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

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          <p>
            <s xml:id="echoid-s5010" xml:space="preserve">
              <pb o="125" file="137" n="137" rhead=""/>
            quidem ſinus eſt arcus BD. </s>
            <s xml:id="echoid-s5011" xml:space="preserve">Eademq́ue ratione erit NK, ſinus rectus arcus
              <lb/>
              <note position="right" xlink:label="note-137-01" xlink:href="note-137-01a" xml:space="preserve">Supputatie
                <lb/>
              ſinus grad.
                <lb/>
              1.</note>
            BH. </s>
            <s xml:id="echoid-s5012" xml:space="preserve">Sit ergo propoſitum inuenire ſinum OK, arcus BD, grad. </s>
            <s xml:id="echoid-s5013" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5014" xml:space="preserve">Quoniam
              <lb/>
            NK, ſinus grad. </s>
            <s xml:id="echoid-s5015" xml:space="preserve">0. </s>
            <s xml:id="echoid-s5016" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5017" xml:space="preserve">45. </s>
            <s xml:id="echoid-s5018" xml:space="preserve">eſt inuentus 130896. </s>
            <s xml:id="echoid-s5019" xml:space="preserve">erit eius tertia pars, nempe
              <lb/>
            43632. </s>
            <s xml:id="echoid-s5020" xml:space="preserve">maior, quàm MN: </s>
            <s xml:id="echoid-s5021" xml:space="preserve">propterea quod, per propof. </s>
            <s xml:id="echoid-s5022" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5023" xml:space="preserve">maior eſt KL, quàm
              <lb/>
            LM, & </s>
            <s xml:id="echoid-s5024" xml:space="preserve">LM, maior, quàm MN, adeo vt MN, mi-
              <lb/>
              <figure xlink:label="fig-137-01" xlink:href="fig-137-01a" number="132">
                <image file="137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/137-01"/>
              </figure>
            nor ſit, quàm tertia pars ipſius NK, hoc eſt, minor,
              <lb/>
            quàm 43632. </s>
            <s xml:id="echoid-s5025" xml:space="preserve">Multo igitur maior erit eadem tertia
              <lb/>
            pars rectæ NK, nempe 43632. </s>
            <s xml:id="echoid-s5026" xml:space="preserve">quàm NO: </s>
            <s xml:id="echoid-s5027" xml:space="preserve">quod, per
              <lb/>
            eandẽ propof. </s>
            <s xml:id="echoid-s5028" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5029" xml:space="preserve">maior quoque ſit MN, quàm NO.
              <lb/>
            </s>
            <s xml:id="echoid-s5030" xml:space="preserve">Quare ſi addamus 43632. </s>
            <s xml:id="echoid-s5031" xml:space="preserve">ad 130896. </s>
            <s xml:id="echoid-s5032" xml:space="preserve">id eſt, ad NK,
              <lb/>
            ſinum Minutorum 45. </s>
            <s xml:id="echoid-s5033" xml:space="preserve">efficiemus numerum 174528. </s>
            <s xml:id="echoid-s5034" xml:space="preserve">
              <lb/>
            qui maior erit, quàm OK, ſinus rectus grad. </s>
            <s xml:id="echoid-s5035" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5036" xml:space="preserve">quan
              <lb/>
            doquidem ad NK, plus addimus, quàm rectã NO,
              <lb/>
            vt dictum eſt. </s>
            <s xml:id="echoid-s5037" xml:space="preserve">Rurſus quia EK, ſinus grad. </s>
            <s xml:id="echoid-s5038" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5039" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5040" xml:space="preserve">
              <lb/>
            30. </s>
            <s xml:id="echoid-s5041" xml:space="preserve">inuentus eſt 261769. </s>
            <s xml:id="echoid-s5042" xml:space="preserve">ſi ex eo detrahamus ſinum NK, Minutorum 45. </s>
            <s xml:id="echoid-s5043" xml:space="preserve">nem
              <lb/>
            pe 130896. </s>
            <s xml:id="echoid-s5044" xml:space="preserve">relinquetur recta EN, partium 130873. </s>
            <s xml:id="echoid-s5045" xml:space="preserve">cuius tertia pars, nempe
              <lb/>
            43624. </s>
            <s xml:id="echoid-s5046" xml:space="preserve">fere, minor erit, quàm NO: </s>
            <s xml:id="echoid-s5047" xml:space="preserve">propterea quod, per propof. </s>
            <s xml:id="echoid-s5048" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5049" xml:space="preserve">maior eſt
              <lb/>
            NO, quàm OP, & </s>
            <s xml:id="echoid-s5050" xml:space="preserve">OP, maior, quàm PE, adeo vt NO, maior ſit, quàm ter-
