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

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        <div xml:id="echoid-div1194" type="section" level="1" n="569">
          <pb o="427" file="439" n="439" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s14959" xml:space="preserve">VTRVM vero angulus A, quæſitus ſit acutus, obtuſusue, ita diſcemus. </s>
            <s xml:id="echoid-s14960" xml:space="preserve">Si arcus
              <lb/>
            AB, recto angulo oppoſitus fuerit quadrante minor, erit vterq; </s>
            <s xml:id="echoid-s14961" xml:space="preserve">arcus AC,
              <emph style="sc">B</emph>
            C, vel
              <lb/>
              <note position="right" xlink:label="note-439-01" xlink:href="note-439-01a" xml:space="preserve">36. huius.</note>
            minor quadrante, vel maior. </s>
            <s xml:id="echoid-s14962" xml:space="preserve">Si ergo datus arcus AC, ſit minor, erit quoque
              <emph style="sc">Bc</emph>
            , mi-
              <lb/>
            nor, ac proinde angulus A, acutus; </s>
            <s xml:id="echoid-s14963" xml:space="preserve">ſi vero AC, ſit quadrante maior, erit & </s>
            <s xml:id="echoid-s14964" xml:space="preserve">BC,
              <lb/>
              <note position="right" xlink:label="note-439-02" xlink:href="note-439-02a" xml:space="preserve">34. huius.</note>
            maior, ac propterea angulus A, obtuſus. </s>
            <s xml:id="echoid-s14965" xml:space="preserve">At ſi arcus AB, fuerit quadrante maior, erit
              <lb/>
              <note position="right" xlink:label="note-439-03" xlink:href="note-439-03a" xml:space="preserve">36. huius.</note>
            alter reliquorum arcuum maior, & </s>
            <s xml:id="echoid-s14966" xml:space="preserve">alter minor: </s>
            <s xml:id="echoid-s14967" xml:space="preserve">Si igitur datus arcus AC, ſit ma-
              <lb/>
              <note position="right" xlink:label="note-439-04" xlink:href="note-439-04a" xml:space="preserve">34. huius.</note>
            ior, erit BC, minor, proptereaq́; </s>
            <s xml:id="echoid-s14968" xml:space="preserve">angulus A, acutus; </s>
            <s xml:id="echoid-s14969" xml:space="preserve">Si vero AC, ſit quadrante mi-
              <lb/>
            nor, erit BC, maior, & </s>
            <s xml:id="echoid-s14970" xml:space="preserve">angulus A, obtuſus:</s>
            <s xml:id="echoid-s14971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1198" type="section" level="1" n="570">
          <head xml:id="echoid-head605" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s14972" xml:space="preserve">IN triangulo ſphærico rectangulo, dato arcu, qui recto angulo
              <lb/>
            opponitur, cum alterurro angulorum non rectorum, inuenire arcum
              <lb/>
            huic angulo adiacentem, cum reliquo arcu, & </s>
            <s xml:id="echoid-s14973" xml:space="preserve">angulo.</s>
            <s xml:id="echoid-s14974" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14975" xml:space="preserve">IN eodem triangulo datus ſit arcus AB, cum angulo A. </s>
            <s xml:id="echoid-s14976" xml:space="preserve">Dico dari quoq; </s>
            <s xml:id="echoid-s14977" xml:space="preserve">arcum
              <lb/>
            AC, &</s>
            <s xml:id="echoid-s14978" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14979" xml:space="preserve">Nam cum ſit, vt ſinus totus ad ſinum complementi anguli A, ita tangens
              <lb/>
              <note position="right" xlink:label="note-439-05" xlink:href="note-439-05a" xml:space="preserve">45. huius.</note>
            arcus AB, ad tangentem arcus AC:</s>
            <s xml:id="echoid-s14980" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14981" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum complementi anguli dati, ita tangens
              <lb/>
              <note position="right" xlink:label="note-439-06" xlink:href="note-439-06a" xml:space="preserve">Praxis.</note>
            arcus recto angulo oppoſiti ad aliud, producetur tangens arcus quæſiti.
