Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div69" type="section" level="1" n="39">
          <p>
            <s xml:id="echoid-s2329" xml:space="preserve">
              <pb file="0045" n="45" rhead="TABVLARVM SINVVM."/>
            26. </s>
            <s xml:id="echoid-s2330" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2331" xml:space="preserve">II, diſtantia ab ♈, quæ interſectio proxima eſt, fuit 62. </s>
            <s xml:id="echoid-s2332" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2333" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2334" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2335" xml:space="preserve">ſinus illius
              <lb/>
            88647. </s>
            <s xml:id="echoid-s2336" xml:space="preserve">hunc ſepone in locum aliquem peculiarem, deinde propone tibi ſinum aſcenſio-
              <lb/>
            nis eius rectæ, quam ex pronunciato 7. </s>
            <s xml:id="echoid-s2337" xml:space="preserve">inueniſti 60. </s>
            <s xml:id="echoid-s2338" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">51. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">86906. </s>
            <s xml:id="echoid-s2342" xml:space="preserve">ſinum illum pu-
              <lb/>
            ta minorem duc in illum totum, productum diuide in maiorem, & </s>
            <s xml:id="echoid-s2343" xml:space="preserve">prouenient in quotien
              <lb/>
            te 98036. </s>
            <s xml:id="echoid-s2344" xml:space="preserve">arcus illius erit 78. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2346" xml:space="preserve">37. </s>
            <s xml:id="echoid-s2347" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2348" xml:space="preserve">quæ etiam quantitas eſt anguli primi, ſcilicet ſe
              <lb/>
            ptentrionalis orientalis, complementum eius de ſemicirculo eſt 101. </s>
            <s xml:id="echoid-s2349" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2350" xml:space="preserve">23. </s>
            <s xml:id="echoid-s2351" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2352" xml:space="preserve">& </s>
            <s xml:id="echoid-s2353" xml:space="preserve">is an-
              <lb/>
            gulus eſt orientalis meridionalis, at in hunc modum uides iam te faciliori uia inueniſſe
              <lb/>
            idem, quod ſuperior propoſitio longa & </s>
            <s xml:id="echoid-s2354" xml:space="preserve">operoſa operatione docuit.</s>
            <s xml:id="echoid-s2355" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div71" type="section" level="1" n="40">
          <head xml:id="echoid-head44" xml:space="preserve">PRONVNCIATVM XXVIII.</head>
          <p>
            <s xml:id="echoid-s2356" xml:space="preserve">Angulos illos eclypticæ & </s>
            <s xml:id="echoid-s2357" xml:space="preserve">meridiani, adhuc tertia quadam ratione, à prio
              <lb/>
            ribus diuerſa, inue ſtigare.</s>
            <s xml:id="echoid-s2358" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2359" xml:space="preserve">Propone hic principio tibi ſinũ cõplementi maximæ declinatiõis ☉(sun), & </s>
            <s xml:id="echoid-s2360" xml:space="preserve">ſinum cõple
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">
                <emph style="it">Per arealẽ</emph>
                <lb/>
                <emph style="it">ingreſſum</emph>
                <lb/>
                <emph style="it">idem aſſe-</emph>
                <lb/>
                <emph style="it">queris.</emph>
              </note>
            menti declinatiõis pũcti propoſiti, minorẽ ex ijs duc in ſinũ ꝑfectũ, ꝓductũ diuide in ma
              <lb/>
            iorem, & </s>
            <s xml:id="echoid-s2361" xml:space="preserve">arcus quotientis oſtendet tibi angulũ quæſitũ iuxta ea quæ docuimus pronun-
              <lb/>
            ciato 26. </s>
            <s xml:id="echoid-s2362" xml:space="preserve">de 4. </s>
            <s xml:id="echoid-s2363" xml:space="preserve">quartis. </s>
            <s xml:id="echoid-s2364" xml:space="preserve">Vbi adhuc tñ admonendus es mihi, ꝙ primũ punctũ ♋, & </s>
            <s xml:id="echoid-s2365" xml:space="preserve">ſimili-
              <lb/>
            ter primũ punctũ ♑ nõ alios niſi rectos faciunt angulos, principiũ autẽ ?</s>
            <s xml:id="echoid-s2366" xml:space="preserve">? in angulo Bo
              <lb/>
            reali orientali, angulũ habet æqualẽ cõplemento maximæ declinationis. </s>
            <s xml:id="echoid-s2367" xml:space="preserve">Conſimilẽ q̊
