Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div77" type="section" level="1" n="43">
          <p>
            <s xml:id="echoid-s2569" xml:space="preserve">
              <pb file="0047" n="47" rhead="TABVLARVM SINVVM."/>
            eclypticæ noſſe deſideras, fuerit in ſigno aliquo deſcendente, tunc addes angulum cõmu
              <lb/>
            nem ad angulum, quem facit idem illud punctum in medio cœli cum eclyptica & </s>
            <s xml:id="echoid-s2570" xml:space="preserve">me
              <lb/>
            ridiano, ſumma ea à ſemicirculo ſubtracta, remanebit tibi angulus cauſſatus ab eclypti-
              <lb/>
            ca iuxta punctum propoſitum cum horizonte. </s>
            <s xml:id="echoid-s2571" xml:space="preserve">Si aũt punctum illud eclypticæ ſit in ſemi
              <lb/>
            circulo eclypticæ aſcendente, tũc ſubtrahe angulum cõmunem ab angulo meridian, & </s>
            <s xml:id="echoid-s2572" xml:space="preserve">
              <lb/>
            remanebit angulus eclypticæ & </s>
            <s xml:id="echoid-s2573" xml:space="preserve">horizontis iuxta propoſitũ punctũ eclypticæ. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">?</s>
            <s xml:id="echoid-s2575" xml:space="preserve">? Ex-
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoopi.</emph>
              </note>
            emplum ſit hoc tibi, ex 30. </s>
            <s xml:id="echoid-s2576" xml:space="preserve">propoſitione iam inueni in ipſa hora & </s>
            <s xml:id="echoid-s2577" xml:space="preserve">minuto intronizatio
              <lb/>
            nis fuiſſe in aſcendente 5. </s>
            <s xml:id="echoid-s2578" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2579" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2580" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2581" xml:space="preserve">♌, declinatio huius eſt 18. </s>
            <s xml:id="echoid-s2582" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2583" xml:space="preserve">58. </s>
            <s xml:id="echoid-s2584" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2585" xml:space="preserve">cõplementũ
              <lb/>
            aũt 71. </s>
            <s xml:id="echoid-s2586" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2587" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2588" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2589" xml:space="preserve">ſinum huius cõplementi propono deinceps 94570. </s>
            <s xml:id="echoid-s2590" xml:space="preserve">ſimul & </s>
            <s xml:id="echoid-s2591" xml:space="preserve">ſinũ cõple-
              <lb/>
            menti maximæ declinationis 91706. </s>
            <s xml:id="echoid-s2592" xml:space="preserve">tunc puta minorem duco in ſinũ ꝑfectum, & </s>
            <s xml:id="echoid-s2593" xml:space="preserve">ꝓdu-
              <lb/>
              <note position="right" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            ctum diuido in 94570: </s>
            <s xml:id="echoid-s2594" xml:space="preserve">in quotiente uideo mihi ꝓueniſſe 96971. </s>
            <s xml:id="echoid-s2595" xml:space="preserve">arcus huius quotientis
              <lb/>
            75. </s>
            <s xml:id="echoid-s2596" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2597" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2598" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2599" xml:space="preserve">oſtendit quãtitatẽ anguli quem facit eclyptica cũ meridiano iuxta 5. </s>
            <s xml:id="echoid-s2600" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s2601" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2602" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2603" xml:space="preserve">♌. </s>
            <s xml:id="echoid-s2604" xml:space="preserve">Deinceps adhuc multiplico ſinũ eleuationis poli 48. </s>
            <s xml:id="echoid-s2605" xml:space="preserve">graduum, ſcilicet 74314. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">
              <lb/>
            (ſiquidem is eſt minor) in ſinũ totũ, & </s>
            <s xml:id="echoid-s2607" xml:space="preserve">diuido ꝓductũ cũ ſinu cõplemẽti declinatiõis pun
              <lb/>
              <note position="right" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve">
                <emph style="it">Arcalis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            cti, ꝓpoſiti 94578. </s>
            <s xml:id="echoid-s2608" xml:space="preserve">quotiens erit 79581 arcus uero 51. </s>
            <s xml:id="echoid-s2609" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2610" xml:space="preserve">48. </s>
            <s xml:id="echoid-s2611" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2612" xml:space="preserve">ꝗ uocatur angulus cõ-
              <lb/>
            munis, & </s>
            <s xml:id="echoid-s2613" xml:space="preserve">quia ♌ eſt inter principiũ ♋ & </s>
            <s xml:id="echoid-s2614" xml:space="preserve">♑, quæ ſigna ſunt deſcendentia, angulũ illum
