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

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        <div xml:id="echoid-div1128" type="section" level="1" n="551">
          <p style="it">
            <s xml:id="echoid-s14271" xml:space="preserve">
              <pb o="412" file="424" n="424" rhead=""/>
            nantur inueſtiganda, primum tamen ſemper potiſsimum eſt, quod quæritur, infer-
              <lb/>
            turq́; </s>
            <s xml:id="echoid-s14272" xml:space="preserve">primò ac per ſe ex ipſo problemate. </s>
            <s xml:id="echoid-s14273" xml:space="preserve">Ex hac igitur propoſitione ſequentia triæ
              <lb/>
            problemata colliguntur.</s>
            <s xml:id="echoid-s14274" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1129" type="section" level="1" n="552">
          <head xml:id="echoid-head587" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s14275" xml:space="preserve">IN triangulo ſphęrico rectangulo, dato arcu, qui recto angulo
              <lb/>
            opponitur & </s>
            <s xml:id="echoid-s14276" xml:space="preserve">alterutro arcuum angulum rectum ambientium; </s>
            <s xml:id="echoid-s14277" xml:space="preserve">in-
              <lb/>
            uenire angulum huic arcui oppoſitum.</s>
            <s xml:id="echoid-s14278" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14279" xml:space="preserve">IN triangulo ABC, cuius angulus C, rectus, dati ſint
              <lb/>
              <figure xlink:label="fig-424-01" xlink:href="fig-424-01a" number="275">
                <image file="424-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/424-01"/>
              </figure>
            arcus
              <emph style="sc">Ab</emph>
            , AC. </s>
            <s xml:id="echoid-s14280" xml:space="preserve">Dico dari quoque angulum
              <emph style="sc">B</emph>
            , arcui
              <lb/>
              <note position="left" xlink:label="note-424-01" xlink:href="note-424-01a" xml:space="preserve">41. huius.</note>
            AC, oppoſitum. </s>
            <s xml:id="echoid-s14281" xml:space="preserve">Quoniam enim eſt, vt ſinus arcus
              <emph style="sc">Ab</emph>
            ,
              <lb/>
            ad ſinum totum anguli recti C, ita ſinus arcus
              <emph style="sc">Ac</emph>
            , ad ſi-
              <lb/>
            num anguli B:</s>
            <s xml:id="echoid-s14282" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14283" xml:space="preserve">S I fiat, vt ſinus arcus dati recto angulo
              <lb/>
            oppoſiti ad ſinum totum, ita ſinus arcus circa
              <lb/>
              <note position="left" xlink:label="note-424-02" xlink:href="note-424-02a" xml:space="preserve">Praxis.</note>
            angulum rectum dati ad aliud, reperietur ſinus
              <lb/>
            anguli quæſiti.</s>
            <s xml:id="echoid-s14284" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14285" xml:space="preserve">VERVM hic diligenter attendendum eſt, num angulus quæſitus
              <emph style="sc">B,</emph>
            ſit acutus,
              <lb/>
            an obtuſus. </s>
            <s xml:id="echoid-s14286" xml:space="preserve">Si enim acutus eſt, dabit arcus ſinui inuento reſpondens angulum B: </s>
            <s xml:id="echoid-s14287" xml:space="preserve">Si
              <lb/>
            vero eſt obtuſus, relinquet idem arcus ex ſemicirculo ſublatus angulum B. </s>
            <s xml:id="echoid-s14288" xml:space="preserve">Pulchre
              <lb/>
            autem arcus datus
              <emph style="sc">AC</emph>
            , circa angulum rectum C, docebit, an angulus
              <emph style="sc">B</emph>
            , acutus ſit,
              <lb/>
              <note position="left" xlink:label="note-424-03" xlink:href="note-424-03a" xml:space="preserve">24. huius.</note>
            vel obtuſus. </s>
            <s xml:id="echoid-s14289" xml:space="preserve">Nam ſi AC, eſt minor quadrante, erit angulus
              <emph style="sc">B</emph>
            , acutus: </s>
            <s xml:id="echoid-s14290" xml:space="preserve">Si vero
