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

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          <p>
            <s xml:id="echoid-s10450" xml:space="preserve">
              <pb o="326" file="338" n="338" rhead=""/>
            13. </s>
            <s xml:id="echoid-s10451" xml:space="preserve">dat AB, ſinum totum partium 100000. </s>
            <s xml:id="echoid-s10452" xml:space="preserve">quid dabit BD, 5? </s>
            <s xml:id="echoid-s10453" xml:space="preserve">inueniemusq́
              <lb/>
            ſinum BD, 38461. </s>
            <s xml:id="echoid-s10454" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s10455" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # BD. # # BD.
            <lb/>
          13. # 100000. # 5? # fit. # 38461.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10456" xml:space="preserve">Ex tabula ergo ſinuum dabitur angulus BAD,
              <lb/>
              <figure xlink:label="fig-338-01" xlink:href="fig-338-01a" number="183">
                <image file="338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/338-01"/>
              </figure>
            grad. </s>
            <s xml:id="echoid-s10457" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10458" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10459" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10460" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s10461" xml:space="preserve">adeo eius complementum
              <lb/>
            B, grad. </s>
            <s xml:id="echoid-s10462" xml:space="preserve">67. </s>
            <s xml:id="echoid-s10463" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10464" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10465" xml:space="preserve">qui eſt vnus angulorum quę-
              <lb/>
            ſitorum. </s>
            <s xml:id="echoid-s10466" xml:space="preserve">Rurſus, quia poſito AC, ſinu toto, CD,
              <lb/>
            ſinus eſt anguli CAD, dicemus iterum per regu-
              <lb/>
            lam auream. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">Si AC, 20. </s>
            <s xml:id="echoid-s10468" xml:space="preserve">dat AC, 100000. </s>
            <s xml:id="echoid-s10469" xml:space="preserve">ſinum
              <lb/>
            totum, quid dabit CD, 16? </s>
            <s xml:id="echoid-s10470" xml:space="preserve">Inueniemuſq; </s>
            <s xml:id="echoid-s10471" xml:space="preserve">ſinum
              <lb/>
            CD, 80000. </s>
            <s xml:id="echoid-s10472" xml:space="preserve">Vt hic patet.</s>
            <s xml:id="echoid-s10473" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # CD. # # CD.
            <lb/>
          20. # 100000. # 16? # fit # 80000.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10474" xml:space="preserve">Qui ſinus in tabula ſinuum monſtrat angulum
              <lb/>
            CAD, grad. </s>
            <s xml:id="echoid-s10475" xml:space="preserve">53. </s>
            <s xml:id="echoid-s10476" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10477" xml:space="preserve">8. </s>
            <s xml:id="echoid-s10478" xml:space="preserve">ac proinde eius comple-
              <lb/>
            mentum C, erit grad. </s>
            <s xml:id="echoid-s10479" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10480" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10481" xml:space="preserve">52. </s>
            <s xml:id="echoid-s10482" xml:space="preserve">qui eſt vnus
              <lb/>
            etiam angulorum quæſitorum. </s>
            <s xml:id="echoid-s10483" xml:space="preserve">Quòd ſi duo an-
              <lb/>
            guli duorum ſinuum inuentorum, nempe grad. </s>
            <s xml:id="echoid-s10484" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10485" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10486" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10487" xml:space="preserve">& </s>
            <s xml:id="echoid-s10488" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s10489" xml:space="preserve">53. </s>
            <s xml:id="echoid-s10490" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s10491" xml:space="preserve">
              <note position="left" xlink:label="note-338-03" xlink:href="note-338-03a" xml:space="preserve">Praxis.</note>
