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

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          <p style="it">
            <s xml:id="echoid-s6478" xml:space="preserve">
              <pb o="174" file="186" n="186" rhead=""/>
            diſtat, inveniatur quarta proportionalis, inuentus erit ſinus rectus declinationis
              <lb/>
              <note position="left" xlink:label="note-186-01" xlink:href="note-186-01a" xml:space="preserve">12. fexti.</note>
            quæſitæ. </s>
            <s xml:id="echoid-s6479" xml:space="preserve">_I_ta autem ſine magno labore quartam proportionalem reperiemus cum _E_u-
              <lb/>
            clide. </s>
            <s xml:id="echoid-s6480" xml:space="preserve">_D_uctis duabus rectis _AB, AC_, angulum quemcunq; </s>
            <s xml:id="echoid-s6481" xml:space="preserve">facientibus in _A_, ſumatur
              <lb/>
            in earum altera, recta _AD_, primæ lineæ, boc eſt, ſinui toti _ED_, æqualis; </s>
            <s xml:id="echoid-s6482" xml:space="preserve">& </s>
            <s xml:id="echoid-s6483" xml:space="preserve">_DB_,
              <lb/>
            æqualis ſecundæ lineæ, vt ſinui maximæ declinationis _FI:_ </s>
            <s xml:id="echoid-s6484" xml:space="preserve">_I_n altera vero, recta _
              <emph style="sc">Ae</emph>
            _,
              <lb/>
            tertiæ lineæ, nempe ſinui _GH_, æqualis. </s>
            <s xml:id="echoid-s6485" xml:space="preserve">_D_einde ducta recta _
              <emph style="sc">De</emph>
            _, ægatur illi per _B_,
              <lb/>
            parallela _BC_. </s>
            <s xml:id="echoid-s6486" xml:space="preserve">_N_am _
              <emph style="sc">E</emph>
            C_, erit quarta proportionalis, boc eſt, ſinus rectus declina-
              <lb/>
            tionis grad. </s>
            <s xml:id="echoid-s6487" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s6488" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6489" xml:space="preserve">_C_uius arcum ita inquiremus. </s>
            <s xml:id="echoid-s6490" xml:space="preserve">_R_ectæ _EC_, inuentæ abſcindemus
              <lb/>
            ex ſemidiametro _
              <emph style="sc">E</emph>
            A_, æqualem _EM_, & </s>
            <s xml:id="echoid-s6491" xml:space="preserve">per _M_, rectæ _EB_, parallelam ducemus _MN_.
              <lb/>
            </s>
            <s xml:id="echoid-s6492" xml:space="preserve">_A_rcus namq; </s>
            <s xml:id="echoid-s6493" xml:space="preserve">_BN_, erit arcus declinationis quæſitæ, cum reſpondeat ſinui recto _
              <emph style="sc">E</emph>
            M_,
              <lb/>
            ſiue _EC:_ </s>
            <s xml:id="echoid-s6494" xml:space="preserve">propterea quod, ducto ſinu recto _NO,_ arcus _NB_, inter ſe æquales ſintre-
              <lb/>
              <note position="left" xlink:label="note-186-02" xlink:href="note-186-02a" xml:space="preserve">@4. primi.</note>
            ctæ _
              <emph style="sc">E</emph>
            M, ON_, ob parallelogrammum _MO_. </s>
            <s xml:id="echoid-s6495" xml:space="preserve">_E_undem tamen arcumita quoq; </s>
            <s xml:id="echoid-s6496" xml:space="preserve">obtine-
              <lb/>
              <figure xlink:label="fig-186-01" xlink:href="fig-186-01a" number="136">
                <image file="186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/186-01"/>
              </figure>
            bimus. </s>
            <s xml:id="echoid-s6497" xml:space="preserve">_R_ectæ inæ
              <lb/>
            uentæ _
              <emph style="sc">E</emph>
            C_, æquæ
              <lb/>
            lem abſcindemus
              <lb/>
            _
              <emph style="sc">Cf</emph>
            _, vt _
              <emph style="sc">E</emph>
            F_,
              <lb/>
            ipſius _EC_, ſit du
              <lb/>
            pla, hoc eſt, chor
              <lb/>
            da illius arcus,
              <lb/>
            qui duplus e§t
              <lb/>
            arcus, cuius ſis
              <lb/>
            nus rectus e§t
              <lb/>
            _
              <emph style="sc">E</emph>
            C_. </s>
            <s xml:id="echoid-s6498" xml:space="preserve">_N_am ſire-
              <lb/>
            ctæ _
              <emph style="sc">E</emph>
            F_, æqua-
              <lb/>
            lem chordã _PQ,_
              <lb/>
            in circulo accommodemus, & </s>
            <s xml:id="echoid-s6499" xml:space="preserve">cius arcum _PQ_, bifariam ſecemus in _R_, erit quoq; </s>
            <s xml:id="echoid-s6500" xml:space="preserve">_QR_,
              <lb/>
            vel _
              <emph style="sc">Pr</emph>
            _, arcus declinationis quæſitæ reſpondens ſinui _
              <emph style="sc">E</emph>
            C_, hoc eſt, dimidiatæ chordæ
              <lb/>
            _PQ_, vt conſtat ex definitione ſinus recti. </s>
            <s xml:id="echoid-s6501" xml:space="preserve">_Q_uadrans porroin _90._ </s>