              <lb/>
            quadrante maior, obtuſus. </s>
            <s xml:id="echoid-s14291" xml:space="preserve">Sumimus autem hic triangulum ſphæricum, in quo vnus
              <lb/>
            tantum angulus rectus eſt, & </s>
            <s xml:id="echoid-s14292" xml:space="preserve">proinde nullus arcus Quadrans, vt in propoſ. </s>
            <s xml:id="echoid-s14293" xml:space="preserve">dictum
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s14294" xml:space="preserve">quod etiam in ſequentibus intelligatur.</s>
            <s xml:id="echoid-s14295" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1133" type="section" level="1" n="553">
          <head xml:id="echoid-head588" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s14296" xml:space="preserve">IN triangulo ſphęrico rectangulo, dato arcu, qui recto angulo
              <lb/>
            opponitur, & </s>
            <s xml:id="echoid-s14297" xml:space="preserve">alterutro angulorum non rectorum; </s>
            <s xml:id="echoid-s14298" xml:space="preserve">inuenire arcum
              <lb/>
            huic angulo oppoſitum.</s>
            <s xml:id="echoid-s14299" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14300" xml:space="preserve">IN eodem triangulo datus ſit arcus
              <emph style="sc">Ab</emph>
            , recto angulo C, oppoſitus, & </s>
            <s xml:id="echoid-s14301" xml:space="preserve">in ſuper
              <lb/>
            angulus B. </s>
            <s xml:id="echoid-s14302" xml:space="preserve">Dico dari quoque arcum AC, angulo B, oppoſitum. </s>
            <s xml:id="echoid-s14303" xml:space="preserve">Cum enim ſit, vt ſinu@
              <lb/>
              <note position="left" xlink:label="note-424-04" xlink:href="note-424-04a" xml:space="preserve">41. huius.</note>
            arcus
              <emph style="sc">Ab</emph>
            , ad ſinum totum anguli recti C, ita ſinus arcus
              <emph style="sc">A</emph>
            C, ad ſinum anguli
              <emph style="sc">B</emph>
            @
              <lb/>
            erit conuertendo, vt ſinus totus ad ſinum arcus
              <emph style="sc">Ab</emph>
            , ita ſinus anguli B, ad ſinum
              <lb/>
            arcus
              <emph style="sc">Ac</emph>
            .</s>
            <s xml:id="echoid-s14304" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14305" xml:space="preserve">SI igitur fiat, vt ſinus totus ad ſinum arcus angulo recto oppoſiti, ita
              <lb/>
              <note position="left" xlink:label="note-424-05" xlink:href="note-424-05a" xml:space="preserve">Praxis.</note>
            ſinus anguli dati ad aliud, inuenietur ſinus arcus quæſiti.</s>
            <s xml:id="echoid-s14306" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14307" xml:space="preserve">Hic autem arcus erit quadrante minor, ſi datus angulus eſt acutus: </s>
            <s xml:id="echoid-s14308" xml:space="preserve">quadrante
              <lb/>
              <note position="left" xlink:label="note-424-06" xlink:href="note-424-06a" xml:space="preserve">34. huius.</note>
            autem maior, ſi obtuſus.</s>
            <s xml:id="echoid-s14309" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1137" type="section" level="1" n="554">
          <head xml:id="echoid-head589" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s14310" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutro arcuũ circa an-
              <lb/>
            gulum rectũ, & </s>
            <s xml:id="echoid-s14311" xml:space="preserve">angulo, qui ei opponitur; </s>
            <s xml:id="echoid-s14312" xml:space="preserve">inuenire arcũ recto angulo
              <lb/>
            oppoſitum. </s>
            <s xml:id="echoid-s14313" xml:space="preserve">Oportet autem conſtare, num tertius angulus ſitacutus,
              <lb/>
            an obtuſus: </s>
            <s xml:id="echoid-s14314" xml:space="preserve">vel an tertius arcus ſit quadrante minor, aut maior.</s>
            <s xml:id="echoid-s14315" xml:space="preserve"/>
          </p>
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