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

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          <p>
            <s xml:id="echoid-s9623" xml:space="preserve">
              <pb o="312" file="324" n="324" rhead=""/>
            cu BAD, bifariam in A, ſecabit ſemidiameter ducta EA, chordam BD, bi-
              <lb/>
              <note position="left" xlink:label="note-324-01" xlink:href="note-324-01a" xml:space="preserve">3. tertij.</note>
            fariam in H, ex lemmate ad defin. </s>
            <s xml:id="echoid-s9624" xml:space="preserve">ſinuum demonſtrato; </s>
            <s xml:id="echoid-s9625" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s9626" xml:space="preserve">ad an-
              <lb/>
              <figure xlink:label="fig-324-01" xlink:href="fig-324-01a" number="172">
                <image file="324-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/324-01"/>
              </figure>
            gulos rectos. </s>
            <s xml:id="echoid-s9627" xml:space="preserve">Quoniam vero proportio ſinus
              <lb/>
            arcus BF, ad ſinum arcus FD, ponitur, vt 10.
              <lb/>
            </s>
            <s xml:id="echoid-s9628" xml:space="preserve">
              <note position="left" xlink:label="note-324-02" xlink:href="note-324-02a" xml:space="preserve">4.huius.</note>
            ad 5. </s>
            <s xml:id="echoid-s9629" xml:space="preserve">eſtq́ue vt ſinus arcus BF, ad ſinum ar-
              <lb/>
            cus FD, ita BG, ad GD; </s>
            <s xml:id="echoid-s9630" xml:space="preserve">erit quoque BG,
              <lb/>
            ad GD, vt 10. </s>
            <s xml:id="echoid-s9631" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9632" xml:space="preserve">Poſita igitur recta BG,
              <lb/>
            10. </s>
            <s xml:id="echoid-s9633" xml:space="preserve">erit GD, 5. </s>
            <s xml:id="echoid-s9634" xml:space="preserve">ac proinde tota BD, 15.
              <lb/>
            </s>
            <s xml:id="echoid-s9635" xml:space="preserve">vtraque vero ſemiſsis BH, HD, 7 {1/2}. </s>
            <s xml:id="echoid-s9636" xml:space="preserve">& </s>
            <s xml:id="echoid-s9637" xml:space="preserve">de-
              <lb/>
            nique HG, differentia inter ſemiſſem BH,
              <lb/>
            & </s>
            <s xml:id="echoid-s9638" xml:space="preserve">maius ſegmentum BG, vel inter ſemiſſem
              <lb/>
            HD, & </s>
            <s xml:id="echoid-s9639" xml:space="preserve">minus ſegmentum GD, erit 2 {1/2}. </s>
            <s xml:id="echoid-s9640" xml:space="preserve">
              <lb/>
            Rurſus quia totus arcus BAD, ponitur grad. </s>
            <s xml:id="echoid-s9641" xml:space="preserve">
              <lb/>
            130. </s>
            <s xml:id="echoid-s9642" xml:space="preserve">erit vtraque ſemiſsis BA, AD, grad. </s>
            <s xml:id="echoid-s9643" xml:space="preserve">
              <lb/>
            65. </s>
            <s xml:id="echoid-s9644" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s9645" xml:space="preserve">vterque angulus BEA,
              <lb/>
            AED, graduum quoque 65. </s>
            <s xml:id="echoid-s9646" xml:space="preserve">Et quoniam ex ijs, quæ ad initium tangentium,
              <lb/>
            ſecantiumq́ue tradidimus, poſito ſinu toto EH, recta BH, tangens eſt angu-
              <lb/>
            li BEH, & </s>
            <s xml:id="echoid-s9647" xml:space="preserve">HG, tangens anguli HEG; </s>
            <s xml:id="echoid-s9648" xml:space="preserve">dabitur, ex tangentium tabula, tan-
              <lb/>
            gens grad. </s>
            <s xml:id="echoid-s9649" xml:space="preserve">65. </s>
            <s xml:id="echoid-s9650" xml:space="preserve">nempe BH, partium 214451. </s>
            <s xml:id="echoid-s9651" xml:space="preserve">Quare, vt tangentem anguli AEF,
              <lb/>
            nimirum HG, inueniamus, dicemus per auream regulam. </s>
            <s xml:id="echoid-s9652" xml:space="preserve">Si BH, ſemiſsis ag-
              <lb/>
            gregati terminorum proportionis datæ, nempe 7 {1/2}. </s>
            <s xml:id="echoid-s9653" xml:space="preserve">dat BH, tangentem ſe-
              <lb/>
            miſsis aggregati angulorum BEF, FED, vel arcuũ BF, FD, partium 214451. </s>
            <s xml:id="echoid-s9654" xml:space="preserve">
              <lb/>
            quid dabit HG, differentia inter ſemiſſem aggregati terminorum datæ pro-
              <lb/>
            portionis, & </s>
            <s xml:id="echoid-s9655" xml:space="preserve">vtrumlibet terminorum eiuſdem proportionis, nimirum 2 {1/2}? </s>
            <s xml:id="echoid-s9656" xml:space="preserve">in-
              <lb/>
            ueniemusq́; </s>
            <s xml:id="echoid-s9657" xml:space="preserve">tangentem HG, partium 71484. </s>
            <s xml:id="echoid-s9658" xml:space="preserve">vt hic factum vides.</s>
            <s xml:id="echoid-s9659" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BH. # BH. # HG. # # HG.
