.</s>
            <s xml:id="echoid-s14514" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14515" xml:space="preserve">IGITVR cum datur arcus cum angulo ſibi oppoſito, ſi fiat, vt ſi.
              <lb/>
            </s>
            <s xml:id="echoid-s14516" xml:space="preserve">
              <note position="right" xlink:label="note-429-02" xlink:href="note-429-02a" xml:space="preserve">Praxis, quã
                <lb/>
              do datur
                <lb/>
              arcus cum
                <lb/>
              angulo op-
                <lb/>
              poſito.</note>
            nus complementi arcus dati ad ſinum complementi anguli dati, ita ſinus
              <lb/>
            totus ad aliud, procreabitur ſinus reliqui anguli, qui quæritur. </s>
            <s xml:id="echoid-s14517" xml:space="preserve">Ex duo-
              <lb/>
            bus ergo angulis non rectis iam cognitis, cognoſcentur reliqui duo arcus,
              <lb/>
            vt in præcedenti problemate monſtrauimus. </s>
            <s xml:id="echoid-s14518" xml:space="preserve">Tertius autem per hypothe-
              <lb/>
            ſim datus est.</s>
            <s xml:id="echoid-s14519" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14520" xml:space="preserve">OPORTET autem conſtare, num reliquus angulus A, ſit acutus, an obtuſus,
              <lb/>
            vt ſciatur, qualis angulus ſinui inuento reſpondens ſit accipiendus, acutuſne, an obtu-
              <lb/>
            ſus. </s>
            <s xml:id="echoid-s14521" xml:space="preserve">Quòd ſi conſtaret de arcu BC, qualis ſit, illico cognoſceretur quoque ſpecies an-
              <lb/>
            guli A. </s>
            <s xml:id="echoid-s14522" xml:space="preserve">Nam ſi arcus
              <emph style="sc">B</emph>
            C, fuerit quadrante minor, erit angulus A, acutus: </s>
            <s xml:id="echoid-s14523" xml:space="preserve">ſi autem
              <lb/>
            quadrante maior, obtuſus. </s>
            <s xml:id="echoid-s14524" xml:space="preserve">Pari ratione, ſi ſciretur, qualis ſit arcus AB, angulo re-
              <lb/>
              <note position="right" xlink:label="note-429-03" xlink:href="note-429-03a" xml:space="preserve">34. huius.</note>
            cto oppoſitus, continuò ſpeciem anguli A, cognoſceremus. </s>
            <s xml:id="echoid-s14525" xml:space="preserve">Nam ſi arcus AB, fuerit
              <lb/>
            minor quadrante, & </s>
            <s xml:id="echoid-s14526" xml:space="preserve">datus quidem angulus B, acutus, erit quoque angulus A, acu-
              <lb/>
              <note position="right" xlink:label="note-429-04" xlink:href="note-429-04a" xml:space="preserve">38. huius.</note>
            tus; </s>
            <s xml:id="echoid-s14527" xml:space="preserve">Si vero datus angulus B, ſit obtuſus, erit quoque obtuſus angulus A. </s>
            <s xml:id="echoid-s14528" xml:space="preserve">At ſi arcus
              <lb/>
            AB, fuerit maior quadrante, & </s>
            <s xml:id="echoid-s14529" xml:space="preserve">datus quidem angulus B, acutus, erit angulus A,
              <lb/>
            obtuſus: </s>
            <s xml:id="echoid-s14530" xml:space="preserve">Si vero datus angulus B, ſit obtuſus, erit angulus A, acutus. </s>
            <s xml:id="echoid-s14531" xml:space="preserve">Itaque non
              <lb/>
            eſt ſatis, dari angulum non rectum, cum arcu oppoſito, vt vult Copernicus propoſ. </s>
            <s xml:id="echoid-s14532" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s14533" xml:space="preserve">de triangulis ſphæricis: </s>
            <s xml:id="echoid-s14534" xml:space="preserve">Id quod ſupra quoque monuimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14535" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14536" xml:space="preserve">ſed
              <lb/>
            debet etiam dari ſpecies tertij anguli, vel ſpecies arcus alterius circa rectum angu-
              <lb/>
            lum; </s>
            <s xml:id="echoid-s14537" xml:space="preserve">vel certe ſpecies arcus recto angulo oppoſiti. </s>
            <s xml:id="echoid-s14538" xml:space="preserve">Qua in re lapſus eſt Nicolaus Co-
              <lb/>
              <note position="right" xlink:label="note-429-05" xlink:href="note-429-05a" xml:space="preserve">Error Co-
                <lb/>
              pernici.</note>
            pernicus, qui voluit in propoſ 4. </s>
            <s xml:id="echoid-s14539" xml:space="preserve">de triangulis ſphæricis, ſatis eſſe, vt detur arcus cir-
              <lb/>
            ca rectum angulum, cum alterutro angulorum non rectorum. </s>
            <s xml:id="echoid-s14540" xml:space="preserve">Falſum enim hoc eſt
              <lb/>
            de angulo dato arcui oppoſito, niſi aliud præterea conſtet, vt hic diximus, & </s>
            <s xml:id="echoid-s14541" xml:space="preserve">in ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s14542" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14543" xml:space="preserve">monuimus.</s>
            <s xml:id="echoid-s14544" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1158" type="section" level="1" n="559">
          <head xml:id="echoid-head594" xml:space="preserve">THEOR. 41. PROPOS. 43.</head>
          <p>
            <s xml:id="echoid-s14545" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cuius
              <lb/>
            nullus arcuum quadrans ſit, ſinus complementi
              <lb/>
            arcus rectum angulum ſubtendẽtis ad ſinum com
              <lb/>
            plementi vtriuſve reliquorum arcuum eandem ha
              <lb/>
            bet proportionem, quam ſinus complementi re-
              <lb/>
            liqui arcus ad ſinum totum.</s>
            <s xml:id="echoid-s14546" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14547" xml:space="preserve">IN triangulo ſphærico rectangulo ABC, angulus B, ſit rectus, & </s>
            <s xml:id="echoid-s14548" xml:space="preserve"/>
          </p>
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