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        <div xml:id="echoid-div75" type="section" level="1" n="42">
          <p>
            <s xml:id="echoid-s2455" xml:space="preserve">
              <pb file="0046" n="46" rhead="GENVINVS VSVS"/>
            eclypticæ cũ ſinu maximæ declinatiõis ☉(sun), ꝓductũ inde diuide in totũ, ſinũ, & </s>
            <s xml:id="echoid-s2456" xml:space="preserve">proueniet
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">illud ex</emph>
                <lb/>
                <emph style="it">quadrante</emph>
                <lb/>
                <emph style="it">inuenitur.</emph>
              </note>
            declinatio medij cœli ab æquatore, quod etiã didiciſtiiam ſupra quærere in pronunciato
              <lb/>
            5. </s>
            <s xml:id="echoid-s2457" xml:space="preserve">Deinde fac inuenias per pronunc. </s>
            <s xml:id="echoid-s2458" xml:space="preserve">27. </s>
            <s xml:id="echoid-s2459" xml:space="preserve">angulũ eclypticæ & </s>
            <s xml:id="echoid-s2460" xml:space="preserve">meridiani in parte orientis,
              <lb/>
            angulũ inquã illum, qui recto minor eſt, eũ inuenies, ſi ſinũ ſecundũ maximæ declinatio-
              <lb/>
            nis tibi proponas, & </s>
            <s xml:id="echoid-s2461" xml:space="preserve">ſinum cõplementi declinationis medij cœli minorẽ duxeris in ſinũ
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">
                <emph style="it">Arealiter</emph>
              </note>
            totum, productũ in maiorẽ diuiſeris, tũc ſanè arcus quotientis erit quantitas eius angu-
              <lb/>
            li. </s>
            <s xml:id="echoid-s2462" xml:space="preserve">Porrò ſi ſinũ diſtantiæ zenith à gradu medij cœli ducas in ſinũ anguli iam inuenti, ꝓ-
              <lb/>
            ductũ in ſinum totũ diuide, arcus quotientis oſtendet diſtantiã zenith à 90. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2464" xml:space="preserve">ab aſcen-
              <lb/>
            dente, qui arcus ſemper ad angulos rectos ſphærales ſup circulũ ma iorem ductũ ex polis
              <lb/>
            zodiaci per zenith capitis cadit. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">Ad hæc quære quantũ 90. </s>
            <s xml:id="echoid-s2466" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">ab aſcendẽte diſtet à me
              <lb/>
            dio cœli, & </s>
            <s xml:id="echoid-s2468" xml:space="preserve">quidẽ ꝓpone tibi ſinũ cõplementi arcus diſtantiæ zenith à 90. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">ab aſcen-
              <lb/>
            dente, & </s>
            <s xml:id="echoid-s2471" xml:space="preserve">ſinũ cõplementi diſtantiæ zenith à medio cœli, minorẽ duc in ſinũ totũ, produ
              <lb/>
              <note position="left" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve">
                <emph style="it">Arealiter</emph>
              </note>
            ctum diuide in maiorẽ, & </s>
            <s xml:id="echoid-s2472" xml:space="preserve">arcus quotiẽtis mõſtrabit arcũ eclypticæ à medio cœli uſ ad
              <lb/>
              <note position="left" xlink:label="note-0046-04" xlink:href="note-0046-04a" xml:space="preserve">
                <emph style="it">Nonageſi-</emph>
                <lb/>
                <emph style="it">mus ab a-</emph>
                <lb/>
                <emph style="it">ſcẽdẽte gra</emph>
                <lb/>
                <emph style="it">dus altißi-</emph>
                <lb/>
                <emph style="it">ma eclypti</emph>
                <lb/>
                <emph style="it">cœ pars eſt</emph>
                <lb/>
                <emph style="it">ſupra hori</emph>
                <lb/>
                <emph style="it">zontem.</emph>
              </note>
            gradũ eclypticæ, qui occidit in parte occidentis: </s>
            <s xml:id="echoid-s2473" xml:space="preserve">ſin aũt ſubtraxeris illũ arcũ à 90. </s>
            <s xml:id="echoid-s2474" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2475" xml:space="preserve">tũc
              <lb/>
            manebit arcus ille diſtantiæ 90. </s>
            <s xml:id="echoid-s2476" xml:space="preserve">gradus ab aſcendente à ſupremo cœli. </s>
            <s xml:id="echoid-s2477" xml:space="preserve">Etſi acceperis gra
              <lb/>
            dum oppoſitũ occidentis, habebis gradũ illum ꝗ oritur in oriente ſuper horizõtem. </s>
            <s xml:id="echoid-s2478" xml:space="preserve">Sin
              <lb/>
            uero punctũ medij cœli fuerit in medietate eclypticæ deſcendenti, tũc adde arcũ quotien
              <lb/>
            tis ad medium cczli, & </s>
            <s xml:id="echoid-s2479" xml:space="preserve">proueniet gradus aſcendentis, cuius contrariũ eſt gradus eclypti-