            <lb/>
          7 {1/2}. # 214451. # 2 {1/2}? # ſit # 71484.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9660" xml:space="preserve">Ex tabula ergo tangentium elicietur angulus HEG, hoc eſt, arcus AF, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s9661" xml:space="preserve">35. </s>
            <s xml:id="echoid-s9662" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9663" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9664" xml:space="preserve">qui additus ſemiſsi AB, grad. </s>
            <s xml:id="echoid-s9665" xml:space="preserve">65. </s>
            <s xml:id="echoid-s9666" xml:space="preserve">componet arcum BF, maiorem,
              <lb/>
            a@q; </s>
            <s xml:id="echoid-s9667" xml:space="preserve">adeo & </s>
            <s xml:id="echoid-s9668" xml:space="preserve">angulum BEF, grad. </s>
            <s xml:id="echoid-s9669" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9670" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9671" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9672" xml:space="preserve">ablatus vero ex ſemiſſe AD,
              <lb/>
            relinquet arcum minorem FD, & </s>
            <s xml:id="echoid-s9673" xml:space="preserve">proinde & </s>
            <s xml:id="echoid-s9674" xml:space="preserve">angulum FED, grad.</s>
            <s xml:id="echoid-s9675" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9676" xml:space="preserve">Min.</s>
            <s xml:id="echoid-s9677" xml:space="preserve">26.</s>
            <s xml:id="echoid-s9678" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9679" xml:space="preserve">ITAQVE, quando duo arcus ſimul minores ſunt, quàm ſemi@ir-
              <lb/>
              <note position="left" xlink:label="note-324-04" xlink:href="note-324-04a" xml:space="preserve">Praxis.</note>
            culus, vel duo anguli ſimul duobus rectis minores: </s>
            <s xml:id="echoid-s9680" xml:space="preserve">Si fiat, vt ſemiſſis ag-
              <lb/>
            gregatiterminorum proportionis datæ ad tangentem ſemiſſis aggregati ar
              <lb/>
            cuum, vel angulorum (quærendo tangentem per partem proportionalem
              <lb/>
            reſpondentem 30. </s>
            <s xml:id="echoid-s9681" xml:space="preserve">ſecundis, ſi forte aggregatum bifariam diuidi nequeat
              <lb/>
            ſine Secundis.) </s>
            <s xml:id="echoid-s9682" xml:space="preserve">ita differentia inter ſemiſſem aggregati terminorum datæ
              <lb/>
            proportionis, & </s>
            <s xml:id="echoid-s9683" xml:space="preserve">alterutrum terminorum, ad aliud, reperietur tangens ar
              <lb/>
            cus, vel anguli, quo vterque arcus, angulusve quæſitus à ſemiſſe aggregati
              <lb/>
            eorundem differt. </s>
            <s xml:id="echoid-s9684" xml:space="preserve">Additus igitur arcus, vel angulus buius inuentæ tan-
              <lb/>
            gentis ad ſemiſſem dabit maiorem arcum, vel angulum; </s>
            <s xml:id="echoid-s9685" xml:space="preserve">ablat us vero ex
              <lb/>
            eadem ſemiſſe relinquet arcum, vel angulum minorem.</s>
            <s xml:id="echoid-s9686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9687" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s9688" xml:space="preserve">Producta ſemidiametro BE, ad K, & </s>
            <s xml:id="echoid-s9689" xml:space="preserve">diametro CF, produ-
              <lb/>
              <note position="left" xlink:label="note-324-05" xlink:href="note-324-05a" xml:space="preserve">Alia demõ.
                <lb/>
              ſtratio.</note>
            cta, donec in L, conueniat cum recta KDL, ex K, per D, ducta, agatur EI, ad
              <lb/>
              <note position="left" xlink:label="note-324-06" xlink:href="note-324-06a" xml:space="preserve">3.tertij.</note>
            DK, perpendicularis, quæ ipſam DK, bifariam ſecabit; </s>
            <s xml:id="echoid-s9690" xml:space="preserve">ac proinde cum </s>
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