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

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          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # AD. # # AD.
            <lb/>
          100000. # 20. # 59996? # fit # 12. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10979" xml:space="preserve">Rurſus, quia poſito ſinu toto AB, recta AD, eſt ſinus anguli B, vt in ſinubus
              <lb/>
            traditum eſt; </s>
            <s xml:id="echoid-s10980" xml:space="preserve">ſi ſiat, vt AB, latus datum ad ſinum totum, ita AD, iam in-
              <lb/>
            uenta ad aliud, inuenietur ſinus AD, 92308. </s>
            <s xml:id="echoid-s10981" xml:space="preserve">vt hic apparet.</s>
            <s xml:id="echoid-s10982" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # AD. # fit # AD.
            <lb/>
          13. # 100000. # 12? # # 92308.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10983" xml:space="preserve">Ex tabula ergo ſinuum dabitur angulus B, grad. </s>
            <s xml:id="echoid-s10984" xml:space="preserve">67. </s>
            <s xml:id="echoid-s10985" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10986" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10987" xml:space="preserve">ac proinde
              <lb/>
            BAC, reliquus duorum rectorum, grad. </s>
            <s xml:id="echoid-s10988" xml:space="preserve">75. </s>
            <s xml:id="echoid-s10989" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10990" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10991" xml:space="preserve">Quoniam vero eſt, vt ſi-
              <lb/>
            nus anguli dati C, ad ſinum anguli A, inuenti, ita latus AB, ad latus BC, in-
              <lb/>
              <note position="right" xlink:label="note-345-03" xlink:href="note-345-03a" xml:space="preserve">1. huius.</note>
            uenietur latus BC, 21. </s>
            <s xml:id="echoid-s10992" xml:space="preserve">ferme: </s>
            <s xml:id="echoid-s10993" xml:space="preserve">vt hic cernis.</s>
            <s xml:id="echoid-s10994" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # BAC. # AB. # # BC.
            <lb/>
          59996. # 96923. # 13? # fit # 21. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10995" xml:space="preserve">DEINDE, ijſdem poſitis, ſit alter angulus B, obtuſus, vt in poſterio-
              <lb/>
              <note position="right" xlink:label="note-345-05" xlink:href="note-345-05a" xml:space="preserve">Schol. 12.
                <lb/>
              ſecundi</note>
            ri triangulo. </s>
            <s xml:id="echoid-s10996" xml:space="preserve">Ducta ex A, ad BC, perpendiculari AD, quæ extra triangu-
              <lb/>
            lum cadet: </s>
            <s xml:id="echoid-s10997" xml:space="preserve">quoniam in triangulo rectangulo ACD, poſito ſinu toto AC,
              <lb/>
            recta AD, ſinus eſt anguli C, vt dictum eſt in tractatione ſinuum; </s>
            <s xml:id="echoid-s10998" xml:space="preserve">ſi fiat, vt
              <lb/>
            finus totus ad @@tum latus AC, ita ſinus dati anguli C, ad aliud, inuenietur
              <lb/>
            AD, ferme 12. </s>
            <s xml:id="echoid-s10999" xml:space="preserve">vt hic apparet.</s>
            <s xml:id="echoid-s11000" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # AD. # # AD.
            <lb/>
          100000. # 20. # 59996? # fit # 12. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s11001" xml:space="preserve">Rurſus, quia poſito ſinu toto AB, recta AD, ſinus eſt anguli ABD, vt in
              <lb/>
            defin. </s>
            <s xml:id="echoid-s11002" xml:space="preserve">ſinuum explicauimus; </s>
            <s xml:id="echoid-s11003" xml:space="preserve">Si fiat, vt latus datum ad ſinum totum, ita AD,
              <lb/>
            proxime inuenta ad aliud, reperietur ſinus AD, 92308. </s>
            <s xml:id="echoid-s11004" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s11005" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # AD. # # AD.
            <lb/>
          13. # 100000. # 12? # fit # 92308.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s11006" xml:space="preserve">Qui ſinus exhibet in tabula ſinuum angulũ ABD, grad. </s>
            <s xml:id="echoid-s11007" xml:space="preserve">67. </s>
            <s xml:id="echoid-s11008" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11009" xml:space="preserve">23. </s>
            <s xml:id="echoid-s11010" xml:space="preserve">ac proin-
              <lb/>
            de reliquum duorum rectorum ABC, grad. </s>
            <s xml:id="echoid-s11011" xml:space="preserve">11. </s>
            <s xml:id="echoid-s11012" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11013" xml:space="preserve">37. </s>
            <s xml:id="echoid-s11014" xml:space="preserve">Ablatis autem duo-
              <lb/>
            bus angulis C, & </s>
            <s xml:id="echoid-s11015" xml:space="preserve">ABC, notis ex grad. </s>
            <s xml:id="echoid-s11016" xml:space="preserve">180. </s>
            <s xml:id="echoid-s11017" xml:space="preserve">remanebit angulus BAC, grad. </s>
            <s xml:id="echoid-s11018" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s11019" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11020" xml:space="preserve">31. </s>
            <s xml:id="echoid-s11021" xml:space="preserve">Hinc, quoniam eſt, vt ſinus anguli C, dati ad ſinum anguli A, in-
              <lb/>
              <note position="right" xlink:label="note-345-08" xlink:href="note-345-08a" xml:space="preserve">1. huius.</note>
            uenti, ita latus AB, datum ad latus BC, inuenietur latus BC, fere 11. </s>
            <s xml:id="echoid-s11022" xml:space="preserve">vt
              <lb/>
            hic manifeſtum eſt.</s>
            <s xml:id="echoid-s11023" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # A. # AB. # # BC.
            <lb/>
          59996. # 50779. # 13? # fit # 11. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s11024" xml:space="preserve">POSTREMO, datis ijſdem lateribus, detur angulus obtuſus ABC,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s11025" xml:space="preserve">112. </s>
            <s xml:id="echoid-s11026" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11027" xml:space="preserve">37. </s>
            <s xml:id="echoid-s11028" xml:space="preserve">vt in poſteriori triangulo, factaq́ue eadem conſtructione;
              <lb/>
            </s>
            <s xml:id="echoid-s11029" xml:space="preserve">quoniam poſito ſinu toto AB, recta AD, ſinus eſt anguli ABD, hoc eſt, an-
              <lb/>
            guli dati ABC, inuenietur rurſum AD, 12. </s>
            <s xml:id="echoid-s11030" xml:space="preserve">ferè, vt hic cernis.</s>
            <s xml:id="echoid-s11031" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # AD. # # AD.
            <lb/>
          100000. # 13. # 92308? # fit # 12. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s11032" xml:space="preserve">Rurſus, quia poſito ſinu toto AC, recta AD, ſinus eſt anguli C, reperietur
              <lb/>
            ſinus AD, 60000. </s>
            <s xml:id="echoid-s11033" xml:space="preserve">Vt hic apparet.</s>
            <s xml:id="echoid-s11034" xml:space="preserve"/>
          </p>
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