              <lb/>
            cæ occidens in parte occidentis. </s>
            <s xml:id="echoid-s2480" xml:space="preserve">Sed ſi arcũ quotientis ſubtrahas à 90. </s>
            <s xml:id="echoid-s2481" xml:space="preserve">reſiduũ etiã ſubtra
              <lb/>
            has à gradu medij cœli, tunc manet gradus 90. </s>
            <s xml:id="echoid-s2482" xml:space="preserve">ab aſcendẽte & </s>
            <s xml:id="echoid-s2483" xml:space="preserve">occidente, ꝗſemper ſupre
              <lb/>
            mus ſiue altiſsimus exiſtit eclypticæ gradus ſupra horizontẽ, nõ ille (ut imperiti putãt)
              <lb/>
              <note position="left" xlink:label="note-0046-05" xlink:href="note-0046-05a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſcopi.</emph>
              </note>
            qui tangit mediũ cœli ?</s>
            <s xml:id="echoid-s2484" xml:space="preserve">? At in ea re operæ preciũ adhuc fuerit exemplũ proponere, q̊
              <lb/>
            facilius intelligas. </s>
            <s xml:id="echoid-s2485" xml:space="preserve">Proximo pronunciato inueni iã mediũ cœli ad horã intr onizationis,
              <lb/>
            gradus ille fuit 15. </s>
            <s xml:id="echoid-s2486" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2487" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">♈, ſinũ quo diſtãtiæ illius à principio ♈, ſcilicet 28680. </s>
            <s xml:id="echoid-s2489" xml:space="preserve">du-
              <lb/>
            xi in ſinũ maximæ declinatiõis, ꝓductũ diuiſi in ſinũ totũ, & </s>
            <s xml:id="echoid-s2490" xml:space="preserve">in q̊tiẽte ecce iam inuenio
              <lb/>
            11435, arcus eius 6, gra, 34. </s>
            <s xml:id="echoid-s2491" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2492" xml:space="preserve">declinatio eſt medij cœli, deinde quæro angulũ eclypticæ
              <lb/>
            & </s>
            <s xml:id="echoid-s2493" xml:space="preserve">meridiani, multiplicando ſinũ cõplementi maximæ declinatiõis ☉(sun) 91706. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">cũ toto ſi-
              <lb/>
            nu, & </s>
            <s xml:id="echoid-s2495" xml:space="preserve">diuidendo ꝓductũ in ſinũ cõplementi declinationis medij cœli 99343. </s>
            <s xml:id="echoid-s2496" xml:space="preserve">in quotiente
              <lb/>
            iã inuenio 92312. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">arcus eius 67. </s>
            <s xml:id="echoid-s2498" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2499" xml:space="preserve">23. </s>
            <s xml:id="echoid-s2500" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2501" xml:space="preserve">angulus ille eſt cauſatus ab eclyptica & </s>
            <s xml:id="echoid-s2502" xml:space="preserve">meri
              <lb/>
            diano orientalis Borealis. </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Adhuc aũt multiplico quotientẽ iſtũ rurſus cũ ſinu diſtantiæ
              <lb/>
            zenith à puncto medij cœli, ſcilicet 66 174. </s>
            <s xml:id="echoid-s2504" xml:space="preserve">& </s>
            <s xml:id="echoid-s2505" xml:space="preserve">diuido productũ in ſinũ perfectum, in quo-
              <lb/>
            tiente inuenio 6 1084. </s>
            <s xml:id="echoid-s2506" xml:space="preserve">arcus quotientis illius eſt 37. </s>
            <s xml:id="echoid-s2507" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2508" xml:space="preserve">39. </s>
            <s xml:id="echoid-s2509" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">quæ & </s>
            <s xml:id="echoid-s2511" xml:space="preserve">diſtãtia eſt zenith
              <lb/>
            à 90. </s>
            <s xml:id="echoid-s2512" xml:space="preserve">gradu, qui cõputatur ab aſcendente. </s>
            <s xml:id="echoid-s2513" xml:space="preserve">Si deinceps ſinũ cõplementi illius 79 175. </s>
            <s xml:id="echoid-s2514" xml:space="preserve">adſer
              <lb/>
            uem in locũ diuiſoris, & </s>
            <s xml:id="echoid-s2515" xml:space="preserve">ſinũ altitudinis medij cœli, ꝓ & </s>
            <s xml:id="echoid-s2516" xml:space="preserve">ſinus eſt cõplementi diſtantiæ ze
              <lb/>
            nith à medio cœlo, ducã in ſinũ totũ, & </s>
            <s xml:id="echoid-s2517" xml:space="preserve">productũ diuidã in ipſum diuiſorem, inueniam u-
              <lb/>
            ti in quotiente 94691. </s>
            <s xml:id="echoid-s2518" xml:space="preserve">arcus eius eſt 71. </s>
            <s xml:id="echoid-s2519" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2520" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2521" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2522" xml:space="preserve">Iam ſi tantũ quo accipias contra
