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

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        <div xml:id="echoid-div1219" type="section" level="1" n="577">
          <p>
            <s xml:id="echoid-s15151" xml:space="preserve">
              <pb o="432" file="444" n="444" rhead=""/>
            tangens complementi anguli A, ad ſinum arcus AD. </s>
            <s xml:id="echoid-s15152" xml:space="preserve">Repetita enim conſtru-
              <lb/>
              <figure xlink:label="fig-444-01" xlink:href="fig-444-01a" number="300">
                <image file="444-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/444-01"/>
              </figure>
            ctione figuræ propoſ. </s>
            <s xml:id="echoid-s15153" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15154" xml:space="preserve">erunt AB, AC,
              <lb/>
            quadrantes, & </s>
            <s xml:id="echoid-s15155" xml:space="preserve">CF, complementum arcus
              <lb/>
            BC, id eſt, anguli A, vt ibi oſtenſum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s15156" xml:space="preserve">Igitur quoniam quadrantes ſunt AB, AC,
              <lb/>
            & </s>
            <s xml:id="echoid-s15157" xml:space="preserve">arcus ED, ad AB, perpendicularis; </s>
            <s xml:id="echoid-s15158" xml:space="preserve">erit,
              <lb/>
            vt ſinus totus ad tangentem arcus ED, ita
              <lb/>
            tangens complementi arcus CB, hoc eſt,
              <lb/>
              <note position="left" xlink:label="note-444-01" xlink:href="note-444-01a" xml:space="preserve">Theor. 7.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            anguli A, ad ſinum arcus AD. </s>
            <s xml:id="echoid-s15159" xml:space="preserve">Eodem mo
              <lb/>
            do oſtendetur, ita eſſe ſinum totum ad tan
              <lb/>
            gentem arcus AD, vt eſt tangens comple-
              <lb/>
            menti anguli E, ad ſinum arcus DE: </s>
            <s xml:id="echoid-s15160" xml:space="preserve">ſi ni-
              <lb/>
            mirum aliter figura conſtruatur. </s>
            <s xml:id="echoid-s15161" xml:space="preserve">In omni
              <lb/>
            ergo trianguloſphærico rectangulo, &</s>
            <s xml:id="echoid-s15162" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15163" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15164" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1221" type="section" level="1" n="578">
          <head xml:id="echoid-head613" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15165" xml:space="preserve">HINC tale problema colligitur, quod per problema 1. </s>
            <s xml:id="echoid-s15166" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15167" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15168" xml:space="preserve">alio modo ab-
              <lb/>
            ſelui quoque potest.</s>
            <s xml:id="echoid-s15169" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15170" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutro arcuum circa
              <lb/>
            angulum rectum, cum angulo oppoſito, reliquum arcum circa re-
              <lb/>
            ctum angulum, & </s>
            <s xml:id="echoid-s15171" xml:space="preserve">arcum recto angulo oppoſitum, cum reliquo an-
              <lb/>
            gulo non recto inquirere: </s>
            <s xml:id="echoid-s15172" xml:space="preserve">ſi modo conſtet, num arcus quæſitus ſit
              <lb/>
            maior quadrante, minorve: </s>
            <s xml:id="echoid-s15173" xml:space="preserve">Vel an reliquus angulus non rectus ſit
              <lb/>
            acutus, obtuſusve.</s>
            <s xml:id="echoid-s15174" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15175" xml:space="preserve">IN triangulo
              <emph style="sc">ABC</emph>
            , cuius angulus
              <emph style="sc">C</emph>
            , rectus, datus ſit arcus
              <emph style="sc">AC</emph>
            , cum angulo
              <lb/>
              <figure xlink:label="fig-444-02" xlink:href="fig-444-02a" number="301">
                <image file="444-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/444-02"/>
              </figure>
            oppoſito
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s15176" xml:space="preserve">Dico dari quoque arcum
              <emph style="sc">BC</emph>
            , &</s>
            <s xml:id="echoid-s15177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15178" xml:space="preserve">Cumenim
              <lb/>
            ſit, vt ſinus totus ad tangentem arcus
              <emph style="sc">AC</emph>
            , ita tangens
              <lb/>
              <note position="left" xlink:label="note-444-02" xlink:href="note-444-02a" xml:space="preserve">49.huius.</note>
            complementi anguli
              <emph style="sc">B</emph>
            , ad ſinum arcus
              <emph style="sc">BC</emph>
            :</s>
            <s xml:id="echoid-s15179" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15180" xml:space="preserve">SI fiat, vt ſinus totus ad tangentem datiar-
              <lb/>
              <note position="left" xlink:label="note-444-03" xlink:href="note-444-03a" xml:space="preserve">Praxis.</note>
            cus, ita tangens complemẽti anguli dati ad aliud,
              <lb/>
            producetur ſinus arcus quæſiti. </s>
            <s xml:id="echoid-s15181" xml:space="preserve">Ex duobus por-
              <lb/>
            ro arcubus circa rectum angulum cognitis in co-
              <lb/>
            gnitionem reliqui arcus, & </s>
            <s xml:id="echoid-s15182" xml:space="preserve">reliqui angulinon re-
              <lb/>
            cti perueniemus, vt in problemate propoſ. </s>
            <s xml:id="echoid-s15183" xml:space="preserve">43. </s>
            <s xml:id="echoid-s15184" xml:space="preserve">demonſtrauimus; </s>
            <s xml:id="echoid-s15185" xml:space="preserve">vel cer-
              <lb/>
            te ex alterutro arcuum circa angulum rectum, & </s>
            <s xml:id="echoid-s15186" xml:space="preserve">dato angulo, vt in pro-
              <lb/>
            blemate 2. </s>
            <s xml:id="echoid-s15187" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15188" xml:space="preserve">42. </s>
            <s xml:id="echoid-s15189" xml:space="preserve">docuimus.</s>
            <s xml:id="echoid-s15190" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15191" xml:space="preserve">OPORTET autem hic conſtare, num arcus quæſitus
              <emph style="sc">BC</emph>
            , ſit quadrante maior,
              <lb/>
            minor ve; </s>
            <s xml:id="echoid-s15192" xml:space="preserve">vel an angulus
              <emph style="sc">A</emph>
            , reliquus ſit acutus, obtuſus ve: </s>
            <s xml:id="echoid-s15193" xml:space="preserve">quemadmodũ in poſteriore
              <lb/>
            parte problematis 1. </s>
            <s xml:id="echoid-s15194" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15195" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15196" xml:space="preserve">traditum eſt: </s>
            <s xml:id="echoid-s15197" xml:space="preserve">Vbi etiam errorẽ Copernici deteximus.</s>
            <s xml:id="echoid-s15198" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1224" type="section" level="1" n="579">
          <head xml:id="echoid-head614" xml:space="preserve">THEOR. 48. PROPOS. 50.</head>
          <p>
            <s xml:id="echoid-s15199" xml:space="preserve">IN omni triangulo ſphærico rectangulo, </s>
          </p>
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