              <lb/>
            cõmunem addo ad angulũ medij cœli 75. </s>
            <s xml:id="echoid-s2615" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2616" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2617" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2618" xml:space="preserve">& </s>
            <s xml:id="echoid-s2619" xml:space="preserve">prouenient 127. </s>
            <s xml:id="echoid-s2620" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2621" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2622" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2623" xml:space="preserve">qui-
              <lb/>
            bus à ſemicirculo ſubtractis, remanent 52. </s>
            <s xml:id="echoid-s2624" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2625" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2626" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2627" xml:space="preserve">qui angulus eſt horizontis & </s>
            <s xml:id="echoid-s2628" xml:space="preserve">ecly-
              <lb/>
            pticæ, quando 5. </s>
            <s xml:id="echoid-s2629" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2630" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">♌ partiliter, ut ſic liceat loqui, in horizõte cõſiſtunt 48. </s>
            <s xml:id="echoid-s2633" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s2634" xml:space="preserve">Accedat adhuc aliud exemplũ, ne quid prætermittamus q̊d ad intelligentiã huius rei fa-
              <lb/>
            cere uideatur, ſi forte punctũ eclypticæ in horizonte conſtitutum fuerit in ſemicirculo e-
              <lb/>
            clypticæ aſcendente, hoc eſt à principio ♑ ad finem II, ego´ cupiam habere angulum
              <lb/>
            eclypticæ & </s>
            <s xml:id="echoid-s2635" xml:space="preserve">horizontis, quem gradus Solis, ſcilicet 2. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">& </s>
            <s xml:id="echoid-s2637" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2639" xml:space="preserve">II in die intronizationis
              <lb/>
            ſub ipſum Solis ortũ effecit (& </s>
            <s xml:id="echoid-s2640" xml:space="preserve">eſto ut Sol eo die proprio ſuo motu ſteterit in eclyptica)
              <lb/>
            ibi principio per 26. </s>
            <s xml:id="echoid-s2641" xml:space="preserve">27. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">aut 28. </s>
            <s xml:id="echoid-s2643" xml:space="preserve">propoſitiones inueni angulum eclypticæ & </s>
            <s xml:id="echoid-s2644" xml:space="preserve">meridiani, ꝗ
              <lb/>
            fuit iuxta gradum Solis, illum inquam inueni 78. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">37. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2648" xml:space="preserve">Deinde ſinũ altitudinis po-
              <lb/>
            li 48. </s>
            <s xml:id="echoid-s2649" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2650" xml:space="preserve">ſcilicet 743 14. </s>
            <s xml:id="echoid-s2651" xml:space="preserve">tan̈ minorẽ duco in ſinũ totum, productũ diuido in ſinũ com-
              <lb/>
              <note position="right" xlink:label="note-0047-04" xlink:href="note-0047-04a" xml:space="preserve">
                <emph style="it">Arealis.</emph>
              </note>
            plementi declinationis Solis, ſcilicet 93544. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">& </s>
            <s xml:id="echoid-s2653" xml:space="preserve">quotiens erit 79335. </s>
            <s xml:id="echoid-s2654" xml:space="preserve">arcus eius 52. </s>
            <s xml:id="echoid-s2655" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s2656" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2657" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2658" xml:space="preserve">angulus ille communis, quem mox ſubtraho ab angulo medij cœli, & </s>
            <s xml:id="echoid-s2659" xml:space="preserve">remane-
              <lb/>
            bunt pro angulo orientis eclypticæ & </s>
            <s xml:id="echoid-s2660" xml:space="preserve">horizontis iuxta gradum Solis 26. </s>
            <s xml:id="echoid-s2661" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2662" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2663" xml:space="preserve">mi.</s>
            <s xml:id="echoid-s2664" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="44">
          <head xml:id="echoid-head48" xml:space="preserve">PRONVNCIATVM XXXII.</head>
          <p>
            <s xml:id="echoid-s2665" xml:space="preserve">Quantitatem anguli ab horizonte & </s>
            <s xml:id="echoid-s2666" xml:space="preserve">eclyptica cauſſati diuerſo modo in
              <lb/>
            quirere, habito tantum prius medij cœli gradu.</s>
            <s xml:id="echoid-s2667" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2668" xml:space="preserve">Quum primũ habueris medij cœli gradũ, ſtatim quære per aliquã propoſitionum 26.
