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

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          <p style="it">
            <s xml:id="echoid-s10610" xml:space="preserve">
              <pb o="328" file="340" n="340" rhead=""/>
            cuius arcus complementum exhibebit angulum _ABD,_ grad. </s>
            <s xml:id="echoid-s10611" xml:space="preserve">_62._ </s>
            <s xml:id="echoid-s10612" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10613" xml:space="preserve">_52._ </s>
            <s xml:id="echoid-s10614" xml:space="preserve">ac propte-
              <lb/>
            rea reliquum duorum rectorum _ABC,_ grad. </s>
            <s xml:id="echoid-s10615" xml:space="preserve">_117._ </s>
            <s xml:id="echoid-s10616" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10617" xml:space="preserve">_8._ </s>
            <s xml:id="echoid-s10618" xml:space="preserve">_I_tem ſi fiat, vt _
              <emph style="sc">Ac</emph>
            , 31._
              <lb/>
            </s>
            <s xml:id="echoid-s10619" xml:space="preserve">ad _AC,_ _100000._ </s>
            <s xml:id="echoid-s10620" xml:space="preserve">ſinum totum, ita _CD, 24 {1/28}._ </s>
            <s xml:id="echoid-s10621" xml:space="preserve">ad aliud, reperietur ſinus _77534._ </s>
            <s xml:id="echoid-s10622" xml:space="preserve">
              <lb/>
            cuius arcus complementum offeret angulum _C,_ grad. </s>
            <s xml:id="echoid-s10623" xml:space="preserve">_39._ </s>
            <s xml:id="echoid-s10624" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s10625" xml:space="preserve">_10._ </s>
            <s xml:id="echoid-s10626" xml:space="preserve">Quòd ſi duo an-
              <lb/>
            guli _
              <emph style="sc">Ab</emph>
            C,_ & </s>
            <s xml:id="echoid-s10627" xml:space="preserve">_
              <emph style="sc">C</emph>
            ,_ ex grad. </s>
            <s xml:id="echoid-s10628" xml:space="preserve">_180._ </s>
            <s xml:id="echoid-s10629" xml:space="preserve">demantur, relinquetur angulus _
              <emph style="sc">B</emph>
              <emph style="sc">Ac</emph>
            ,_ grad. </s>
            <s xml:id="echoid-s10630" xml:space="preserve">_23._ </s>
            <s xml:id="echoid-s10631" xml:space="preserve">
              <lb/>
            _M_in. </s>
            <s xml:id="echoid-s10632" xml:space="preserve">_42._ </s>
            <s xml:id="echoid-s10633" xml:space="preserve">_R_atio huius operationis colligitur ex tractatione ſinuum, vbi oſtendimus, ſi
              <lb/>
            _
              <emph style="sc">Ab</emph>
            ,_ ſtatuatur ſinus totus, _BD,_ eſſe ſinum anguli _
              <emph style="sc">B</emph>
            AD:_ </s>
            <s xml:id="echoid-s10634" xml:space="preserve">_I_tem ſi _
              <emph style="sc">Ac</emph>
            ,_ ponatur ſinus
              <lb/>
            totus, _CD,_ eſſe ſinum anguli _
              <emph style="sc">C</emph>
            AD,_ &</s>
            <s xml:id="echoid-s10635" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10636" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div878" type="section" level="1" n="470">
          <head xml:id="echoid-head502" xml:space="preserve">PROBL. 8. PROPOS. 12.</head>
          <p>
            <s xml:id="echoid-s10637" xml:space="preserve">DATIS duobus lateribus trianguli non re-
              <lb/>
              <note position="left" xlink:label="note-340-01" xlink:href="note-340-01a" xml:space="preserve">In triágulo
                <lb/>
              nõ rectágu
                <lb/>
              lo ex duo-
                <lb/>
              bus lateri-
                <lb/>
              bus notis,
                <lb/>
              velex eorũ
                <lb/>
              proportio-
                <lb/>
              ne nota, cũ
                <lb/>
              angulo ab
                <lb/>
              ipſis com-
                <lb/>
              prehenſo,
                <lb/>
              tertium la-
                <lb/>
              tus, & reli-
                <lb/>
              qui anguli
                <lb/>
              exquirũt̃.</note>
            ctanguli, cum angulo ab ipſis comprehenſo; </s>
            <s xml:id="echoid-s10638" xml:space="preserve">vel
              <lb/>
            data proportione duorum laterum angulum da-
              <lb/>
            tum continentium: </s>
            <s xml:id="echoid-s10639" xml:space="preserve">tertium latus, & </s>
            <s xml:id="echoid-s10640" xml:space="preserve">reliquos an-
              <lb/>
            gulos inuenire.</s>
            <s xml:id="echoid-s10641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10642" xml:space="preserve">IN triangulo ABC, data ſint primum duo latera AB, AC, illud 3. </s>
            <s xml:id="echoid-s10643" xml:space="preserve">hoc
              <lb/>
            5. </s>
            <s xml:id="echoid-s10644" xml:space="preserve">ambientia angulum A, obtuſum, qui datus etiam ſit gnad. </s>
            <s xml:id="echoid-s10645" xml:space="preserve">93. </s>
            <s xml:id="echoid-s10646" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10647" xml:space="preserve">50.
