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

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          <p>
            <s xml:id="echoid-s9690" xml:space="preserve">
              <pb o="313" file="325" n="325" rhead=""/>
            ra DE, EI, lateribus KE, EI, æqualia ſint, & </s>
            <s xml:id="echoid-s9691" xml:space="preserve">baſis DI, baſi KI; </s>
            <s xml:id="echoid-s9692" xml:space="preserve">angulus DEI,
              <lb/>
            angulo KEI, æqualis erit. </s>
            <s xml:id="echoid-s9693" xml:space="preserve">Quia ergo arcus BFD, datus eſt grad. </s>
            <s xml:id="echoid-s9694" xml:space="preserve">130. </s>
            <s xml:id="echoid-s9695" xml:space="preserve">dabi-
              <lb/>
              <note position="right" xlink:label="note-325-01" xlink:href="note-325-01a" xml:space="preserve">8.primi.</note>
            tur reliquus DK, de ſemicirculo grad. </s>
            <s xml:id="echoid-s9696" xml:space="preserve">50. </s>
            <s xml:id="echoid-s9697" xml:space="preserve">& </s>
            <s xml:id="echoid-s9698" xml:space="preserve">eius ſemiſsis, id eſt, angulus DEI,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9699" xml:space="preserve">25. </s>
            <s xml:id="echoid-s9700" xml:space="preserve">Rurſus quia finus arcus BF, ad ſinum arcus FD, ponitur, ut 10. </s>
            <s xml:id="echoid-s9701" xml:space="preserve">ad
              <lb/>
            5. </s>
            <s xml:id="echoid-s9702" xml:space="preserve">eſtq́ue idem ſinus arcus KF, qui arcus BF, vt in defin. </s>
            <s xml:id="echoid-s9703" xml:space="preserve">ſinuum oſtenſum eſt:
              <lb/>
            </s>
            <s xml:id="echoid-s9704" xml:space="preserve">erit quoque ſinus arcus KF, ad ſinum arcus DF, vt 10.</s>
            <s xml:id="echoid-s9705" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9706" xml:space="preserve">Cum ergo ſit, vt
              <lb/>
            ſinus arcus KF, ad ſinum arcus DF, ita KL, ad DL; </s>
            <s xml:id="echoid-s9707" xml:space="preserve">erit etiam KL, ad DL, vt
              <lb/>
              <note position="right" xlink:label="note-325-02" xlink:href="note-325-02a" xml:space="preserve">5.huius.</note>
            10.</s>
            <s xml:id="echoid-s9708" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9709" xml:space="preserve">Poſita igitur KL, 10. </s>
            <s xml:id="echoid-s9710" xml:space="preserve">erit DL, 5: </s>
            <s xml:id="echoid-s9711" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s9712" xml:space="preserve">reliqua KD, 5. </s>
            <s xml:id="echoid-s9713" xml:space="preserve">& </s>
            <s xml:id="echoid-s9714" xml:space="preserve">eius
              <lb/>
            ſemiſsis ID, 2 {1/2}. </s>
            <s xml:id="echoid-s9715" xml:space="preserve">At quoniam, vt ad initium tangentium & </s>
            <s xml:id="echoid-s9716" xml:space="preserve">ſecantiũ diximus,
              <lb/>
            poſito ſinu toto EI, recta ID, tangens eſt anguli DEI, hoc eſt, grad. </s>
            <s xml:id="echoid-s9717" xml:space="preserve">25. </s>
            <s xml:id="echoid-s9718" xml:space="preserve">da-
              <lb/>
            bitur ID, ex tabula tangẽtium, partium 46631. </s>
            <s xml:id="echoid-s9719" xml:space="preserve">Dicemus ergo per auream re
              <lb/>
            gulam. </s>
            <s xml:id="echoid-s9720" xml:space="preserve">Si ID, ſemiſsis differentiæ inter terminos proportionis datæ, nempe
              <lb/>
            2 {1/2}. </s>