              <lb/>
            </s>
            <s xml:id="echoid-s2669" xml:space="preserve">27. </s>
            <s xml:id="echoid-s2670" xml:space="preserve">uel 28. </s>
            <s xml:id="echoid-s2671" xml:space="preserve">angulũ quem facit eclyptica cum meridiano, deinde duc ſinũ anguli illius in ſi
              <lb/>
              <note position="right" xlink:label="note-0047-05" xlink:href="note-0047-05a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">hoc aſſe-</emph>
                <lb/>
                <emph style="it">queris.</emph>
              </note>
            num diſtantiæ zenith à gradu medij cœli, productũ diuide in totum, & </s>
            <s xml:id="echoid-s2672" xml:space="preserve">cõplementũ arcus
              <lb/>
            quotientis erit angulus eclypticæ & </s>
            <s xml:id="echoid-s2673" xml:space="preserve">horizontis, qualiſcun tandem fuerit in aſcenden-
              <lb/>
            te gradus. </s>
            <s xml:id="echoid-s2674" xml:space="preserve">?</s>
            <s xml:id="echoid-s2675" xml:space="preserve">? Id adeo tali confirmabimus exemplo. </s>
            <s xml:id="echoid-s2676" xml:space="preserve">ꝓpono ecce mihi gradũ medij cœli
              <lb/>
              <note position="right" xlink:label="note-0047-06" xlink:href="note-0047-06a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            15. </s>
            <s xml:id="echoid-s2677" xml:space="preserve">& </s>
            <s xml:id="echoid-s2678" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2679" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2680" xml:space="preserve">♈, quẽ iam ſupra pronunciato 26. </s>
            <s xml:id="echoid-s2681" xml:space="preserve">ad horã intronizationis inueni in medio
              <lb/>
            cœli, & </s>
            <s xml:id="echoid-s2682" xml:space="preserve">per tres illas propoſitiones per 26. </s>
            <s xml:id="echoid-s2683" xml:space="preserve">27. </s>
            <s xml:id="echoid-s2684" xml:space="preserve">ſiue 28. </s>
            <s xml:id="echoid-s2685" xml:space="preserve">reperi etiam angulum meridiani
              <lb/>
            & </s>
            <s xml:id="echoid-s2686" xml:space="preserve">eclypticæ ad idem illud momentum 67. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2688" xml:space="preserve">23. </s>
            <s xml:id="echoid-s2689" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2690" xml:space="preserve">ſinus ipſius eſt 92309. </s>
            <s xml:id="echoid-s2691" xml:space="preserve">eum ſi du-
              <lb/>
            cam in ſinum diſtantiæ zenith à medio cœli, quæ eſt 41. </s>
            <s xml:id="echoid-s2692" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2693" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2694" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">ſcilicet 66 174. </s>
            <s xml:id="echoid-s2696" xml:space="preserve">& </s>
            <s xml:id="echoid-s2697" xml:space="preserve">di-
              <lb/>
            uidam productum in ſinum perfectum, inueniam in quotiente 61084. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">complementum
              <lb/>
            eius arcus oſtendit quantitatem anguli quem facit eclyptica cum horizonte in parte ori
              <lb/>
            entis & </s>
            <s xml:id="echoid-s2699" xml:space="preserve">occidentis, ſunt´ gradus 25. </s>
            <s xml:id="echoid-s2700" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2701" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">in quibus quærendis laboratum eſt.</s>
            <s xml:id="echoid-s2703" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div81" type="section" level="1" n="45">
          <head xml:id="echoid-head49" xml:space="preserve">PRONVNCIATVM XXXIII.</head>
          <p>
            <s xml:id="echoid-s2704" xml:space="preserve">Angulum occidentis, quem eclyptica cum horizonte efficit in parte occi-
              <lb/>
            dua, prompte & </s>
            <s xml:id="echoid-s2705" xml:space="preserve">facile inueſtigare.</s>
            <s xml:id="echoid-s2706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2707" xml:space="preserve">Operæpreciũ nõ eſt hoc ꝓnunciatũ multis explicare, quũ ſuperiori 31. </s>
            <s xml:id="echoid-s2708" xml:space="preserve">planê ſimilis
              <lb/>
            fit, niſi q̊d hic addẽdũ eſt, ubi illic ſubtractũ, & </s>
            <s xml:id="echoid-s2709" xml:space="preserve">uiciſsim ſubtrahẽdũ, ubi additũ eſt illic, qñ
              <lb/>
              <note position="right" xlink:label="note-0047-07" xlink:href="note-0047-07a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            angulũ horizõtis et eclypticæ quærebas, ſicuti ſequens monſtrabit exemplũ. </s>
            <s xml:id="echoid-s2710" xml:space="preserve">?</s>
            <s xml:id="echoid-s2711" xml:space="preserve">? Cupio
              <lb/>
            ſcire angulũ quẽ facit eclyptica in 5. </s>
            <s xml:id="echoid-s2712" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2713" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2714" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2715" xml:space="preserve">♌, cum horizonte occiduo, ex 31. </s>
            <s xml:id="echoid-s2716" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>