              <lb/>
            ſignorũ ordinem à puncto medij cœli, finietur arcus in 5. </s>
            <s xml:id="echoid-s2523" xml:space="preserve">gradu. </s>
            <s xml:id="echoid-s2524" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2525" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2526" xml:space="preserve">♒, qui gradus eſt
              <lb/>
            occidens in parte occidentis ipſo tempore iutronizationis, 5. </s>
            <s xml:id="echoid-s2527" xml:space="preserve">etiam gra. </s>
            <s xml:id="echoid-s2528" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2529" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2530" xml:space="preserve">♌, eſt a-
              <lb/>
            ſcendens quem quærebam. </s>
            <s xml:id="echoid-s2531" xml:space="preserve">Si autem ſubtrahas 71. </s>
            <s xml:id="echoid-s2532" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2533" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2534" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2535" xml:space="preserve">à 90. </s>
            <s xml:id="echoid-s2536" xml:space="preserve">remanebunt tibi 18.
              <lb/>
            </s>
            <s xml:id="echoid-s2537" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2538" xml:space="preserve">45. </s>
            <s xml:id="echoid-s2539" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2540" xml:space="preserve">& </s>
            <s xml:id="echoid-s2541" xml:space="preserve">tantum quidem diſtat gradus ille 90. </s>
            <s xml:id="echoid-s2542" xml:space="preserve">ab aſcendente à medio cœli uerſus or-
              <lb/>
            tum, ſi autem addas medium cœli, puta 16. </s>
            <s xml:id="echoid-s2543" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2544" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2545" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2546" xml:space="preserve">ad 18. </s>
            <s xml:id="echoid-s2547" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2548" xml:space="preserve">45. </s>
            <s xml:id="echoid-s2549" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2550" xml:space="preserve">tunc attingit
              <lb/>
            planè 5. </s>
            <s xml:id="echoid-s2551" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2552" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2553" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2554" xml:space="preserve">♉, qui & </s>
            <s xml:id="echoid-s2555" xml:space="preserve">gradus eſt nonageſimus ab aſcendente.</s>
            <s xml:id="echoid-s2556" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div77" type="section" level="1" n="43">
          <head xml:id="echoid-head47" xml:space="preserve">PRONVNCIATVM XXXI.</head>
          <p>
            <s xml:id="echoid-s2557" xml:space="preserve">Angulum ab horizonte obliquo cum eclyptica cauſſatum, per expeditam
              <lb/>
            ſupputationem cognoſcere.</s>
            <s xml:id="echoid-s2558" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2559" xml:space="preserve">Inuento iam gradu aſcendente ex 30. </s>
            <s xml:id="echoid-s2560" xml:space="preserve">ꝓnunc. </s>
            <s xml:id="echoid-s2561" xml:space="preserve">quære deinceps per aliquã ex tribus illis
              <lb/>
            pronunc. </s>
            <s xml:id="echoid-s2562" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2563" xml:space="preserve">27. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">aut 28. </s>
            <s xml:id="echoid-s2565" xml:space="preserve">angulũ quẽ effecit eclyptica præciſe in gradu aſcendentis cũ me
              <lb/>
            ridiano uerſus orientẽ. </s>
            <s xml:id="echoid-s2566" xml:space="preserve">Porrô aũt ubi ſcire cupis etiam illũ angulũ, quem facit eclyptica
              <lb/>
            in ipſo puncto aſcendentis cum horizonte, tunc tibi propone ſinum cõplementi declina
              <lb/>
              <note position="left" xlink:label="note-0046-06" xlink:href="note-0046-06a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            tionis illius gradus eclypticæ, ſimiliter & </s>
            <s xml:id="echoid-s2567" xml:space="preserve">ſinũ eleuationis poli, minorẽ ex ijs duc in ſinũ
              <lb/>
            totũ, productũ diuide in ſinũ maiorẽ, & </s>
            <s xml:id="echoid-s2568" xml:space="preserve">arcũ quotientis dico angulũ cõmunem, id'´ eo
              <lb/>
            maxime, qñ ſi punctũ illud eclypticæ aſcendens, uel penes quod angulum horizontis &</s>
            <s xml:id="echoid-s2569" xml:space="preserve"/>
          </p>
        </div>
      </text>
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