              <lb/>
              <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſcopi.</emph>
              </note>
            quantitatẽ ſeruat principiũ ♎ in angulo Auſtrali orientali. </s>
            <s xml:id="echoid-s2368" xml:space="preserve">?</s>
            <s xml:id="echoid-s2369" xml:space="preserve">? Sed hic forſitan exem
              <lb/>
            plum adhuc deſideras? </s>
            <s xml:id="echoid-s2370" xml:space="preserve">en habe. </s>
            <s xml:id="echoid-s2371" xml:space="preserve">Scire cupio quantus quiſ ſit angulus, quẽ eclyptica iu-
              <lb/>
            xta gradũ ☉(sun), in q̊ ſaltẽ ipſe fuit in die intronizationis, facit cũ meridiano. </s>
            <s xml:id="echoid-s2372" xml:space="preserve">Gradus ita
              <lb/>
            Solis fuit 2. </s>
            <s xml:id="echoid-s2373" xml:space="preserve">II. </s>
            <s xml:id="echoid-s2374" xml:space="preserve">26 mi. </s>
            <s xml:id="echoid-s2375" xml:space="preserve">declinationẽ ipſius inueni ꝑ 5. </s>
            <s xml:id="echoid-s2376" xml:space="preserve">ꝓnunc. </s>
            <s xml:id="echoid-s2377" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2378" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2379" xml:space="preserve">42. </s>
            <s xml:id="echoid-s2380" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2381" xml:space="preserve">cõplemẽtum
              <lb/>
            eius eſt 69. </s>
            <s xml:id="echoid-s2382" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2383" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2384" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">Propono deinde mihi etiã cõplemẽtũ maxiæ declinatiõis ☉(sun), ſinus
              <lb/>
            prioris cõplementi eſt 93544. </s>
            <s xml:id="echoid-s2386" xml:space="preserve">alterius aũt 91706. </s>
            <s xml:id="echoid-s2387" xml:space="preserve">iã minorem duco in totũ, & </s>
            <s xml:id="echoid-s2388" xml:space="preserve">productũ
              <lb/>
            diuido in maiorem, at in q̊tiente ꝓueniũt 98035. </s>
            <s xml:id="echoid-s2389" xml:space="preserve">arcus eius eſt 78. </s>
            <s xml:id="echoid-s2390" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2391" xml:space="preserve">37. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2393" xml:space="preserve">Borealis
              <lb/>
            & </s>
            <s xml:id="echoid-s2394" xml:space="preserve">orientalis. </s>
            <s xml:id="echoid-s2395" xml:space="preserve">Ecce quomodo hac triplici ratione inueniangulũ iſtum æqualis ſemper
              <lb/>
            quantitatis, reliquos angulos tres ipſe facile colligere poteris, ſed aliud adhuc exemplũ
              <lb/>
            dabimus hic tibi ad mediũ cœli, q̊d & </s>
            <s xml:id="echoid-s2396" xml:space="preserve">cõtingit ſub ipſam horã intronizationis, nam ne
              <lb/>
            ceſſe fuerit etiã deinceps hoc exemplũ cognoſcere. </s>
            <s xml:id="echoid-s2397" xml:space="preserve">Ex 25. </s>
            <s xml:id="echoid-s2398" xml:space="preserve">pronunciato inueni in medio
              <lb/>
            cœli ſtetiſſe 16. </s>
            <s xml:id="echoid-s2399" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2401" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2402" xml:space="preserve">♈, duco igitur ſinũ cõplementi maximæ declinationis 91706
              <lb/>
            in ſinum perfectum, & </s>
            <s xml:id="echoid-s2403" xml:space="preserve">diuido in ſinum rectum ſecundum declinationis gradus medij cœ
              <lb/>
            li, ſcilicet 99343. </s>
            <s xml:id="echoid-s2404" xml:space="preserve">at in ipſo quotiente inueni 92312. </s>
            <s xml:id="echoid-s2405" xml:space="preserve">arcus eius eſt 67. </s>
            <s xml:id="echoid-s2406" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2407" xml:space="preserve">23. </s>
            <s xml:id="echoid-s2408" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2409" xml:space="preserve">qui & </s>
            <s xml:id="echoid-s2410" xml:space="preserve">
              <lb/>
            angulus eſt eclypticæ & </s>
            <s xml:id="echoid-s2411" xml:space="preserve">meridiani in parte Boreali orientali.</s>
            <s xml:id="echoid-s2412" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div73" type="section" level="1" n="41">
          <head xml:id="echoid-head45" xml:space="preserve">PRONVNCIATVM XXIX.</head>