            <s xml:id="echoid-s9721" xml:space="preserve">dat ID, tangentem ſemiſsis differentiæ inter aggregatum datum, & </s>
            <s xml:id="echoid-s9722" xml:space="preserve">ſemi-
              <lb/>
            circulum, partium 46631. </s>
            <s xml:id="echoid-s9723" xml:space="preserve">quid dabit IL, compoſita ex ſemiſſe differentiæ in-
              <lb/>
            ter terminos datæ proportionis, & </s>
            <s xml:id="echoid-s9724" xml:space="preserve">conſequente eiuſdem proportionis, nimi-
              <lb/>
            rum 7 {1/2}? </s>
            <s xml:id="echoid-s9725" xml:space="preserve">reperiemusq́ue IL, partium 139893. </s>
            <s xml:id="echoid-s9726" xml:space="preserve">qualium ID, eſt 46631. </s>
            <s xml:id="echoid-s9727" xml:space="preserve">vel
              <lb/>
            EI, 100000. </s>
            <s xml:id="echoid-s9728" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s9729" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          ID. # ID. # IL. # # IL.
            <lb/>
          2 {1/2}. # 46631. # 7 {1/2}? # ſit # 139893.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9730" xml:space="preserve">Cum ergo IL, ſit tangens anguli IEL, poſito ſinu toto EI, vt in tractatione
              <lb/>
            tangentium ac ſecantium tradidimus; </s>
            <s xml:id="echoid-s9731" xml:space="preserve">dabitur, ex tangentium tabula, angulus
              <lb/>
            IEF, grad. </s>
            <s xml:id="echoid-s9732" xml:space="preserve">54. </s>
            <s xml:id="echoid-s9733" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9734" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9735" xml:space="preserve">Ablato ergo angulo DEI, grad.</s>
            <s xml:id="echoid-s9736" xml:space="preserve">25. </s>
            <s xml:id="echoid-s9737" xml:space="preserve">nimirum ſemiſſe
              <lb/>
            differentiæ inter datum aggregatum, & </s>
            <s xml:id="echoid-s9738" xml:space="preserve">ſemicirculum, reliquus erit angulus
              <lb/>
            FED, ac propterea & </s>
            <s xml:id="echoid-s9739" xml:space="preserve">arcus FD, minor, grad.</s>
            <s xml:id="echoid-s9740" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9741" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9742" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9743" xml:space="preserve">qui ſubtractus ex da-
              <lb/>
            to aggregato grad. </s>
            <s xml:id="echoid-s9744" xml:space="preserve">130. </s>
            <s xml:id="echoid-s9745" xml:space="preserve">relinquet angulum BEF, & </s>
            <s xml:id="echoid-s9746" xml:space="preserve">proinde & </s>
            <s xml:id="echoid-s9747" xml:space="preserve">arcum BF,
              <lb/>
            maiorem, grad.</s>
            <s xml:id="echoid-s9748" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9749" xml:space="preserve">Min.</s>
            <s xml:id="echoid-s9750" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9751" xml:space="preserve">vt prius.</s>
            <s xml:id="echoid-s9752" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9753" xml:space="preserve">IGITVR ſi fiat, vt ſemiſſis differentiæ inter terminos proportio-
              <lb/>
              <note position="right" xlink:label="note-325-04" xlink:href="note-325-04a" xml:space="preserve">Praxis.</note>
            nis datæ ad tangentem ſemiſſis diff rentiæ inter aggregatum datum, & </s>
            <s xml:id="echoid-s9754" xml:space="preserve">
              <lb/>
            ſemicirculum, ita aggregatum ex ſemiſſe differentiæ inter terminos datæ
              <lb/>
            proportionis, & </s>
