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

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        <div xml:id="echoid-div1239" type="section" level="1" n="585">
          <p>
            <s xml:id="echoid-s15343" xml:space="preserve">
              <pb o="437" file="449" n="449" rhead=""/>
            arcus AB. </s>
            <s xml:id="echoid-s15344" xml:space="preserve">Simili modo oſtendemus, ita eſſe ſinum totum ad ſinum comple-
              <lb/>
            menti arcus AB, vt eſt ſecans arcus AC, ad ſecantem arcus BC, ſi nimitum
              <lb/>
            figura paulo aliter conſtruatur. </s>
            <s xml:id="echoid-s15345" xml:space="preserve">In omni ergo triangulo ſphærico rectangu-
              <lb/>
            lo, &</s>
            <s xml:id="echoid-s15346" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15347" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15348" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1241" type="section" level="1" n="586">
          <head xml:id="echoid-head621" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15349" xml:space="preserve">SEQVENS problema ex hoc theoremate colligitur.</s>
            <s xml:id="echoid-s15350" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15351" xml:space="preserve">IN triangulo ſphærico rectangulo, dato arcu, quirecto angulo
              <lb/>
            opponitur, cum alterutro arcuum circa rectum angulum, inueſtiga-
              <lb/>
            re tertium arcum, cum duobus angulis non rectis.</s>
            <s xml:id="echoid-s15352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15353" xml:space="preserve">IN triangulo
              <emph style="sc">ABC</emph>
            , cuius angulus
              <emph style="sc">C</emph>
            , rectus, datus ſit arcus
              <emph style="sc">AB</emph>
            , vnà cum ar-
              <lb/>
            cu
              <emph style="sc">AC</emph>
            . </s>
            <s xml:id="echoid-s15354" xml:space="preserve">Dico dari quoque arcum
              <emph style="sc">BC</emph>
            , cum angulis
              <emph style="sc">A, B</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s15355" xml:space="preserve">
              <figure xlink:label="fig-449-01" xlink:href="fig-449-01a" number="309">
                <image file="449-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/449-01"/>
              </figure>
            Camenimſit, vt ſinus totus ad ſinum complementi arcus
              <lb/>
              <note position="right" xlink:label="note-449-01" xlink:href="note-449-01a" xml:space="preserve">53. huius.</note>
              <emph style="sc">AC</emph>
            , ita ſecans arcus
              <emph style="sc">AB</emph>
            , ad ſecantem arcus
              <emph style="sc">BC</emph>
            :</s>
            <s xml:id="echoid-s15356" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15357" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum complementi
              <lb/>
              <note position="right" xlink:label="note-449-02" xlink:href="note-449-02a" xml:space="preserve">Praxis.</note>
            dati arcus circa angulum rectum, ita ſecans arcus
              <lb/>
            angulo recto oppoſiti ad aliud, producetur ſecans
              <lb/>
            tertij arcus, qui inquiritur. </s>
            <s xml:id="echoid-s15358" xml:space="preserve">Hinc ex duobus ar-
              <lb/>
            cubus circa rectum angulum cognitis, vterlibet
              <lb/>
            angulorum non rectorum cognoſcetur, vt in 5. </s>
            <s xml:id="echoid-s15359" xml:space="preserve">problemate ſcholij propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s15360" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15361" xml:space="preserve">vel in problemate ſcholij propoſ. </s>
            <s xml:id="echoid-s15362" xml:space="preserve">48. </s>
            <s xml:id="echoid-s15363" xml:space="preserve">docuimus.</s>
            <s xml:id="echoid-s15364" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15365" xml:space="preserve">VTRVM vero quæſitus arcus
              <emph style="sc">BC</emph>
            , ſit quadrante maior, minorve, diſcemus eæ
              <lb/>
            datis duobus arcubus, vt ad finem problematis ſcholij 1. </s>
            <s xml:id="echoid-s15366" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15367" xml:space="preserve">43. </s>
            <s xml:id="echoid-s15368" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s15369" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1244" type="section" level="1" n="587">
          <head xml:id="echoid-head622" xml:space="preserve">THEOR. 52. PROPOS. 54.</head>
          <p>
            <s xml:id="echoid-s15370" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius omnes arcus quadrante ſint minores: </s>
            <s xml:id="echoid-s15371" xml:space="preserve">ſinus to-
              <lb/>
            tus ad ſinum vtriuſlibet angulorum non rectorum
              <lb/>
            proportionem habet eandem, quam ſecans com-
              <lb/>
            plementi arcus illi angulo oppoſiti ad ſecantem
              <lb/>
            complementi arcus recto angulo oppoſiti.</s>
            <s xml:id="echoid-s15372" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15373" xml:space="preserve">IN triangulo ABC, cuius arcus omnes ſint minores quadrante, ſit angu-
              <lb/>
            lus B, rectus. </s>
            <s xml:id="echoid-s15374" xml:space="preserve">Dico ita eſſe ſinum totum ad ſinum anguli A, vt eſt ſecans com-
              <lb/>
            plementi arcus BC, ad ſecantem complementi arcus AC. </s>
            <s xml:id="echoid-s15375" xml:space="preserve">Repetita enim
              <lb/>
            conſtructione figuræ propoſ. </s>
            <s xml:id="echoid-s15376" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15377" xml:space="preserve">erit angulus I, rectus, vt in propoſ. </s>
            <s xml:id="echoid-s15378" xml:space="preserve">52.
              <lb/>
            </s>
            <s xml:id="echoid-s15379" xml:space="preserve">monſtratum eſt; </s>
            <s xml:id="echoid-s15380" xml:space="preserve">necnon & </s>
            <s xml:id="echoid-s15381" xml:space="preserve">angulus G. </s>
            <s xml:id="echoid-s15382" xml:space="preserve">Item GH, EH, DF, BF, AE, qua-
              <lb/>
            drantes, vt ex demonſtratis in propoſ. </s>
            <s xml:id="echoid-s15383" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15384" xml:space="preserve">& </s>
            <s xml:id="echoid-s15385" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15386" xml:space="preserve">conſtat. </s>
            <s xml:id="echoid-s15387" xml:space="preserve">Quia igitur in </s>
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