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

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          <p>
            <s xml:id="echoid-s10765" xml:space="preserve">
              <pb o="330" file="342" n="342" rhead=""/>
            AB, maius ſit latere AC, erit & </s>
            <s xml:id="echoid-s10766" xml:space="preserve">angulus C, angulo B, maior. </s>
            <s xml:id="echoid-s10767" xml:space="preserve">Quare B, acu-
              <lb/>
              <note position="left" xlink:label="note-342-01" xlink:href="note-342-01a" xml:space="preserve">19. primi.</note>
              <figure xlink:label="fig-342-01" xlink:href="fig-342-01a" number="187">
                <image file="342-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/342-01"/>
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            tus erit. </s>
            <s xml:id="echoid-s10768" xml:space="preserve">Nam ſi rectus eſſet, aut maior, eſſet C, etiam
              <lb/>
            maior recto. </s>
            <s xml:id="echoid-s10769" xml:space="preserve">quod eſt abſurdum; </s>
            <s xml:id="echoid-s10770" xml:space="preserve">quòd B, C, ſint mino-
              <lb/>
              <note position="left" xlink:label="note-342-02" xlink:href="note-342-02a" xml:space="preserve">17. primi.</note>
            res duobus rectis. </s>
            <s xml:id="echoid-s10771" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s10772" xml:space="preserve">A, ponatur acutus, ca-
              <lb/>
            det perpendicularis CD, intra triangulum. </s>
            <s xml:id="echoid-s10773" xml:space="preserve">In trian-
              <lb/>
              <note position="left" xlink:label="note-342-03" xlink:href="note-342-03a" xml:space="preserve">Schol. 13.
                <lb/>
              ſecundi.</note>
            gulo igitur rectangulo ACD, cum angulus A, ſit grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10774" xml:space="preserve">38. </s>
            <s xml:id="echoid-s10775" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10776" xml:space="preserve">16. </s>
            <s xml:id="echoid-s10777" xml:space="preserve">erit eius complementum ACD, grad. </s>
            <s xml:id="echoid-s10778" xml:space="preserve">51. </s>
            <s xml:id="echoid-s10779" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s10780" xml:space="preserve">44. </s>
            <s xml:id="echoid-s10781" xml:space="preserve">Quare cum ſit, vt ſinus totus anguli recti D,
              <lb/>
              <note position="left" xlink:label="note-342-04" xlink:href="note-342-04a" xml:space="preserve">1. huius.</note>
            ad ſinum anguli A, ita latus AC, 24. </s>
            <s xml:id="echoid-s10782" xml:space="preserve">ad latus CD:
              <lb/>
            </s>
            <s xml:id="echoid-s10783" xml:space="preserve">inuenietur latus CD, per regulã auream, 14 {2699/3125}. </s>
            <s xml:id="echoid-s10784" xml:space="preserve">
              <lb/>
            Vt hic apparet.</s>
            <s xml:id="echoid-s10785" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          D. # A. # AC. # # CD.
            <lb/>
          100000. # 61932. # 24? # fit # 14 {2699/3125}.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10786" xml:space="preserve">Eadem ratione, cum ſit, vt ſinus totus anguli recti D, ad ſinum anguli ACD,
              <lb/>
              <note position="left" xlink:label="note-342-06" xlink:href="note-342-06a" xml:space="preserve">1. huius.</note>
            ita latus AC, 24. </s>
            <s xml:id="echoid-s10787" xml:space="preserve">ad latus AD: </s>
            <s xml:id="echoid-s10788" xml:space="preserve">reperietur latus AD, 18 {5271/6250}. </s>
            <s xml:id="echoid-s10789" xml:space="preserve">vt hic
              <lb/>
            vides.</s>
            <s xml:id="echoid-s10790" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          D. # ACD. # AC. # # AD.
            <lb/>
          100000. # 78514. # 24? # fit # 18 {5271/6250}.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10791" xml:space="preserve">Ablata autem AD, inuenta ex AB, data 29. </s>
            <s xml:id="echoid-s10792" xml:space="preserve">relinquetur BD, 10 {979/6250}.
              <lb/>
            </s>
            <s xml:id="echoid-s10793" xml:space="preserve">Et quia, vt in tractatu tangentium oſtendimus, poſito ſinu toto BD, recta
              <lb/>
            CD, tangens eſt anguli B, inuenietur CD, tangens 146344. </s>
            <s xml:id="echoid-s10794" xml:space="preserve">vt hic manife-
              <lb/>
            ſtum eſt.</s>
            <s xml:id="echoid-s10795" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BD. # BD. # CD. # # CD.