              <lb/>
            </s>
            <s xml:id="echoid-s10648" xml:space="preserve">Oportet ex his tertium latus BC, & </s>
            <s xml:id="echoid-s10649" xml:space="preserve">reliquos angulos B, C, inueſtigare. </s>
            <s xml:id="echoid-s10650" xml:space="preserve">Quo-
              <lb/>
            niam datur angulus A, grad. </s>
            <s xml:id="echoid-s10651" xml:space="preserve">93. </s>
            <s xml:id="echoid-s10652" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10653" xml:space="preserve">50. </s>
            <s xml:id="echoid-s10654" xml:space="preserve">ſi detrahatur ex grad. </s>
            <s xml:id="echoid-s10655" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10656" xml:space="preserve">hoc eſt,
              <lb/>
            ex duobus rectis, reliquum erit aggregatum duorum angulorum B, C, grad. </s>
            <s xml:id="echoid-s10657" xml:space="preserve">
              <lb/>
            86. </s>
            <s xml:id="echoid-s10658" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10659" xml:space="preserve">10. </s>
            <s xml:id="echoid-s10660" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s10661" xml:space="preserve">proportio ſinuum angulorum C, B, data, nempe ea-
              <lb/>
            dem, quæ lateris AB, 3. </s>
            <s xml:id="echoid-s10662" xml:space="preserve">ad latus AC, 5. </s>
            <s xml:id="echoid-s10663" xml:space="preserve">propterea quod eſt, vt latus AB, ad
              <lb/>
            latus AC, ita ſinus anguli C, ad ſinum anguli B. </s>
            <s xml:id="echoid-s10664" xml:space="preserve">Quare vterq; </s>
            <s xml:id="echoid-s10665" xml:space="preserve">angulus C,
              <lb/>
              <note position="left" xlink:label="note-340-02" xlink:href="note-340-02a" xml:space="preserve">1. huius.</note>
            B, ſigillatim cognitus erit, ille grad. </s>
            <s xml:id="echoid-s10666" xml:space="preserve">29. </s>
            <s xml:id="echoid-s10667" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10668" xml:space="preserve">55. </s>
            <s xml:id="echoid-s10669" xml:space="preserve">hic vero grad. </s>
            <s xml:id="echoid-s10670" xml:space="preserve">56. </s>
            <s xml:id="echoid-s10671" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10672" xml:space="preserve">15.
              <lb/>
            </s>
            <s xml:id="echoid-s10673" xml:space="preserve">
              <note position="left" xlink:label="note-340-03" xlink:href="note-340-03a" xml:space="preserve">6. huius.</note>
            Quia vero latera ſunt ſinubus angulorum op-
              <lb/>
              <figure xlink:label="fig-340-01" xlink:href="fig-340-01a" number="185">
                <image file="340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/340-01"/>
              </figure>
              <note position="left" xlink:label="note-340-04" xlink:href="note-340-04a" xml:space="preserve">1. huius.</note>
            poſitorum proportionalia, erit, vt ſinus anguli
              <lb/>
            C, ad ſinum anguli A, ita latus AB, ad latus
              <lb/>
            BC: </s>
            <s xml:id="echoid-s10674" xml:space="preserve">vel vt ſinus anguli B, ad ſinum anguli A,
              <lb/>
            ita latus AC, ad latus BC. </s>
            <s xml:id="echoid-s10675" xml:space="preserve">Per auream ergo
              <lb/>
            regulam inuenietur latus BC, ferme 6. </s>
            <s xml:id="echoid-s10676" xml:space="preserve">vt hic
              <lb/>
            apparet.</s>
            <s xml:id="echoid-s10677" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # A. # # AB. # # BC.
            <lb/>
          49874. # 99776. # # 3? # fit # 6. ferè
            <lb/>
          # # Vel.
            <lb/>
          B. # A. # # AC. # # BC.
            <lb/>
          83147. # 99776. # # 5? # fit # 6. ferè.
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s10678" xml:space="preserve">VT ergo totam praxim complectamur: </s>
            <s xml:id="echoid-s10679" xml:space="preserve">Si (ablato angulo dato ex
              <lb/>
              <note position="left" xlink:label="note-340-06" xlink:href="note-340-06a" xml:space="preserve">Praxis.</note>
            grad. </s>
            <s xml:id="echoid-s10680" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10681" xml:space="preserve">vt ſumma aliorum duorum habeatur) fiat, vt ſemiſſis ſummæ
              <lb/>
            duorum lat erum datorum, nempe ſemiſſis ſummæ terminorum proportio-
              <lb/>
            nis ſinuum angulorum reliquorum, ad tangentem ſemiſſis ſummæ reliquo-
              <lb/>
            rum angulorum, ita differentia inter ſemiſſem ſummæ datorum </s>
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