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

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          <pb o="331" file="343" n="343" rhead=""/>
          <p>
            <s xml:id="echoid-s10852" xml:space="preserve">Addita autem AD, inuenta 5. </s>
            <s xml:id="echoid-s10853" xml:space="preserve">ad latus AC, datum 11. </s>
            <s xml:id="echoid-s10854" xml:space="preserve">fiet tota CD, 16. </s>
            <s xml:id="echoid-s10855" xml:space="preserve">Cum
              <lb/>
            ergo, poſito ſinu toto CD, recta BD, ſit tangens anguli C; </s>
            <s xml:id="echoid-s10856" xml:space="preserve">reperietur tan-
              <lb/>
            gens BD, 75000. </s>
            <s xml:id="echoid-s10857" xml:space="preserve">vt hic cernis.</s>
            <s xml:id="echoid-s10858" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          CD. # CD. # BD. # # BD.
            <lb/>
          16. # 100000. # 12? # fit # 75000.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10859" xml:space="preserve">Quæ tangens offeret in tangentium tabula angulum C, grad. </s>
            <s xml:id="echoid-s10860" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10861" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10862" xml:space="preserve">52. </s>
            <s xml:id="echoid-s10863" xml:space="preserve">& </s>
            <s xml:id="echoid-s10864" xml:space="preserve">
              <lb/>
            proinde duo anguli A, C, grad. </s>
            <s xml:id="echoid-s10865" xml:space="preserve">112. </s>
            <s xml:id="echoid-s10866" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10867" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10868" xml:space="preserve">& </s>
            <s xml:id="echoid-s10869" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s10870" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10871" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10872" xml:space="preserve">52. </s>
            <s xml:id="echoid-s10873" xml:space="preserve">ex grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10874" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10875" xml:space="preserve">ablatirelinquent angulum ABC, grad. </s>
            <s xml:id="echoid-s10876" xml:space="preserve">30. </s>
            <s xml:id="echoid-s10877" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10878" xml:space="preserve">31. </s>
            <s xml:id="echoid-s10879" xml:space="preserve">Quoniam tandem
              <lb/>
            eſt, vt ſinus anguli C, cogniti ad ſinum anguli BAC, dati, ita latus AB, 13. </s>
            <s xml:id="echoid-s10880" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-343-02" xlink:href="note-343-02a" xml:space="preserve">1. huius.</note>
            datum ad BC, inuenietur latus BC, 20. </s>
            <s xml:id="echoid-s10881" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s10882" xml:space="preserve">vt hic apparet.</s>
            <s xml:id="echoid-s10883" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # BAC. # AB. # # BC.
            <lb/>
          59996. # 92310. # 13? # fit # 20. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10884" xml:space="preserve">Verum, vt vides, prior ratio multò eſt breuior, & </s>
            <s xml:id="echoid-s10885" xml:space="preserve">ex peditior.</s>
            <s xml:id="echoid-s10886" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10887" xml:space="preserve">QVOD ſi quando data duo latera datum angulum ambientia fuerint
              <lb/>
              <note position="right" xlink:label="note-343-04" xlink:href="note-343-04a" xml:space="preserve">Quado da
                <lb/>
              ta latera sũt
                <lb/>
              æqualia.</note>
            æqualia, facilius erit problema. </s>
            <s xml:id="echoid-s10888" xml:space="preserve">Sint namq; </s>
            <s xml:id="echoid-s10889" xml:space="preserve">in triangulo ABC, duo latera
              <lb/>
              <figure xlink:label="fig-343-01" xlink:href="fig-343-01a" number="189">
                <image file="343-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/343-01"/>
              </figure>
            AB, AC, æqualia, quodlibet 9. </s>
            <s xml:id="echoid-s10890" xml:space="preserve">& </s>
            <s xml:id="echoid-s10891" xml:space="preserve">angulus A, com-
              <lb/>
            prehenſus grad. </s>
            <s xml:id="echoid-s10892" xml:space="preserve">80. </s>
            <s xml:id="echoid-s10893" xml:space="preserve">Ablato hoc angulo ex grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10894" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10895" xml:space="preserve">dabit ſemiſsis reſidui, quod eſt grad. </s>
            <s xml:id="echoid-s10896" xml:space="preserve">100. </s>
            <s xml:id="echoid-s10897" xml:space="preserve">vtrum-
              <lb/>
            que angulorum B, C, grad. </s>
            <s xml:id="echoid-s10898" xml:space="preserve">50. </s>
            <s xml:id="echoid-s10899" xml:space="preserve">Si autem fiat, vt ſinus
              <lb/>
            anguli B, vel C, ad ſinum anguli A, ita latus AC,
              <lb/>
            vel AB, ad aliud, prodibit latus BC, 11 {43685/76604}. </s>
            <s xml:id="echoid-s10900" xml:space="preserve">
              <lb/>
            vt hic vides.</s>
            <s xml:id="echoid-s10901" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          B, vel C. # A. # AB, vel AC. # # BC.