            <lb/>
          10 {979/6250}. # 100000. # 14 {2699/3125}? # fit # 146344.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10796" xml:space="preserve">Tangens autem 146344. </s>
            <s xml:id="echoid-s10797" xml:space="preserve">monſtrat in tabula tangentium angulum B, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10798" xml:space="preserve">55. </s>
            <s xml:id="echoid-s10799" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10800" xml:space="preserve">40. </s>
            <s xml:id="echoid-s10801" xml:space="preserve">ac proinde duo anguli A, B, grad. </s>
            <s xml:id="echoid-s10802" xml:space="preserve">38. </s>
            <s xml:id="echoid-s10803" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10804" xml:space="preserve">16. </s>
            <s xml:id="echoid-s10805" xml:space="preserve">& </s>
            <s xml:id="echoid-s10806" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s10807" xml:space="preserve">55. </s>
            <s xml:id="echoid-s10808" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10809" xml:space="preserve">
              <lb/>
            40. </s>
            <s xml:id="echoid-s10810" xml:space="preserve">ex grad 180. </s>
            <s xml:id="echoid-s10811" xml:space="preserve">ſubducti reliquum facient angulum ACB, grad. </s>
            <s xml:id="echoid-s10812" xml:space="preserve">86. </s>
            <s xml:id="echoid-s10813" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10814" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10815" xml:space="preserve">
              <lb/>
            Quoniam autem eſt, vt ſinus anguli B, noti ad ſinum anguli A, dati, ita latus
              <lb/>
              <note position="left" xlink:label="note-342-09" xlink:href="note-342-09a" xml:space="preserve">1. huius.</note>
            datum AC, 24. </s>
            <s xml:id="echoid-s10816" xml:space="preserve">adlatus BC, reperietur latus BC, 18. </s>
            <s xml:id="echoid-s10817" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s10818" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s10819" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          B. # A. # AC. # # BC.
            <lb/>
          82577. # 61932. # 24? # fit # 18. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10820" xml:space="preserve">RVRSVS in triangulo ABC, datum ſit latus AB, 13. </s>
            <s xml:id="echoid-s10821" xml:space="preserve">AC, 11. </s>
            <s xml:id="echoid-s10822" xml:space="preserve">& </s>
            <s xml:id="echoid-s10823" xml:space="preserve">an-
              <lb/>
            gulus A, ab ipſis comprehenſus obtuſus, & </s>
            <s xml:id="echoid-s10824" xml:space="preserve">datus grad. </s>
            <s xml:id="echoid-s10825" xml:space="preserve">112. </s>
            <s xml:id="echoid-s10826" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10827" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10828" xml:space="preserve">Duca-
              <lb/>
              <figure xlink:label="fig-342-02" xlink:href="fig-342-02a" number="188">
                <image file="342-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/342-02"/>
              </figure>
            tur ex alterutro angulorum acutorum, vt ex B,
              <lb/>
            ad oppoſitum latus CA, perpendicularis: </s>
            <s xml:id="echoid-s10829" xml:space="preserve">quæ
              <lb/>
              <note position="left" xlink:label="note-342-11" xlink:href="note-342-11a" xml:space="preserve">Schol. 12.
                <lb/>
              ſecundi.</note>
            extra triangulum cadet. </s>
            <s xml:id="echoid-s10830" xml:space="preserve">Quia igitur angulus
              <lb/>
            BAC, ponitur grad. </s>
            <s xml:id="echoid-s10831" xml:space="preserve">112. </s>
            <s xml:id="echoid-s10832" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10833" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10834" xml:space="preserve">erit BAD,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s10835" xml:space="preserve">67. </s>
            <s xml:id="echoid-s10836" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10837" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10838" xml:space="preserve">eiusq́ complementum pro-
              <lb/>
            pterea ABD, neceſſariò grad. </s>
            <s xml:id="echoid-s10839" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10840" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10841" xml:space="preserve">37.</s>
            <s xml:id="echoid-s10842" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10843" xml:space="preserve">Quare cum ſit, vt ſinus totus anguli recti D, ad
              <lb/>
              <note position="left" xlink:label="note-342-12" xlink:href="note-342-12a" xml:space="preserve">1. huius.</note>
            ſinum anguli BAD, ita latus AB, datum 13. </s>
            <s xml:id="echoid-s10844" xml:space="preserve">ad latus BD: </s>
            <s xml:id="echoid-s10845" xml:space="preserve">Item vt ſinus to-
              <lb/>
            tus anguli recti D, ad ſinum anguli ABD, ita latus datum AB, 13. </s>
            <s xml:id="echoid-s10846" xml:space="preserve">ad latus
              <lb/>
            AD; </s>
            <s xml:id="echoid-s10847" xml:space="preserve">in uenietur BD, quidem 12. </s>
            <s xml:id="echoid-s10848" xml:space="preserve">at AD, 5. </s>
            <s xml:id="echoid-s10849" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s10850" xml:space="preserve">vt hic apparet.</s>
            <s xml:id="echoid-s10851" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          D. # BAD. # # AB. # # BD.
            <lb/>
          100000. # 92310. # # 13? # fit # 12. ferè.
            <lb/>
          # # Item.
            <lb/>
          D. # ABD. # # AB. # # AD.
            <lb/>
          100000. # 38456. # # 13? # fit # 5. ferè.
            <lb/>
          </note>
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