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

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          <p>
            <s xml:id="echoid-s15199" xml:space="preserve">
              <pb o="433" file="445" n="445" rhead=""/>
            omnes arcus quadrante ſint minores: </s>
            <s xml:id="echoid-s15200" xml:space="preserve">ſinus totus
              <lb/>
            ad tangentem complementi vtriusvis angulorum
              <lb/>
            non rectorum habet proportionem eãdem, quam
              <lb/>
            tangens complemẽti reliqui anguli ad ſinum com
              <lb/>
            plementi arcus recto angulo oppoſiti.</s>
            <s xml:id="echoid-s15201" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15202" xml:space="preserve">IN triangulo ABC, cuius omnes arcus quadrante minores, ſit angulus
              <lb/>
            B, rectus. </s>
            <s xml:id="echoid-s15203" xml:space="preserve">Dico ita eſſe ſinum totum ad tangentem complementi anguli A, vt
              <lb/>
            eſt tangens complementi anguli C, ad ſinum complementi arcus AC. </s>
            <s xml:id="echoid-s15204" xml:space="preserve">Repe-
              <lb/>
            tita namq; </s>
            <s xml:id="echoid-s15205" xml:space="preserve">figura propoſ. </s>
            <s xml:id="echoid-s15206" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15207" xml:space="preserve">cum CG, CI, qua-
              <lb/>
              <figure xlink:label="fig-445-01" xlink:href="fig-445-01a" number="302">
                <image file="445-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/445-01"/>
              </figure>
            drãtes ſint ſe interſecãtes in C, & </s>
            <s xml:id="echoid-s15208" xml:space="preserve">arcus IG, FE,
              <lb/>
            ad CG, perpendiculares, vt ex conſtructione ibi-
              <lb/>
            dem facta perſpicuum eſt; </s>
            <s xml:id="echoid-s15209" xml:space="preserve">erit, vt ſinus totus ad
              <lb/>
              <note position="right" xlink:label="note-445-01" xlink:href="note-445-01a" xml:space="preserve">Theor. 7.
                <lb/>
              ſcholij 40,
                <lb/>
              huius.</note>
            tangentem arcus EF, qui complementũ eſt arcus
              <lb/>
            DE, hoc eſt, anguli A, ita tangens complementi
              <lb/>
            arcus IG, id eſt, anguli C, ad ſinum arcus CE,
              <lb/>
            hoc eſt, complementi arcus AC, recto angulo
              <lb/>
            oppoſiti. </s>
            <s xml:id="echoid-s15210" xml:space="preserve">Simili ratione oſtendemus, ſi aliter figuræ conſtructio inſtituatur,
              <lb/>
            ita eſſe ſinum totum ad tangentem complementi anguli C, vt eſt tangens com
              <lb/>
            plementi anguli A, ad ſinum complementi arcus AC. </s>
            <s xml:id="echoid-s15211" xml:space="preserve">Quam ob rem in omni
              <lb/>
            triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s15212" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15213" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s15214" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1226" type="section" level="1" n="580">
          <head xml:id="echoid-head615" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15215" xml:space="preserve">INFEREMVS ex hac propoſ. </s>
            <s xml:id="echoid-s15216" xml:space="preserve">theorema ſequens.</s>
            <s xml:id="echoid-s15217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15218" xml:space="preserve">IN triangulo ſphærico rectangulo, datis duobus angulis non re-
              <lb/>
            ctis, inquirere arcum angulo recto oppoſitum, & </s>
            <s xml:id="echoid-s15219" xml:space="preserve">reliquos duos ar-
              <lb/>
            cus circa angulum rectum.</s>
            <s xml:id="echoid-s15220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15221" xml:space="preserve">IN triangulo
              <emph style="sc">ABC</emph>
            , cuius angulus
              <emph style="sc">C</emph>
            , rectus, dati
              <lb/>
              <figure xlink:label="fig-445-02" xlink:href="fig-445-02a" number="303">
                <image file="445-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/445-02"/>
              </figure>
            ſint duo anguli non recti
              <emph style="sc">A, B</emph>
            . </s>
            <s xml:id="echoid-s15222" xml:space="preserve">Dico dari quoque arcum
              <lb/>
              <emph style="sc">AB</emph>
            , vnà cum arcubus
              <emph style="sc">AC, BC</emph>
            . </s>
            <s xml:id="echoid-s15223" xml:space="preserve">Quoniam enim eſt, vt
              <lb/>
            ſinus totus ad tangentem complementi anguli
              <emph style="sc">A</emph>
            , ita tan-
              <lb/>
              <note position="right" xlink:label="note-445-02" xlink:href="note-445-02a" xml:space="preserve">50. huius.</note>
            gens complementi anguli
              <emph style="sc">B</emph>
            , ad ſinum complementi ar-
              <lb/>
            cus
              <emph style="sc">AB</emph>
            :</s>
            <s xml:id="echoid-s15224" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Praxis.</note>
          <p style="it">
            <s xml:id="echoid-s15225" xml:space="preserve">SI fiat, vt ſinus totus ad tangentem comple-
              <lb/>
            menti vtriusvis angulorum datorum, ita tangens
              <lb/>
            complementi alterius dati anguli ad aliud, procre abitur ſinus complemen
              <lb/>
            ti arcus recto angulo oppoſiti. </s>
            <s xml:id="echoid-s15226" xml:space="preserve">Iam ex arcu, qui recto angulo opponitur,
              <lb/>
            & </s>
            <s xml:id="echoid-s15227" xml:space="preserve">vtrolibet angulorum non rectorum, inuenietur arcus ei oppoſitus, vt
              <lb/>
            in 2. </s>
            <s xml:id="echoid-s15228" xml:space="preserve">problemate propoſ. </s>
            <s xml:id="echoid-s15229" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15230" xml:space="preserve">monſtr auimus.</s>
            <s xml:id="echoid-s15231" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15232" xml:space="preserve">PORRO an arcus quæſitus quadrante ſit maior, aut minor, ita diſcemus. </s>
            <s xml:id="echoid-s15233" xml:space="preserve">Si
              <lb/>
            vterq; </s>
            <s xml:id="echoid-s15234" xml:space="preserve">angulorum
              <emph style="sc">A, B</emph>
            , fuerit obtuſus, vel acutus, erit arcus
              <emph style="sc">AB</emph>
            , quadrante minor,
              <lb/>
              <note position="right" xlink:label="note-445-04" xlink:href="note-445-04a" xml:space="preserve">37. huius.</note>
            ſi vero alter eorum acutus fuerit, et alter obtuſus, erit idem arcus quadrante maior.</s>
            <s xml:id="echoid-s15235" xml:space="preserve"/>
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