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

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          <p>
            <s xml:id="echoid-s15003" xml:space="preserve">
              <pb o="428" file="440" n="440" rhead=""/>
            complementi arcus AB, ad tangentem complementi arcus AC. </s>
            <s xml:id="echoid-s15004" xml:space="preserve">Facta namque
              <lb/>
            conſtructione, vt in pręcedẽti propoſ. </s>
            <s xml:id="echoid-s15005" xml:space="preserve">quoniam duo circuli maximi in ſphæra
              <lb/>
            BF, DF, ſe mutuo ſecãt in F, productiq́; </s>
            <s xml:id="echoid-s15006" xml:space="preserve">ſunt
              <lb/>
              <figure xlink:label="fig-440-01" xlink:href="fig-440-01a" number="293">
                <image file="440-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/440-01"/>
              </figure>
            ex pũctis B, C, arcus BF, ad arcum DF, arcus
              <lb/>
            perpendiculares BD, CE; </s>
            <s xml:id="echoid-s15007" xml:space="preserve">erit, vt ſinus totus
              <lb/>
            quadrantis DF, ad rangentem arcus BD, ita
              <lb/>
            ſinus arcus EF, ad tangentem arcus CE: </s>
            <s xml:id="echoid-s15008" xml:space="preserve">Et
              <lb/>
              <note position="left" xlink:label="note-440-01" xlink:href="note-440-01a" xml:space="preserve">Theor. 6.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            permutando, vt ſinus totus ad ſinũ arcus EF,
              <lb/>
            hoc eſt, ad ſinum complementi anguli A, ita
              <lb/>
            tangens arcus BD, hoc eſt, ita tangens com-
              <lb/>
            plementi arcus AB, ad tangentem arcus CE,
              <lb/>
            hoc eſt, ad tangentẽ complementi arcus AC.
              <lb/>
            </s>
            <s xml:id="echoid-s15009" xml:space="preserve">Non aliter demonſtrabimus, ita eſſe ſinum to
              <lb/>
            tum ad ſinum complementi anguli C, vt eſt
              <lb/>
            tangens complementi arcus BC, ad tangentem complementi arcus AC, ſi ni-
              <lb/>
            mirum arcus CB, CA, angulum C, continentes producantur, &</s>
            <s xml:id="echoid-s15010" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15011" xml:space="preserve">In omni
              <lb/>
            igitur triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s15012" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s15014" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1204" type="section" level="1" n="572">
          <head xml:id="echoid-head607" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s15015" xml:space="preserve">INFEREMVS hinc problema ſequens, quod quamuis in problemate prima
              <lb/>
            antecedentis propoſ. </s>
            <s xml:id="echoid-s15016" xml:space="preserve">demonſtratum quoque ſit, facilius tamen hic abſoluitur, cùm in
              <lb/>
            aurea regula primum locum ſortiatur ſinus totus.</s>
            <s xml:id="echoid-s15017" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15018" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutto arcuum cir-
              <lb/>
            ca angulum rectum, cum angulo non recto adiacente, inuenire ar-
              <lb/>
            cum recto angulo oppoſitum, vnà cum reliquo arcu circa angulum
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s15019" xml:space="preserve">reliquo angulo non recto.</s>
            <s xml:id="echoid-s15020" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15021" xml:space="preserve">IN triangulo
              <emph style="sc">A</emph>
            BC, cuius angulus C, rectus, datus
              <lb/>
              <figure xlink:label="fig-440-02" xlink:href="fig-440-02a" number="294">
                <image file="440-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/440-02"/>
              </figure>
            ſit arcus AC, cum angulo A, ſibi adiacente. </s>
            <s xml:id="echoid-s15022" xml:space="preserve">Dico dari
              <lb/>
            quoque arcum
              <emph style="sc">AB</emph>
            , vnà cum arcu
              <emph style="sc">BC</emph>
            , & </s>
            <s xml:id="echoid-s15023" xml:space="preserve">angulo B.</s>
            <s xml:id="echoid-s15024" xml:space="preserve">
              <lb/>
            Nam cum ſit, vt ſinus totus ad ſinum complementi angu-
              <lb/>
            li A, ita tangens complementi arcus
              <emph style="sc">AC</emph>
            , ad tangentem
              <lb/>
              <note position="left" xlink:label="note-440-02" xlink:href="note-440-02a" xml:space="preserve">46. huius.</note>
            complementi arcus
              <emph style="sc">AB</emph>
            :</s>
            <s xml:id="echoid-s15025" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15026" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum complemen-
              <lb/>
              <note position="left" xlink:label="note-440-03" xlink:href="note-440-03a" xml:space="preserve">Praxis.</note>
            ti anguli dati, ita tangens complementi arcus da-
              <lb/>
            ti ad aliud, producetur tangens complementi ar-
              <lb/>
            cus recto angulo oppoſiti, qui quæritur. </s>
            <s xml:id="echoid-s15027" xml:space="preserve">Reliqua inuenientur, vt in pro-
              <lb/>
            blemate 1. </s>
            <s xml:id="echoid-s15028" xml:space="preserve">propoſitionis antecedentis dictum eſt.</s>
            <s xml:id="echoid-s15029" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15030" xml:space="preserve">
              <emph style="sc">A</emph>
            RCVM autem
              <emph style="sc">AB</emph>
            , quæſitum eße quadrante minorem, maioremve, cognoſce-
              <lb/>
            mus, vt in dicto problemate 1. </s>
            <s xml:id="echoid-s15031" xml:space="preserve">ſuperioris propoſ. </s>
            <s xml:id="echoid-s15032" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s15033" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1207" type="section" level="1" n="573">
          <head xml:id="echoid-head608" xml:space="preserve">THEOR. 45. PROPOS. 47.</head>
          <p>
            <s xml:id="echoid-s15034" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cuius
              <lb/>
            omnes arcus quadrante ſint minores: </s>
            <s xml:id="echoid-s15035" xml:space="preserve">ſinus </s>
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