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

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          <p>
            <s xml:id="echoid-s15035" xml:space="preserve">
              <pb o="429" file="441" n="441" rhead=""/>
            ad ſinum complementi arcus recto angulo oppo-
              <lb/>
            ſiti eandem proportionem habet, quam tangens
              <lb/>
            vtriusvis angulorum non rectorum ad tangentem
              <lb/>
            complementi reliqui anguli.</s>
            <s xml:id="echoid-s15036" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15037" xml:space="preserve">IN triangulo ABC, cuius omnes arcus quadrante minores, ſit angulus
              <lb/>
            B, rectus. </s>
            <s xml:id="echoid-s15038" xml:space="preserve">Dico, ita eſſe ſinum totum ad ſinum complementi arcus AC, vt
              <lb/>
            eſt tangens anguli C, ad tangentem complementi anguli A. </s>
            <s xml:id="echoid-s15039" xml:space="preserve">Facta conſtru-
              <lb/>
            ctione, vt in propoſ. </s>
            <s xml:id="echoid-s15040" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15041" xml:space="preserve">productoq́; </s>
            <s xml:id="echoid-s15042" xml:space="preserve">arcu CE, ad G, vt CG, ſit quadrans,
              <lb/>
            deſcribatur ex polo C, ad interual lum quadran
              <lb/>
              <figure xlink:label="fig-441-01" xlink:href="fig-441-01a" number="295">
                <image file="441-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/441-01"/>
              </figure>
            tis CG, arcus circuli maximi GH, ſecans ar-
              <lb/>
            cus CF, EF, productos in I, H: </s>
            <s xml:id="echoid-s15043" xml:space="preserve">eritq́; </s>
            <s xml:id="echoid-s15044" xml:space="preserve">CI, qua-
              <lb/>
            drans quoque; </s>
            <s xml:id="echoid-s15045" xml:space="preserve">cum circulus GH, à polo C, ab-
              <lb/>
              <note position="right" xlink:label="note-441-01" xlink:href="note-441-01a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. Theod.
                <lb/>
              25. huius.</note>
            ſit quadrante. </s>
            <s xml:id="echoid-s15046" xml:space="preserve">Arcus item GH, EH, quadran-
              <lb/>
            tes erunt, propter rectos angulos G, E. </s>
            <s xml:id="echoid-s15047" xml:space="preserve">Eſt enim
              <lb/>
            angulus E, rectus, vt propoſ. </s>
            <s xml:id="echoid-s15048" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15049" xml:space="preserve">oſtenſum eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s15050" xml:space="preserve">at G, rectus eſt, propterea quòd circulus CG,
              <lb/>
            ad circulum GH, rectus eſt. </s>
            <s xml:id="echoid-s15051" xml:space="preserve">Rurſus IG, ar-
              <lb/>
              <note position="right" xlink:label="note-441-02" xlink:href="note-441-02a" xml:space="preserve">15.1. Theod.</note>
            cus eſt anguli C; </s>
            <s xml:id="echoid-s15052" xml:space="preserve">& </s>
            <s xml:id="echoid-s15053" xml:space="preserve">CE, complementum arcus AC, recto angulo oppoſiti;
              <lb/>
            </s>
            <s xml:id="echoid-s15054" xml:space="preserve">& </s>
            <s xml:id="echoid-s15055" xml:space="preserve">FE, complementum arcus DE, id eſt, anguli A. </s>
            <s xml:id="echoid-s15056" xml:space="preserve">Quoniam igitur duo cir-
              <lb/>
            culi maximi CG, CI, in ſphæra ſe interſecant in C, ductiq́; </s>
            <s xml:id="echoid-s15057" xml:space="preserve">ſunt ex arcus CI,
              <lb/>
            punctis F, I, ad arcum CG, arcus perpendiculares FE, IG; </s>
            <s xml:id="echoid-s15058" xml:space="preserve">erit, vt ſinus to-
              <lb/>
              <note position="right" xlink:label="note-441-03" xlink:href="note-441-03a" xml:space="preserve">Theor. 6.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            tus quadrantis CG, ad tangentem arcus IG, hoc eſt, anguli C, ita ſinus ar-
              <lb/>
            cus CE, hoc eſt, complementiarcus AC, ad tangentem arcus FE, hoc eſt,
              <lb/>
            complementi anguli A: </s>
            <s xml:id="echoid-s15059" xml:space="preserve">Et permutando erit, vt ſinus totus ad ſinum comple-
              <lb/>
            mentiarcus AC, recto angulo oppoſiti, ita tangens anguli C, ad tangentem
              <lb/>
            complementi anguli A. </s>
            <s xml:id="echoid-s15060" xml:space="preserve">Similimodo, aliter conſtructa figura, demonſtrabi-
              <lb/>
            mus, ita eſſe ſinum totum ad ſinum complementi arcus AC vt eſt tangens
              <lb/>
            anguli A, ad tangentem complementi anguli C. </s>
            <s xml:id="echoid-s15061" xml:space="preserve">In omni igitur triangulo
              <lb/>
            ſphærico rectangulo, &</s>
            <s xml:id="echoid-s15062" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15063" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s15064" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1209" type="section" level="1" n="574">
          <head xml:id="echoid-head609" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s15065" xml:space="preserve">EX hoc theoremate ſequens problema colligitur.</s>
            <s xml:id="echoid-s15066" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15067" xml:space="preserve">IN triangulo ſphærico rectangulo, dato arcu, qui recto angulo
              <lb/>
            opponitur, cum alterutro angulorum non rectorum, inuenire alte-
              <lb/>
            rum angulum non rectum, & </s>
            <s xml:id="echoid-s15068" xml:space="preserve">duos arcus circa angulum rectum.</s>
            <s xml:id="echoid-s15069" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15070" xml:space="preserve">IN triangulo
              <emph style="sc">ABC</emph>
            , cuius angulus C, rectus, datus
              <lb/>
              <figure xlink:label="fig-441-02" xlink:href="fig-441-02a" number="296">
                <image file="441-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/441-02"/>
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            ſit arcus
              <emph style="sc">AB</emph>
            , cum angulo
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s15071" xml:space="preserve">Dico dari quoque reliquum
              <lb/>
            angulum
              <emph style="sc">A</emph>
            , & </s>
            <s xml:id="echoid-s15072" xml:space="preserve">duos arcus
              <emph style="sc">AC, CB</emph>
            . </s>
            <s xml:id="echoid-s15073" xml:space="preserve">Cum enim ſit, vt
              <lb/>
              <note position="right" xlink:label="note-441-04" xlink:href="note-441-04a" xml:space="preserve">47. huius.</note>
            ſinus totus ad ſinum complementi arcus
              <emph style="sc">AB</emph>
            , ita tangens
              <lb/>
            anguli
              <emph style="sc">B</emph>
            , ad tangentem complementi anguli
              <emph style="sc">A</emph>
            :</s>
            <s xml:id="echoid-s15074" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15075" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum complementi
              <lb/>
              <note position="right" xlink:label="note-441-05" xlink:href="note-441-05a" xml:space="preserve">Praxis.</note>
            arcus recto angulo oppoſiti, & </s>
            <s xml:id="echoid-s15076" xml:space="preserve">dati, ita tangens
              <lb/>
            anguli dati ad aliud, reperietur tangens </s>
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