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        <div xml:id="echoid-div81" type="section" level="1" n="45">
          <p>
            <s xml:id="echoid-s2716" xml:space="preserve">
              <pb file="0048" n="48" rhead="GENVINVS VSVS"/>
            pronunciato iam inueni angulum, quem iuxta prædictũ gradum eclyptica cũ meridia-
              <lb/>
            no efficit, is autem eſt 75. </s>
            <s xml:id="echoid-s2717" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2718" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2719" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2720" xml:space="preserve">Angulũ deinceps cõmunem ſic quæro, ſinũ eleuatio
              <lb/>
            nis poli 48. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">ſcilicet 743 14. </s>
            <s xml:id="echoid-s2723" xml:space="preserve">quia minor eſt, duco in totũ, ꝓductũ diuido in ſinũ cõple
              <lb/>
              <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
                <lb/>
                <emph style="it">ſimile de-</emph>
                <lb/>
                <emph style="it">prchendet.</emph>
              </note>
            menti declinationis 5. </s>
            <s xml:id="echoid-s2724" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2725" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2726" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2727" xml:space="preserve">♌ qui eſt 94570. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">in quotiente inueni 78581. </s>
            <s xml:id="echoid-s2729" xml:space="preserve">arcus eius
              <lb/>
            eſt 31. </s>
            <s xml:id="echoid-s2730" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2731" xml:space="preserve">48. </s>
            <s xml:id="echoid-s2732" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2733" xml:space="preserve">angulus ille communis, per quem inuenire poſſum angulũ orientalem
              <lb/>
            & </s>
            <s xml:id="echoid-s2734" xml:space="preserve">occidentalem. </s>
            <s xml:id="echoid-s2735" xml:space="preserve">At quũ ♌ ſit ex ſignis deſcendentibus, angulũ hunc cõmunem ſub-
              <lb/>
            traho ab angulo meridiani & </s>
            <s xml:id="echoid-s2736" xml:space="preserve">eclypticæ. </s>
            <s xml:id="echoid-s2737" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2738" xml:space="preserve">75. </s>
            <s xml:id="echoid-s2739" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2740" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2741" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2742" xml:space="preserve">& </s>
            <s xml:id="echoid-s2743" xml:space="preserve">remanent 24. </s>
            <s xml:id="echoid-s2744" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2745" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2746" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2747" xml:space="preserve">an-
              <lb/>
            gulus ſcilicet eclypticæ & </s>
            <s xml:id="echoid-s2748" xml:space="preserve">horizontis occidẽtalis. </s>
            <s xml:id="echoid-s2749" xml:space="preserve">?</s>
            <s xml:id="echoid-s2750" xml:space="preserve">? Vis adhuc aliud exemplũ, id´ de
              <lb/>
              <note position="left" xlink:label="note-0048-02" xlink:href="note-0048-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            ſumptum ex medietate ſignorũ aſcendentiũ? </s>
            <s xml:id="echoid-s2751" xml:space="preserve">Ecce ꝓpono mibi 2. </s>
            <s xml:id="echoid-s2752" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2753" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2754" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2755" xml:space="preserve">II, ubi ☉(sun)
              <lb/>
            fuit ipſo die intronizationis, iam autem inquirere cupio quantitatẽ anguli, quẽ facit ecly
              <lb/>
            ptica iuxta gradum illum cũ horizonte occidentali, per 26. </s>
            <s xml:id="echoid-s2756" xml:space="preserve">pronunc. </s>
            <s xml:id="echoid-s2757" xml:space="preserve">inueni angulũ eius
              <lb/>
            cum meridiano, qui erat 78. </s>
            <s xml:id="echoid-s2758" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2759" xml:space="preserve">37. </s>
            <s xml:id="echoid-s2760" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2761" xml:space="preserve">Nunc ergo ta ntũ quæro angulũ cõmunẽ, & </s>
            <s xml:id="echoid-s2762" xml:space="preserve">hic
              <lb/>
            quidẽ adſumo ſinum altitudinis poli 48. </s>