          <p>
            <s xml:id="echoid-s2413" xml:space="preserve">Diſtantiam zenich à 90. </s>
            <s xml:id="echoid-s2414" xml:space="preserve">gradu ab aſcendẽte, & </s>
            <s xml:id="echoid-s2415" xml:space="preserve">breuiſsime & </s>
            <s xml:id="echoid-s2416" xml:space="preserve">exactiſsime
              <lb/>
            reperire.</s>
            <s xml:id="echoid-s2417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2418" xml:space="preserve">Quandoquidem diſtantia hæc deinceps quo ad multa cõducet, ideo & </s>
            <s xml:id="echoid-s2419" xml:space="preserve">eam hic pau
              <lb/>
              <note position="right" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus.</emph>
              </note>
            eis docebimus inuenire, ubi iã angulũ meridiani & </s>
            <s xml:id="echoid-s2420" xml:space="preserve">eclypticæ ex aliqua triũ illarũ propoſi
              <lb/>
            tionũ, ex 25. </s>
            <s xml:id="echoid-s2421" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2422" xml:space="preserve">aut 27. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">cognitã habes (angulũ inquã minorem uerſus ortũ) & </s>
            <s xml:id="echoid-s2424" xml:space="preserve">eius angu
              <lb/>
            li ſinũ ducis in ſinũ cõplementi altitudinis meridianæ, productũ uero diuidis in totũ, ar-
              <lb/>
              <note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            cus uti q̊tientis iſtius erit diſtãtia zenith à 90. </s>
            <s xml:id="echoid-s2425" xml:space="preserve">gradu ab aſcendẽte. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">?</s>
            <s xml:id="echoid-s2427" xml:space="preserve">? Id ut magis in-
              <lb/>
            telligas, exemplũ cape huiuſmodi. </s>
            <s xml:id="echoid-s2428" xml:space="preserve">Eſto utinuenerim mediũ cœli ad ipſam horã introni-
              <lb/>
            zationis ex ꝓnunciato 28. </s>
            <s xml:id="echoid-s2429" xml:space="preserve">16. </s>
            <s xml:id="echoid-s2430" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2431" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2433" xml:space="preserve">♈, ſimiliter & </s>
            <s xml:id="echoid-s2434" xml:space="preserve">angulũ meridiani at eclypti-
              <lb/>
            cæ per ꝓnunciatũ 26. </s>
            <s xml:id="echoid-s2435" xml:space="preserve">uel 27. </s>
            <s xml:id="echoid-s2436" xml:space="preserve">uel 28. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">repererim 67 gra. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">23. </s>
            <s xml:id="echoid-s2439" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2440" xml:space="preserve">ſinũ eius 92309. </s>
            <s xml:id="echoid-s2441" xml:space="preserve">duxi dein-
              <lb/>
            de in ſinum cõplementi altitudinis meridianæ, ſcilicet 66174. </s>
            <s xml:id="echoid-s2442" xml:space="preserve">productum diuiſi in ſinum
              <lb/>
            perfectũ, quotiens uti erit 61084. </s>
            <s xml:id="echoid-s2443" xml:space="preserve">arcus eius 37. </s>
            <s xml:id="echoid-s2444" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2445" xml:space="preserve">39. </s>
            <s xml:id="echoid-s2446" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2447" xml:space="preserve">diſtãtia nimi℞ illa quæſita.</s>
            <s xml:id="echoid-s2448" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div75" type="section" level="1" n="42">
          <head xml:id="echoid-head46" xml:space="preserve">PRONVNCIATVM XXX.</head>
          <p>
            <s xml:id="echoid-s2449" xml:space="preserve">Aſcendentem, hoc eſt gradum eclypticæ, qui partiliter in horizonte con-
              <lb/>
            ſtituitur, quacun & </s>
            <s xml:id="echoid-s2450" xml:space="preserve">regione & </s>
            <s xml:id="echoid-s2451" xml:space="preserve">hora expedite cognoſcere.</s>
            <s xml:id="echoid-s2452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2453" xml:space="preserve">Principio quære diſtantiã nonageſimiab abſcendente gradus à medio cœli in hũc mo
              <lb/>
            dum: </s>
            <s xml:id="echoid-s2454" xml:space="preserve">Multiplica ſinum diſtãtiæ gradus medij cœli à proxima interſectione æquatoris &</s>
            <s xml:id="echoid-s2455" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>