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

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          <pb o="332" file="344" n="344" rhead=""/>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AC. # C. # # B.
            <lb/>
          13. # 20. # 59996? # fit # 92302.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10926" xml:space="preserve">Qui ſinus in tabula ſinuum exhibet angulum B, ferè grad. </s>
            <s xml:id="echoid-s10927" xml:space="preserve">67. </s>
            <s xml:id="echoid-s10928" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10929" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10930" xml:space="preserve">ſi acu
              <lb/>
            tus fuerit, vt in priori triangulo: </s>
            <s xml:id="echoid-s10931" xml:space="preserve">ſi autem obtuſus, vt in triangulo poſterio-
              <lb/>
            ri, grad. </s>
            <s xml:id="echoid-s10932" xml:space="preserve">112. </s>
            <s xml:id="echoid-s10933" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10934" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10935" xml:space="preserve">vtpote qui cum illo ſemicirculum compleat; </s>
            <s xml:id="echoid-s10936" xml:space="preserve">cum ob-
              <lb/>
            tuſus, & </s>
            <s xml:id="echoid-s10937" xml:space="preserve">acutus conficientes grad. </s>
            <s xml:id="echoid-s10938" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10939" xml:space="preserve">eundem ſinum habeant, vt ad deſini-
              <lb/>
              <figure xlink:label="fig-344-01" xlink:href="fig-344-01a" number="190">
                <image file="344-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/344-01"/>
              </figure>
            tiones ſinuum demõſtraui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s10940" xml:space="preserve">Ablatis autem duo-
              <lb/>
            bus angulis C, B, ex grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10941" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10942" xml:space="preserve">relinquetur in priori
              <lb/>
            triangulo angulus A, grad. </s>
            <s xml:id="echoid-s10943" xml:space="preserve">
              <lb/>
            75. </s>
            <s xml:id="echoid-s10944" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10945" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10946" xml:space="preserve">In poſteriori
              <lb/>
            vero grad. </s>
            <s xml:id="echoid-s10947" xml:space="preserve">30. </s>
            <s xml:id="echoid-s10948" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10949" xml:space="preserve">31. </s>
            <s xml:id="echoid-s10950" xml:space="preserve">La-
              <lb/>
            tus autem BC, inuenietur,
              <lb/>
            per auream regulam, par-
              <lb/>
            tium ferè 21. </s>
            <s xml:id="echoid-s10951" xml:space="preserve">in priori trian
              <lb/>
            gulo; </s>
            <s xml:id="echoid-s10952" xml:space="preserve">in poſteriori autem
              <lb/>
            ferè 11. </s>
            <s xml:id="echoid-s10953" xml:space="preserve">quòd ſit, vt ſinus anguli C, ad ſinum anguli A, ita latus AB, ad la-
              <lb/>
              <note position="left" xlink:label="note-344-02" xlink:href="note-344-02a" xml:space="preserve">1. huius.</note>
            tus BC. </s>
            <s xml:id="echoid-s10954" xml:space="preserve">vt in hac operatione apparet.</s>
            <s xml:id="echoid-s10955" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # A. # # AB. # # BC.
            <lb/>
          59996. # 96923. # # 13? # fit # 21. ferè.
            <lb/>
          # # Item
            <lb/>
          C. # A. # # AB. # # BC.
            <lb/>
          59996. # 50779. # # 13? # fit # 11. ferè.
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s10956" xml:space="preserve">ITAQVE, ſi fiat, vt latus datum dato angulo oppoſitum ad al-
              <lb/>
              <note position="left" xlink:label="note-344-04" xlink:href="note-344-04a" xml:space="preserve">Praxis.</note>
            terum latus datum, ita ſinus dati anguli ad aliud, reperietur ſinus, cuius
              <lb/>
            arcus dabit angulum alteri lateri dato oppoſitum, ſi acutus fuerit, (quod
              <lb/>
            quidem ſemper contingit, quando datus angulus eſt obtuſus) aut certe ex
              <lb/>
            ſemicirculo ſublatus dabit illum angulum, ſi obtuſus fuerit: </s>
            <s xml:id="echoid-s10957" xml:space="preserve">Summa ve-
              <lb/>
            ro ex dato angulo, & </s>
            <s xml:id="echoid-s10958" xml:space="preserve">inuento angulo conflata ex grad. </s>
            <s xml:id="echoid-s10959" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10960" xml:space="preserve">ſubducta
              <lb/>
            exhibebit tertium angulum. </s>
            <s xml:id="echoid-s10961" xml:space="preserve">Si deni fiat, vt ſinus anguli dati ad ſinum
              <lb/>
            tertij anguli à datis lateribus comprehenſi, qui vltimo inuentus eſt, ita
              <lb/>
            latus datum dato angulo oppoſitum ad aliud, producetur tertium latus.</s>
            <s xml:id="echoid-s10962" xml:space="preserve"/>
          </p>
          <figure number="191">
            <image file="344-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/344-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s10963" xml:space="preserve">QVOD ſi detur duorum laterum proportio,
              <lb/>
              <note position="left" xlink:label="note-344-05" xlink:href="note-344-05a" xml:space="preserve">Quãdo pro
                <lb/>
              portio duo
                <lb/>
              rum laterũ
                <lb/>
              datur.</note>
            ſi lateribus illis numeri proportionis aſcribantur,
              <lb/>
            eodem modo problema exequemur.</s>
            <s xml:id="echoid-s10964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10965" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s10966" xml:space="preserve">Dentur rurſum duo latera AB, 13.
              <lb/>
            </s>
            <s xml:id="echoid-s10967" xml:space="preserve">& </s>
            <s xml:id="echoid-s10968" xml:space="preserve">AC, 20. </s>
            <s xml:id="echoid-s10969" xml:space="preserve">vnà cum angulo C, acuto grad. </s>
            <s xml:id="echoid-s10970" xml:space="preserve">36 Min. </s>
            <s xml:id="echoid-s10971" xml:space="preserve">
              <lb/>
            52. </s>
            <s xml:id="echoid-s10972" xml:space="preserve">ſitq́; </s>
            <s xml:id="echoid-s10973" xml:space="preserve">primum alter angulus B, acutus etiam, vt
              <lb/>
            in priori triangulo. </s>
            <s xml:id="echoid-s10974" xml:space="preserve">Ducta ex A, ad BC, perpendi-
              <lb/>
            culari AD, quæ intra triangulum cadet: </s>
            <s xml:id="echoid-s10975" xml:space="preserve">quoniam
              <lb/>
              <note position="left" xlink:label="note-344-06" xlink:href="note-344-06a" xml:space="preserve">Schol. 13.
                <lb/>
              ſecundi.</note>
            in triãgulo rectangulo ACD, poſito ſinu toto AC,
              <lb/>
            recta AD, ſinus eſt anguli dati C, vt in tractatu ſi-
              <lb/>
            nuum docuimus; </s>
            <s xml:id="echoid-s10976" xml:space="preserve">ſi fiat, vt AC, ſinus totus ad AC,
              <lb/>
            latus datum, ita AD, ſinus dati anguli C, ad aliud,
              <lb/>
            reperietur AD, 12. </s>
            <s xml:id="echoid-s10977" xml:space="preserve">ferè, vt hic vides.</s>
            <s xml:id="echoid-s10978" xml:space="preserve"/>
          </p>
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