            <s xml:id="echoid-s2763" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2764" xml:space="preserve">ſcilicet 74114. </s>
            <s xml:id="echoid-s2765" xml:space="preserve">& </s>
            <s xml:id="echoid-s2766" xml:space="preserve">ſinũ complementi declina
              <lb/>
            tionis gradus Solis, ſcilicet 93544. </s>
            <s xml:id="echoid-s2767" xml:space="preserve">ſinum altitudinis poli duco in ſinũ totũ, & </s>
            <s xml:id="echoid-s2768" xml:space="preserve">ꝓductum
              <lb/>
            diuido in ſinũ alterũ, tunc quotiens producet 79442. </s>
            <s xml:id="echoid-s2769" xml:space="preserve">arcus eius eſt 52. </s>
            <s xml:id="echoid-s2770" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2771" xml:space="preserve">36. </s>
            <s xml:id="echoid-s2772" xml:space="preserve">min. </s>
            <s xml:id="echoid-s2773" xml:space="preserve">& </s>
            <s xml:id="echoid-s2774" xml:space="preserve">is ſa
              <lb/>
              <note position="left" xlink:label="note-0048-03" xlink:href="note-0048-03a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            nè angulus eſt communis, quem ſi addam ad angulum meridiani & </s>
            <s xml:id="echoid-s2775" xml:space="preserve">eclypticæ, inueniã
              <lb/>
            tunc 131. </s>
            <s xml:id="echoid-s2776" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2777" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2778" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2779" xml:space="preserve">qui angulus eſt ſeptentrionalis eclypticæ & </s>
            <s xml:id="echoid-s2780" xml:space="preserve">horizontis occidui, gra
              <lb/>
            dibus illis à ſemicirculo ſubtractis, remanent 48. </s>
            <s xml:id="echoid-s2781" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2782" xml:space="preserve">47. </s>
            <s xml:id="echoid-s2783" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">angulus nimirũ eclypticæ
              <lb/>
            & </s>
            <s xml:id="echoid-s2785" xml:space="preserve">horizontis occidui meridionalis, quem adeo anxie pequiſiuimus.</s>
            <s xml:id="echoid-s2786" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div83" type="section" level="1" n="46">
          <head xml:id="echoid-head50" xml:space="preserve">PRONVNCIATVM XXXIIII.</head>
          <p>
            <s xml:id="echoid-s2787" xml:space="preserve">Altitudinem Solis ſuper horizontem quotidie & </s>
            <s xml:id="echoid-s2788" xml:space="preserve">in ſingulas horas toto
              <lb/>
            terrarum orbe ex ſolerti quadam ſupputatione colligere.</s>
            <s xml:id="echoid-s2789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2790" xml:space="preserve">Hic principio præſcire operæpreciũ eſt ipſam Solis declinationẽ, eã ſubtrahe â 90. </s>
            <s xml:id="echoid-s2791" xml:space="preserve">re-
              <lb/>
            ſidui quære ſinũ rectũ, deinde etiã ſinũ rectũ differentiæ aſcenſionalis ex pronunciato 15.
              <lb/>
            </s>
            <s xml:id="echoid-s2792" xml:space="preserve">habito ſinu differentiæ, colloca eum in regulã philoſophorũ, ſiue, ut alij loquũtur, de Trl,
              <lb/>
            in hunc modum, ultimo loco, primo aũt ſinũ totũ, & </s>
            <s xml:id="echoid-s2793" xml:space="preserve">in medio ſinũ cõplementi declinatio
              <lb/>
            nis, ſi ergo ſecundũ operationẽ regulæ quotientẽ addas ad ſinũ cõplementi declinatiõis,
              <lb/>
            habebis tunc ſinũ huius operationis. </s>
            <s xml:id="echoid-s2794" xml:space="preserve">Mox ꝓpone etiã horã uel ante uel pomeridianã ad
              <lb/>
            quamcũ cupis ſcire Solis altitudinẽ, horã illã aut horas (ſi modo plures fuerint) redige
              <lb/>
            in gradus, quo℞ ſemꝑ 15. </s>
            <s xml:id="echoid-s2795" xml:space="preserve">ꝓ hora cõnumeres, gradus eos horarũ ſubduc à 90. </s>
            <s xml:id="echoid-s2796" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2797" xml:space="preserve">& </s>
            <s xml:id="echoid-s2798" xml:space="preserve">reſi-
              <lb/>
            dui ſinũ quære rectũ, ipſum´ ſubtrahe à ſinu toto, reſiduũ uocabit̃ ſinus uerſus horarũ,
              <lb/>
            eũ ſinũ uerſum cõpone in regulã ꝓportionũ tertio loco, primo aũt ſinũ totũ, & </s>
            <s xml:id="echoid-s2799" xml:space="preserve">in medio
              <lb/>
            ſinũ cõplemẽti declinationis Solis, operatiõe illa ad præſcriptũ regulæ perfecta, ſubtra-
              <lb/>