              <lb/>
            tia parsipſius EN, hoc eſt, maior, quàm 43624. </s>
            <s xml:id="echoid-s5051" xml:space="preserve">Quare ſi addamus 43624. </s>
            <s xml:id="echoid-s5052" xml:space="preserve">ad
              <lb/>
            130896. </s>
            <s xml:id="echoid-s5053" xml:space="preserve">id eſt, ad NK, ſinum Min. </s>
            <s xml:id="echoid-s5054" xml:space="preserve">45. </s>
            <s xml:id="echoid-s5055" xml:space="preserve">efficiemus numerum 174520. </s>
            <s xml:id="echoid-s5056" xml:space="preserve">qui minor
              <lb/>
            erit, quàm OK, ſinus re ctus grad. </s>
            <s xml:id="echoid-s5057" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5058" xml:space="preserve">quandoquidem ad NK, minus addimus,
              <lb/>
            quàm rectam NO. </s>
            <s xml:id="echoid-s5059" xml:space="preserve">Conſtatigitur, ſinum rectum grad. </s>
            <s xml:id="echoid-s5060" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5061" xml:space="preserve">conſiſtere inter hos
              <lb/>
            duos numeros, 174528. </s>
            <s xml:id="echoid-s5062" xml:space="preserve">174520. </s>
            <s xml:id="echoid-s5063" xml:space="preserve">cum ille maior ſit, hic auté minor. </s>
            <s xml:id="echoid-s5064" xml:space="preserve">Statuamus
              <lb/>
            ergo eum eſſe, 174524. </s>
            <s xml:id="echoid-s5065" xml:space="preserve">inter illos numeros omnino medium. </s>
            <s xml:id="echoid-s5066" xml:space="preserve">Ita enim non dif-
              <lb/>
            feret ſenſibiliter hic numerus à vero ſinu grad. </s>
            <s xml:id="echoid-s5067" xml:space="preserve">1.</s>
            <s xml:id="echoid-s5068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5069" xml:space="preserve">EX hoc ſinu grad. </s>
            <s xml:id="echoid-s5070" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5071" xml:space="preserve">inueniemus, per propoſ. </s>
            <s xml:id="echoid-s5072" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5073" xml:space="preserve">ſinum eius cõplementi, hoc
              <lb/>
              <note position="right" xlink:label="note-137-02" xlink:href="note-137-02a" xml:space="preserve">Supputatio
                <lb/>
              ſinus grad.
                <lb/>
              89.</note>
            eſt, ſinum arcus grad. </s>
            <s xml:id="echoid-s5074" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5075" xml:space="preserve">eſſe 9998477. </s>
            <s xml:id="echoid-s5076" xml:space="preserve">Quem hoc etiã modo reperiemus. </s>
            <s xml:id="echoid-s5077" xml:space="preserve">Quo-
              <lb/>
            niam numerus 174528. </s>
            <s xml:id="echoid-s5078" xml:space="preserve">maior eſt, quam ſinus grad. </s>
            <s xml:id="echoid-s5079" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5080" xml:space="preserve">vt diximus: </s>
            <s xml:id="echoid-s5081" xml:space="preserve">ſit, vt per eum
              <lb/>
            inueſtigatus, iuxta doctrinam propof. </s>
            <s xml:id="echoid-s5082" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5083" xml:space="preserve">ſinus cóplementi grad. </s>
            <s xml:id="echoid-s5084" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5085" xml:space="preserve">hoc eſt, ſinus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5086" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5087" xml:space="preserve">ſit numerus 9998476. </s>
            <s xml:id="echoid-s5088" xml:space="preserve">& </s>
            <s xml:id="echoid-s5089" xml:space="preserve">paulo amplius, qui minor erit neceſſario,
              <lb/>
            quàm verus ſinus arcus grad. </s>
            <s xml:id="echoid-s5090" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5091" xml:space="preserve">quandoquidem pro ſinu grad. </s>
            <s xml:id="echoid-s5092" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5093" xml:space="preserve">numerum
              <lb/>
            ſumpſimus vero ſinu maiorem. </s>
            <s xml:id="echoid-s5094" xml:space="preserve">Rurſus quia numerus 174520. </s>
            <s xml:id="echoid-s5095" xml:space="preserve">minor eſt, quàm
              <lb/>
            ſinus grad. </s>
            <s xml:id="echoid-s5096" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5097" xml:space="preserve">vt diximus; </s>
            <s xml:id="echoid-s5098" xml:space="preserve">fit, vt per eum inueſtigatus, iuxta doctrinam propof.