            <s xml:id="echoid-s6502" xml:space="preserve">gradus diuiſus mon-
              <lb/>
            ſtrabit, (ſihoc etiam ſcire lubeat) quot gradus ac _M_inuta in _BN_, vel _PR,_ arcu declina
              <lb/>
            tionis contineantur: </s>
            <s xml:id="echoid-s6503" xml:space="preserve">quamuis _M_inuta ſecundũ exiſtimationẽ accipienda ſint; </s>
            <s xml:id="echoid-s6504" xml:space="preserve">proptereæ
              <lb/>
            quòd gradus quadrantis, niſi admodum magnus eſſet, in _M_inuta diuidi non poßit.</s>
            <s xml:id="echoid-s6505" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6506" xml:space="preserve">_RVRSVS_ inueſtiganda ſit aſcenſio recta grad. </s>
            <s xml:id="echoid-s6507" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s6508" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6509" xml:space="preserve">_Q_uoniamigitur, vtin ſch@
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s6510" xml:space="preserve">_9_. </s>
            <s xml:id="echoid-s6511" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6512" xml:space="preserve">_2._ </s>
            <s xml:id="echoid-s6513" xml:space="preserve">_G_nomonices demonſtrauimus, eadem eſt proportio ſinus complemen
              <lb/>
            ti declinationis puncti propoſiti ad ſinum complementi arcus, quo datũ punctũ à vicia
              <lb/>
            niori puncto æquinoctij abeſt, quæ ſinus totius ad ſinum complemẽti aſcenſionis rectæ:
              <lb/>
            </s>
            <s xml:id="echoid-s6514" xml:space="preserve">ſumatur in eadem figura arcus _
              <emph style="sc">B</emph>
            N_, declinationis grad. </s>
            <s xml:id="echoid-s6515" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6516" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6517" xml:space="preserve">quæ in tabula declina-
              <lb/>
            tionis continet grad. </s>
            <s xml:id="echoid-s6518" xml:space="preserve">_17_. </s>
            <s xml:id="echoid-s6519" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6520" xml:space="preserve">_47_. </s>
            <s xml:id="echoid-s6521" xml:space="preserve">ducaturq́; </s>
            <s xml:id="echoid-s6522" xml:space="preserve">_NM_, ad _
              <emph style="sc">E</emph>
            A_, perpendicularis, quæ ſinus erit
              <lb/>
            complementi dictæ declinationis. </s>
            <s xml:id="echoid-s6523" xml:space="preserve">_C_apiatur quoq; </s>
            <s xml:id="echoid-s6524" xml:space="preserve">arcus _DG_, grad. </s>
            <s xml:id="echoid-s6525" xml:space="preserve">_50_. </s>
            <s xml:id="echoid-s6526" xml:space="preserve">quo datum pun
              <lb/>
            ctum ab æquinoctio verno abeſt, & </s>
            <s xml:id="echoid-s6527" xml:space="preserve">ad _
              <emph style="sc">E</emph>
            A_, perpendicularis ducatur _GS_, nempe ſinus
              <lb/>
            complementi dicti arcus _DG_. </s>
            <s xml:id="echoid-s6528" xml:space="preserve">_P_oſt hæc tribus rectis _NM_, ſinui complemẽti declinationis
              <lb/>
            dati puncti, & </s>
            <s xml:id="echoid-s6529" xml:space="preserve">_GS_, ſinui complementi arcus _DG_, quo datũ punctum ab æquinoctij pun
              <lb/>
            cto diſtat, et _
              <emph style="sc">E</emph>
            D_, ſinui toti, quarta proportionalis inueniatur _LI_, vtin lineis _GH, GI_,
              <lb/>
            ſeſein _G_, ſecantibus factũ eſt: </s>
            <s xml:id="echoid-s6530" xml:space="preserve">_S_umpta enim ibi eſt _
              <emph style="sc">G</emph>
            K_, ipſi _NM_, & </s>
            <s xml:id="echoid-s6531" xml:space="preserve">_KH,_ ipſi _GS_, & </s>
            <s xml:id="echoid-s6532" xml:space="preserve">_GL_,
              <lb/>
            ſinui toti _ED_, æqualis, &</s>
            <s xml:id="echoid-s6533" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6534" xml:space="preserve">_N_am _LI_, inuenta erit ſinus complementi aſcenſionis rectæ
              <lb/>
            dati grad. </s>
            <s xml:id="echoid-s6535" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6536" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6537" xml:space="preserve">_Q_uare ſi ipſi _LI_, ex ſemidiametro _EC_, abſcindatur æqualis recta _
              <emph style="sc">E</emph>
            T_,
              <lb/>
            ducaturq; </s>
            <s xml:id="echoid-s6538" xml:space="preserve">_TV_, ipſi _EB_, parallela, & </s>
            <s xml:id="echoid-s6539" xml:space="preserve">_VX_, ipſi _
              <emph style="sc">E</emph>
            C_, parallela, erunt æquales rectæ _
              <emph style="sc">E</emph>
            T,_
              <lb/>
              <note position="left" xlink:label="note-186-03" xlink:href="note-186-03a" xml:space="preserve">34. primi.</note>
            _VX. </s>
            <s xml:id="echoid-s6540" xml:space="preserve">C_um ergo ſinui _VX_, reſpondeat arcus _BV_, erit huius complementũ _VC_, </s>
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