              <lb/>
            </s>
            <s xml:id="echoid-s14982" xml:space="preserve">Reliqua inuer. </s>
            <s xml:id="echoid-s14983" xml:space="preserve">ientur, vt in primo problemate huius propoſ.</s>
            <s xml:id="echoid-s14984" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14985" xml:space="preserve">NVM autem quæſitus arcus AC, ſit minor quadrante, maiorue, hinc cognoſce-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s14986" xml:space="preserve">Si arcus AB, angulo recto oppoſitus fuerit minor quadrante, erit vterq; </s>
            <s xml:id="echoid-s14987" xml:space="preserve">angu-
              <lb/>
            lus A, B, vel acutus, vel obtuſus. </s>
            <s xml:id="echoid-s14988" xml:space="preserve">Quare ſi datus angulus A, ſit acutus, erit quoque
              <lb/>
              <note position="right" xlink:label="note-439-07" xlink:href="note-439-07a" xml:space="preserve">38 huius.</note>
            B, acutus, atque adeo arcus AC, quadrante minor; </s>
            <s xml:id="echoid-s14989" xml:space="preserve">Si vero A, ſit obtuſus, erit & </s>
            <s xml:id="echoid-s14990" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-439-08" xlink:href="note-439-08a" xml:space="preserve">34 huius.</note>
            B, obtuſus, ideoq́; </s>
            <s xml:id="echoid-s14991" xml:space="preserve">arcus
              <emph style="sc">AC</emph>
            , quadrante maior. </s>
            <s xml:id="echoid-s14992" xml:space="preserve">At ſi arcus AB, ſuuerit maior qua-
              <lb/>
            drante, erit alter reliquorum angulorum acutus, & </s>
            <s xml:id="echoid-s14993" xml:space="preserve">alter obtuſus. </s>
            <s xml:id="echoid-s14994" xml:space="preserve">Siergo A, datus
              <lb/>
              <note position="right" xlink:label="note-439-09" xlink:href="note-439-09a" xml:space="preserve">38. huius.</note>
            ſit acutus, erit B, obtuſus, & </s>
            <s xml:id="echoid-s14995" xml:space="preserve">idcirco arcus AC, quadrante maior; </s>
            <s xml:id="echoid-s14996" xml:space="preserve">Si vero A, ſit
              <lb/>
              <note position="right" xlink:label="note-439-10" xlink:href="note-439-10a" xml:space="preserve">34. huius.</note>
            obtuſus, erit B, acutus, & </s>
            <s xml:id="echoid-s14997" xml:space="preserve">arcus
              <emph style="sc">A</emph>
            C, quadrante minor.</s>
            <s xml:id="echoid-s14998" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1202" type="section" level="1" n="571">
          <head xml:id="echoid-head606" xml:space="preserve">THEOR. 44. PROPOS. 46.</head>
          <p>
            <s xml:id="echoid-s14999" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius omnes arcus quadrante ſint minores: </s>
            <s xml:id="echoid-s15000" xml:space="preserve">ſinus to-
              <lb/>
            tus ad ſinum complementi vtriuſuis angulorum
              <lb/>
            acutorum eandem proportionem habet, quam
              <lb/>
            tangens complementi arcus circa angulum rectũ
              <lb/>
            dicto angulo adiacentis ad tangentem comple-
              <lb/>
            menti arcus recto angulo oppoſiti.</s>
            <s xml:id="echoid-s15001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15002" xml:space="preserve">IN triangulo ABC, cuius omnes arcus quadrante minores, ſit angulus B,
              <lb/>
            rectus. </s>
            <s xml:id="echoid-s15003" xml:space="preserve">Dico ita eſſe ſinum totum ad ſinũ complemẽti anguli A, vt eſt </s>
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