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

Table of figures

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        <div xml:id="echoid-div1147" type="section" level="1" n="557">
          <head xml:id="echoid-head592" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s14469" xml:space="preserve">IN triangulo ſphętico rectangulo, datis duobus angulis non
              <lb/>
            rectis; </s>
            <s xml:id="echoid-s14470" xml:space="preserve">inuenire arcum vtrilibet eorum oppoſitum, vna cum arcu,
              <lb/>
            qui recto angulo opponitur.</s>
            <s xml:id="echoid-s14471" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14472" xml:space="preserve">IN triangulo
              <emph style="sc">Ab</emph>
            C, cuius angulus C, rectus, dati ſint anguli A,
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s14473" xml:space="preserve">Dice
              <lb/>
            vtrumuis arcuum
              <emph style="sc">AC</emph>
            , BC, quoque dari, cum arcu
              <lb/>
              <figure xlink:label="fig-428-01" xlink:href="fig-428-01a" number="281">
                <image file="428-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/428-01"/>
              </figure>
            AB. </s>
            <s xml:id="echoid-s14474" xml:space="preserve">Quoniam enim eſt, vt ſinus anguli A, ad ſinum
              <lb/>
            totum, ita ſinus complementi anguli B, ad ſinum com-
              <lb/>
              <note position="left" xlink:label="note-428-01" xlink:href="note-428-01a" xml:space="preserve">41. huius.</note>
            plementi arcus
              <emph style="sc">A</emph>
            C. </s>
            <s xml:id="echoid-s14475" xml:space="preserve">Item, vt ſinus anguli
              <emph style="sc">B</emph>
            , ad ſinum
              <lb/>
            totum, ita ſinus complementi anguli
              <emph style="sc">A</emph>
            , ad ſinum com-
              <lb/>
            plementi arcus BC;</s>
            <s xml:id="echoid-s14476" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14477" xml:space="preserve">SI fiat, vt ſinus anguli dati, qui quæſito la
              <lb/>
              <note position="left" xlink:label="note-428-02" xlink:href="note-428-02a" xml:space="preserve">Praxit.</note>
            teri adiacet, ad ſinum totum, ita ſinus com-
              <lb/>
            plementi reliqui anguli dati ad aliud, produ-
              <lb/>
            cetur ſinus complementi arcus huic posteriori angulo oppoſiti, qui quæ-
              <lb/>
            ritur. </s>
            <s xml:id="echoid-s14478" xml:space="preserve">Inuento autem vtroque arcu circa angulum rectum, reperietur
              <lb/>
            quoque ex vtrolibet illorum, & </s>
            <s xml:id="echoid-s14479" xml:space="preserve">ex angulo, qui ei opponuntur dato, ar-
              <lb/>
            cus recto angulo oppoſitus, vt in problemate 3. </s>
            <s xml:id="echoid-s14480" xml:space="preserve">propoſitionis 41. </s>
            <s xml:id="echoid-s14481" xml:space="preserve">oſten-
              <lb/>
            dimus.</s>
            <s xml:id="echoid-s14482" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14483" xml:space="preserve">VTRVM autem arcus AC,
              <emph style="sc">BC</emph>
            , ſint minores quadrante, aut maiores, ita
              <lb/>
            diſcemus. </s>
            <s xml:id="echoid-s14484" xml:space="preserve">Si angulus
              <emph style="sc">B</emph>
            , eſt acutus, erit arcus AC, ei oppoſitus quadrante minor: </s>
            <s xml:id="echoid-s14485" xml:space="preserve">Si
              <lb/>
              <note position="left" xlink:label="note-428-03" xlink:href="note-428-03a" xml:space="preserve">14. huius.</note>
            vero obtuſus, quadrante maior. </s>
            <s xml:id="echoid-s14486" xml:space="preserve">Eadem ratione ſi angulus A, fuerit acutus, erit ar-
              <lb/>
            cus ei oppoſitus
              <emph style="sc">B</emph>
            C, quadrante minor: </s>
            <s xml:id="echoid-s14487" xml:space="preserve">ſi vero obtuſus, quadrante maior.</s>
            <s xml:id="echoid-s14488" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1151" type="section" level="1" n="558">
          <head xml:id="echoid-head593" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s14489" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutro angulorum
              <lb/>
            non rectorum, cum alterutro arcuum circa angulum rectum; </s>
            <s xml:id="echoid-s14490" xml:space="preserve">inue-
              <lb/>
            nire alium angulum non rectum, & </s>
            <s xml:id="echoid-s14491" xml:space="preserve">reliquos duos arcus.</s>
            <s xml:id="echoid-s14492" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14493" xml:space="preserve">IN eodem triangulo datus ſit primum arcus AC, cum angulo A, ſibi adiacente.
              <lb/>
            </s>
            <s xml:id="echoid-s14494" xml:space="preserve">Dico dari quoque angulum B, cum arcubus
              <emph style="sc">BC</emph>
            ,
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s14495" xml:space="preserve">Cum enim ſit, vt ſinus an-
              <lb/>
            guli
              <emph style="sc">A</emph>
            , ad ſinum totum, ita ſinus complementi anguli
              <emph style="sc">B</emph>
            , ad ſinum complementi ar-
              <lb/>
              <note position="left" xlink:label="note-428-04" xlink:href="note-428-04a" xml:space="preserve">42. huius.</note>
            cus
              <emph style="sc">A</emph>
            C; </s>
            <s xml:id="echoid-s14496" xml:space="preserve">erit conuertendo, vt ſinus totus ad ſinum anguli A, dati, ita ſinus comple-
              <lb/>
            menti dati arcus AC, ad ſinum complementi anguli
              <emph style="sc">B</emph>
            , qui quæritur.</s>
            <s xml:id="echoid-s14497" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14498" xml:space="preserve">QVANDO ergo datur arcus cum angulo ſibi adiacẽte, ſi fiat, vt ſi-
              <lb/>
              <note position="left" xlink:label="note-428-05" xlink:href="note-428-05a" xml:space="preserve">Praxis, quã
                <lb/>
              do datur
                <lb/>
              areus cum
                <lb/>
              angulo a-
                <lb/>
              diacente.</note>
            nus totus ad ſinum anguli dati, ita ſinus complementi arcus dati ad aliud,
              <lb/>
            reperietur ſinus complementi alterius anguli, qui quæritur. </s>
            <s xml:id="echoid-s14499" xml:space="preserve">Hinc ex duo-
              <lb/>
            bus angulis non rectis iam cognitis, cognoſcentur reliqui duo arcus, vt
              <lb/>
            in proximè antecedenti problemate demonſtratum eſt: </s>
            <s xml:id="echoid-s14500" xml:space="preserve">Tertius autem da-
              <lb/>
            tus eſt ex hypotheſi.</s>
            <s xml:id="echoid-s14501" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14502" xml:space="preserve">NVM vero angulus
              <emph style="sc">B</emph>
            , quæſitus ſit acutus, obtuſusue, docebit datus arcus AC.
              <lb/>
            </s>
            <s xml:id="echoid-s14503" xml:space="preserve">Si enim fuerit quadrante minor, erit angulus
              <emph style="sc">B</emph>
            , acutus: </s>
            <s xml:id="echoid-s14504" xml:space="preserve">ſi vero maior quadrante,
              <lb/>
              <note position="left" xlink:label="note-428-06" xlink:href="note-428-06a" xml:space="preserve">44. huius.</note>
            @btuſus.</s>
            <s xml:id="echoid-s14505" xml:space="preserve"/>
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