            8. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">ſimul componantur, fiet tertius angulus BAC, grad. </s>
            <s xml:id="echoid-s10493" xml:space="preserve">75. </s>
            <s xml:id="echoid-s10494" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10495" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10496" xml:space="preserve">Vel cer-
              <lb/>
            te ſi ſumma duorum angulorum B, C, inuentorum ex grad. </s>
            <s xml:id="echoid-s10497" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10498" xml:space="preserve">auferatur,
              <lb/>
            reliquus fiet tertius angulus BAC, grad. </s>
            <s xml:id="echoid-s10499" xml:space="preserve">75. </s>
            <s xml:id="echoid-s10500" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10501" xml:space="preserve">45.</s>
            <s xml:id="echoid-s10502" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10503" xml:space="preserve">ITAQVE, (vt totam praxim complectamur) ſi fiat, vt maximum
              <lb/>
            latus (in quod perpendicularis ducta eſt) ad ſummam aliorum duorum,
              <lb/>
            ita differentia eorundem duorum ad aliud, reperietur numerus, qui ex
              <lb/>
            maximo latere ſubductus relinquet numerum, cuius ſemiſſis dabit minus
              <lb/>
            ſegmentum baſis, hoc autem ex baſi detractum relinquet maius ſegmen-
              <lb/>
            tum, vt conſtat ex ſecunda praxi propoſ. </s>
            <s xml:id="echoid-s10504" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10505" xml:space="preserve">Quòd ſi rurſum fiat, vt mi-
              <lb/>
            nimum latus ad ſinum totum, ita ſegmentum baſis minus ad aliud, inue-
              <lb/>
            nietur ſinus, cuius arcus complementum dabit angulum ſupra baſim me-
              <lb/>
            dio lateri oppoſitum. </s>
            <s xml:id="echoid-s10506" xml:space="preserve">Deinde ſi rurſum fiat, vt medium latus ad ſinum
              <lb/>
            totum, ita maius ſegmentum baſis ad aliud, reperietur ſinus, cuius ar-
              <lb/>
            cus complementum dabit angulum ſupra baſim minimo lateri oppoſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s10507" xml:space="preserve">Tertius vero angulus maximo lateri oppoſitus conflabitur ex duobus il-
              <lb/>
            lis arcubus duorum ſinuum inuentorum: </s>
            <s xml:id="echoid-s10508" xml:space="preserve">vel certè relinquetur poſt de-
              <lb/>
            tractionem duorum angulorum inuentorum ex duobus rectis.</s>
            <s xml:id="echoid-s10509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10510" xml:space="preserve">RVRSVS in poſteriori triangulo datum ſit latus AB, 11. </s>
            <s xml:id="echoid-s10511" xml:space="preserve">AC, 13. </s>
            <s xml:id="echoid-s10512" xml:space="preserve">& </s>
            <s xml:id="echoid-s10513" xml:space="preserve">
              <lb/>
            BC, 20. </s>
            <s xml:id="echoid-s10514" xml:space="preserve">Demiſſa in maximum latus BC, perpendiculari AD, inuenietur
              <lb/>
            ſegmentum BD, 8 {4/5}. </s>
            <s xml:id="echoid-s10515" xml:space="preserve">at CD, 11{@/5}. </s>
            <s xml:id="echoid-s10516" xml:space="preserve">vt hic apparet ſecundum praxim poſte-
              <lb/>
            riorem propoſ. </s>
            <s xml:id="echoid-s10517" xml:space="preserve">9.</s>
            <s xml:id="echoid-s10518" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BC. # AB. AB. # Differ. inter # AB, AC.
            <lb/>
          20. # 24. # 2? # fit # 2 {2/5}.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10519" xml:space="preserve">Hic numerus ex baſe 20. </s>
            <s xml:id="echoid-s10520" xml:space="preserve">ablatus relinquit 17 {3/5}. </s>
            <s xml:id="echoid-s10521" xml:space="preserve">cuius ſemiſsis 8 {4/5}. </s>
            <s xml:id="echoid-s10522" xml:space="preserve">dat ſeg-
              <lb/>
            mentum minus BD. </s>
            <s xml:id="echoid-s10523" xml:space="preserve">Ergo maius CD, erit 11 {1/5}. </s>
            <s xml:id="echoid-s10524" xml:space="preserve">Hinc inuenietur </s>
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