            <s xml:id="echoid-s9755" xml:space="preserve">conſequente eiuſdem proportionis, ad aliud, inuenietur
              <lb/>
            tangens anguli, à quo ſi dematur ſemiſſis differentiæ inter datum aggrega-
              <lb/>
            tum, & </s>
            <s xml:id="echoid-s9756" xml:space="preserve">ſemicir culum, reliquus erit angulus, ſeu arcus minor quæſitus: </s>
            <s xml:id="echoid-s9757" xml:space="preserve">qui
              <lb/>
            detractus ex aggregato dato, relinquet maiorẽ angulum, ſine arcũ quęſitũ.</s>
            <s xml:id="echoid-s9758" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9759" xml:space="preserve">ALITER adhuc per ſolos ſinus ſine tangentibus. </s>
            <s xml:id="echoid-s9760" xml:space="preserve">Ijsdem poſitis, quo-
              <lb/>
              <note position="right" xlink:label="note-325-05" xlink:href="note-325-05a" xml:space="preserve">Aliter abs-
                <lb/>
              que tangẽ-
                <lb/>
              tibus.</note>
            niam vt in ſinubus declarauimus, poſito ſinu toto EB, recta BH, eſt ſinus an-
              <lb/>
            guli BEH, nempe ſemiſsis aggregati angulorum, vel arcuũ dati, nempe grad.
              <lb/>
            </s>
            <s xml:id="echoid-s9761" xml:space="preserve">65. </s>
            <s xml:id="echoid-s9762" xml:space="preserve">& </s>
            <s xml:id="echoid-s9763" xml:space="preserve">HE, ſinus anguli EBH, grad. </s>
            <s xml:id="echoid-s9764" xml:space="preserve">25. </s>
            <s xml:id="echoid-s9765" xml:space="preserve">vtpote complementi anguli BEH; </s>
            <s xml:id="echoid-s9766" xml:space="preserve">
              <lb/>
            dabitur ex tabula ſinuum, BH, partium 90631. </s>
            <s xml:id="echoid-s9767" xml:space="preserve">at HE, partiũ 42262. </s>
            <s xml:id="echoid-s9768" xml:space="preserve">Quòd
              <lb/>
            ſi dicamus. </s>
            <s xml:id="echoid-s9769" xml:space="preserve">Si BH, ſemiſsis aggregati terminorum proportionis datæ, nempe
              <lb/>
            7 {1/2}.</s>
            <s xml:id="echoid-s9770" xml:space="preserve">dat BH, ſinum ſemiſsis aggregati angulorum, vel arcuum, partiũ 90631. </s>
            <s xml:id="echoid-s9771" xml:space="preserve">
              <lb/>
            quid dabit HG, differentia inter ſemiſſem aggregati terminorum proportio-
              <lb/>
            nis datæ, & </s>
            <s xml:id="echoid-s9772" xml:space="preserve">alterutrum terminorum, nimirum 2 {1/2}? </s>
            <s xml:id="echoid-s9773" xml:space="preserve">reperiemus HG, partium
              <lb/>
            30210. </s>
            <s xml:id="echoid-s9774" xml:space="preserve">qualium ſinus totus EB, eſt 100000. </s>
            <s xml:id="echoid-s9775" xml:space="preserve">vel EH, 42262. </s>
            <s xml:id="echoid-s9776" xml:space="preserve">vt hic patet.</s>
            <s xml:id="echoid-s9777" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BH. # BH. # HG. # # HG.
            <lb/>
          7 {1/2}. # 90631. # 2 {1/2}? # ſit # 30210.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9778" xml:space="preserve">Quia vero quadrata rectarum HE, HG, nempe 1786076644. </s>
            <s xml:id="echoid-s9779" xml:space="preserve">912644100.
              <lb/>
            </s>
            <s xml:id="echoid-s9780" xml:space="preserve">
              <note position="right" xlink:label="note-325-07" xlink:href="note-325-07a" xml:space="preserve">47. primi.</note>
            </s>
          </p>
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