            <lb/>
          76604. # 98481. # 9? # fit # 11 {43685/76604}.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10902" xml:space="preserve">Datis ergo duobus lateribus trianguli non rectanguli, cum angulo ab ipſis
              <lb/>
            comprehenſo, &</s>
            <s xml:id="echoid-s10903" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10904" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s10905" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div891" type="section" level="1" n="471">
          <head xml:id="echoid-head503" xml:space="preserve">PROBL. 9. PROPOS. 13.</head>
          <note position="right" xml:space="preserve">In triãgule
            <lb/>
          non rectan
            <lb/>
          gulo ex da-
            <lb/>
          tis duobus
            <lb/>
          lateribꝰ da
            <lb/>
          tis, vel ex eo
            <lb/>
          rũ propor-
            <lb/>
          cũ vno an-
            <lb/>
          gulo nõ ab
            <lb/>
          ipſis cõpre-
            <lb/>
          henſo, ter-
            <lb/>
          tium latus,
            <lb/>
          & reliqui
            <lb/>
          anguli in-
            <lb/>
          ueſtigãtur.</note>
          <p>
            <s xml:id="echoid-s10906" xml:space="preserve">DATIS duobus lateribus trianguli non re-
              <lb/>
            ctanguli, vel eorum proportione data, vnà cum
              <lb/>
            angulo, qui alteri datorum laterum opponitur:
              <lb/>
            </s>
            <s xml:id="echoid-s10907" xml:space="preserve">reliquos angulos, & </s>
            <s xml:id="echoid-s10908" xml:space="preserve">tertium latus in quirere. </s>
            <s xml:id="echoid-s10909" xml:space="preserve">Opor
              <lb/>
            tet autem conſtare, num alter angulus reliquo la-
              <lb/>
            teri dato oppoſitus ſit acutus, an obtuſus, ſi datus
              <lb/>
            angulus acutus eſt.</s>
            <s xml:id="echoid-s10910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10911" xml:space="preserve">SINT in triangulo ABC, data duo latera AB, AC. </s>
            <s xml:id="echoid-s10912" xml:space="preserve">13. </s>
            <s xml:id="echoid-s10913" xml:space="preserve">& </s>
            <s xml:id="echoid-s10914" xml:space="preserve">20. </s>
            <s xml:id="echoid-s10915" xml:space="preserve">datusq́; </s>
            <s xml:id="echoid-s10916" xml:space="preserve">ſit
              <lb/>
            acutus angulus C, grad. </s>
            <s xml:id="echoid-s10917" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10918" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10919" xml:space="preserve">52. </s>
            <s xml:id="echoid-s10920" xml:space="preserve">lateri dato AB, oppoſitus, conſtetq́ue
              <lb/>
            de angulo B, qui alteri dato lateri AC, opponitur, num acutus ſit, an obtu-
              <lb/>
            ſus: </s>
            <s xml:id="echoid-s10921" xml:space="preserve">alias enim nihil certi colligi poſſet, vt ex ſequenti ſcholio patebit. </s>
            <s xml:id="echoid-s10922" xml:space="preserve">Quo-
              <lb/>
            niam ergo eſt, vt latus AB, ad latus AC, ita ſinus anguli C, ad ſinum anguli
              <lb/>
              <note position="right" xlink:label="note-343-07" xlink:href="note-343-07a" xml:space="preserve">1. huiun</note>
            B; </s>
            <s xml:id="echoid-s10923" xml:space="preserve">ſuntque tria primadata, inuenietur per auream regulam quartum, hoc eſt,
              <lb/>
            ſinus anguli B, 92302. </s>
            <s xml:id="echoid-s10924" xml:space="preserve">vt hic liquet.</s>
            <s xml:id="echoid-s10925" xml:space="preserve"/>
          </p>
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