              <lb/>
            </s>
            <s xml:id="echoid-s5099" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5100" xml:space="preserve">ſinus eius complementi, nimirum ſinus grad. </s>
            <s xml:id="echoid-s5101" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5102" xml:space="preserve">ſit numerus 9998477. </s>
            <s xml:id="echoid-s5103" xml:space="preserve">& </s>
            <s xml:id="echoid-s5104" xml:space="preserve">pau
              <lb/>
            lo amplius, qui maior erit neceſſario, quàm verus ſinus grad. </s>
            <s xml:id="echoid-s5105" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5106" xml:space="preserve">quandoqui-
              <lb/>
            dem pro ſinu grad. </s>
            <s xml:id="echoid-s5107" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5108" xml:space="preserve">numerum accepimus vero ſinu minorem. </s>
            <s xml:id="echoid-s5109" xml:space="preserve">Conſtitutus er-
              <lb/>
            go erit ſinus grad. </s>
            <s xml:id="echoid-s5110" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5111" xml:space="preserve">inter duos hos numeros 9998476. </s>
            <s xml:id="echoid-s5112" xml:space="preserve">& </s>
            <s xml:id="echoid-s5113" xml:space="preserve">paulo amplius, at-
              <lb/>
            que 9998477. </s>
            <s xml:id="echoid-s5114" xml:space="preserve">& </s>
            <s xml:id="echoid-s5115" xml:space="preserve">paulo amplius: </s>
            <s xml:id="echoid-s5116" xml:space="preserve">ac proinde ſine notabili errore eum ſtatuemus
              <lb/>
            eſſe 9998477. </s>
            <s xml:id="echoid-s5117" xml:space="preserve">quantum videlicet eundem inuenimus ex ſinugrad. </s>
            <s xml:id="echoid-s5118" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5119" xml:space="preserve">Ex quo
              <lb/>
            conſtat, recte conſtitutum eſſe ſinum grad. </s>
            <s xml:id="echoid-s5120" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5121" xml:space="preserve">partium 174524. </s>
            <s xml:id="echoid-s5122" xml:space="preserve">cum ex eo, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s5123" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5124" xml:space="preserve">repertus ſit ſinus complementiipſius tot particularum, quot vere ac
              <lb/>
            reipſa continere debet.</s>
            <s xml:id="echoid-s5125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5126" xml:space="preserve">PRAETEREA ex finu arcus grad. </s>
            <s xml:id="echoid-s5127" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5128" xml:space="preserve">reperiemus, per coroll. </s>
            <s xml:id="echoid-s5129" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s5130" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s5131" xml:space="preserve">
              <note position="right" xlink:label="note-137-03" xlink:href="note-137-03a" xml:space="preserve">Supputatie
                <lb/>
              ſinus Min.
                <lb/>
              30. & ſinus
                <lb/>
              grad. 89.
                <lb/>
              Min. 30. It@
                <lb/>
              ſinus Min.
                <lb/>
              15. & ſinus
                <lb/>
              grad. 89.
                <lb/>
              Min. 45.</note>
            ſinum rectum arcus Min. </s>
            <s xml:id="echoid-s5132" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5133" xml:space="preserve">& </s>
            <s xml:id="echoid-s5134" xml:space="preserve">ex hoc, per propoſ. </s>
            <s xml:id="echoid-s5135" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5136" xml:space="preserve">ſinum complementi, nem-
              <lb/>
            pe ſinum grad. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5138" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5139" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5140" xml:space="preserve">Item ex ſinu arcus Min. </s>
            <s xml:id="echoid-s5141" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5142" xml:space="preserve">inueniemus, per coroll.
              <lb/>
            </s>
            <s xml:id="echoid-s5143" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s5144" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5145" xml:space="preserve">ſinum arcus Min. </s>
            <s xml:id="echoid-s5146" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5147" xml:space="preserve">atque ex hoe ſinum complementi, hoc eſt, ſi-
              <lb/>
            num grad. </s>
            <s xml:id="echoid-s5148" xml:space="preserve">89. </s>
            <s xml:id="echoid-s5149" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5150" xml:space="preserve">45.</s>
            <s xml:id="echoid-s5151" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5152" xml:space="preserve">QVEMADMODVM autem ſupra ex ſinubus rectis grad. </s>
            <s xml:id="echoid-s5153" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5154" xml:space="preserve">& </s>
            <s xml:id="echoid-s5155" xml:space="preserve">54.</s>
            <s xml:id="echoid-s5156" xml:space="preserve"/>
          </p>
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