            he q̊tientẽ à ſinu huius operatiõis toto, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">reſiduũ rurſus cõpone in poſtremũ regulæ, pri-
              <lb/>
            mo aũt ſinũ totũ, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">in medio ſinũ cõplementi altitudinis poli, quicquid ex hac operatio
              <lb/>
            ne prouenerit, ſinus eſt altitudinis Solis ad horã ꝓpoſitã. </s>
            <s xml:id="echoid-s2802" xml:space="preserve">Vnum hoc admonendus es mi
              <lb/>
            hi, ꝙ operatio talis, ſicut à nobis deſcripta hactenus eſt, ueritatem quidẽ obtinet, ſed Sole
              <lb/>
            exiſtente in ſignis ſeptẽtrionalibus, qui ſi forſitan in meridionalibus fuerit, tũc ſubtrahen
              <lb/>
            dus à ſinu cõplementi declinatiõis, eſt ſinus differentiæ aſcenſionalis, cõuerſus iam per re
              <lb/>
            gulã ꝓportionũ, & </s>
            <s xml:id="echoid-s2803" xml:space="preserve">ſic reliquus tibi manebit ſinus ꝑfectus huius oꝑationis. </s>
            <s xml:id="echoid-s2804" xml:space="preserve">?</s>
            <s xml:id="echoid-s2805" xml:space="preserve">? Quam ut
              <lb/>
              <note position="left" xlink:label="note-0048-04" xlink:href="note-0048-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            intelligas cõmodius, en exemplũ tibi ꝓponimus huiuſmodi. </s>
            <s xml:id="echoid-s2806" xml:space="preserve">Cupio forte ſcire altitudinẽ
              <lb/>
            ☉(sun) ad ipſam horã intronizationis, q̊ fuit Sol, ſicuti ſæpe diximus, in 2. </s>
            <s xml:id="echoid-s2807" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2808" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2810" xml:space="preserve">II, decli
              <lb/>
            nationẽ eius inueni ꝓnunciato 5. </s>
            <s xml:id="echoid-s2811" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2812" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2813" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2815" xml:space="preserve">quibus ſubtractis à 90. </s>
            <s xml:id="echoid-s2816" xml:space="preserve">remanẽt 69. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s2818" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2819" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">ſinus illius 93544. </s>
            <s xml:id="echoid-s2821" xml:space="preserve">eſt, qui numerus in hac ſupputatione, ꝗa frequẽtiſsime uſurpa
              <lb/>
            tur, ideo etiã creditur eſſe oĩm ꝑfectiſsimus. </s>
            <s xml:id="echoid-s2822" xml:space="preserve">Deinde per 15. </s>
            <s xml:id="echoid-s2823" xml:space="preserve">ꝓnunciatũ adinueni differen
              <lb/>
            tiã aſcenſionalẽ 24. </s>
            <s xml:id="echoid-s2824" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2825" xml:space="preserve">49. </s>
            <s xml:id="echoid-s2826" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">ſinũ quo eius 41971. </s>
            <s xml:id="echoid-s2828" xml:space="preserve">cõuerto, ita, ut uter fiat æqualis
              <lb/>
            ſinui cõplementi declinationis, quia locũ gerũt totius cuiuſdã ſinus. </s>
            <s xml:id="echoid-s2829" xml:space="preserve">Pono ergo 100000. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">
              <lb/>
            in primũ locum, deinde ſinum cõplementi declinationis Solis, ſcilicet 93544. </s>
            <s xml:id="echoid-s2831" xml:space="preserve">poſtremò
              <lb/>
            ſinum huius differentiæ 41971. </s>
            <s xml:id="echoid-s2832" xml:space="preserve">hinc operor multiplicando & </s>
            <s xml:id="echoid-s2833" xml:space="preserve">diuidendo iuxta regulam
              <lb/>
            ꝓportionũ, & </s>
            <s xml:id="echoid-s2834" xml:space="preserve">inuenio in q̊tiente 39261. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">ea addo(quando quidẽ ſignũ ☉(sun) eſt in medieta-
              <lb/>
            te ſeptẽtrionali) ad ſinũ cõplemẽti declinatiõis Solis, & </s>
            <s xml:id="echoid-s2836" xml:space="preserve">ꝓueniet talis ſumma 132805. </s>
            <s xml:id="echoid-s2837" xml:space="preserve">ſi-
              <lb/>
            nus. </s>
            <s xml:id="echoid-s2838" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2839" xml:space="preserve">perfectus huius operationis. </s>
            <s xml:id="echoid-s2840" xml:space="preserve">Adhuc deinceps ex 3. </s>
            <s xml:id="echoid-s2841" xml:space="preserve">horis feci gradus 45. </s>
            <s xml:id="echoid-s2842" xml:space="preserve">eas </s>
          </p>
        </div>
      </text>
    </echo>
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