Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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        <div xml:id="echoid-div230" type="section" level="1" n="149">
          <p>
            <s xml:id="echoid-s11232" xml:space="preserve">
              <pb o="111" file="0131" n="135" rhead="Liber Decimus."/>
            cæ, qui numquam occidit, quot enim gr. </s>
            <s xml:id="echoid-s11233" xml:space="preserve">ille arcus continebit, tot ferè dies naturales continebit dies ille con-
              <lb/>
            tinuus. </s>
            <s xml:id="echoid-s11234" xml:space="preserve">idem intellige proportionaliter de nocte continua. </s>
            <s xml:id="echoid-s11235" xml:space="preserve">Sicigitur quantitates omnium dierum poſſunt
              <lb/>
            inueniri. </s>
            <s xml:id="echoid-s11236" xml:space="preserve">& </s>
            <s xml:id="echoid-s11237" xml:space="preserve">quoniam dies omnes ſemicirculo Zodiaci deſcendentis, ideſt, à Cancro ad Capricornum, ſunt
              <lb/>
            æquales ſingulis diebus alterius ſemicirculi aſcendentis a Capricorno ad Cancrum; </s>
            <s xml:id="echoid-s11238" xml:space="preserve">ideo ſatis eſt vnius tan-
              <lb/>
            tum ſemicirculi quantitates explorare. </s>
            <s xml:id="echoid-s11239" xml:space="preserve">vnde & </s>
            <s xml:id="echoid-s11240" xml:space="preserve">Tabulæ quantitatis dierum conſtrui poſſunt. </s>
            <s xml:id="echoid-s11241" xml:space="preserve">Verum infra ali-
              <lb/>
            ter hanc quantitatum ſimul cum quantitate crepuſculi explorabimus.</s>
            <s xml:id="echoid-s11242" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div231" type="section" level="1" n="150">
          <head xml:id="echoid-head162" style="it" xml:space="preserve">De crepuſculorum quantitate. Cap. XVI.</head>
          <p>
            <s xml:id="echoid-s11243" xml:space="preserve">SVpra in tractatu de aere dictum eſt, quid ſit crepuſculum, & </s>
            <s xml:id="echoid-s11244" xml:space="preserve">quomodo fiat. </s>
            <s xml:id="echoid-s11245" xml:space="preserve">quod vero ad eius quãtitatem,
              <lb/>
            ſciendum eſt eam eſſe variam, non ſolum in eodem loco, ſed etiam in diuerſis poli eleuationibus. </s>
            <s xml:id="echoid-s11246" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s11247" xml:space="preserve">va-
              <lb/>
            riatur ſecundum dierum varietatem, ſed peculiari modo, in æſtate enim quando dies ſunt longiſſimi, longiſ-
              <lb/>
            ſima pariter ſunt crepu
              <unsure/>
            ſcula; </s>
            <s xml:id="echoid-s11248" xml:space="preserve">at vero in ſumma hyeme cum breuiſſimi dies ſunt, non itidem breuiſſima ſunt
              <lb/>
            crepuſcula, quam
              <unsure/>
            uis breuiora fiant, quam in æſtate. </s>
            <s xml:id="echoid-s11249" xml:space="preserve">breuiſſima tandem (quod mirum videtur) circum dimi-
              <lb/>
            diam Libiã, ac dimidios Piſces contingunt; </s>
            <s xml:id="echoid-s11250" xml:space="preserve">etiam ſi dies tunc non ſint breuiſſimi. </s>
            <s xml:id="echoid-s11251" xml:space="preserve">quare crepuſculorum quan-
              <lb/>
            titas non ſequetur dierum quantitatem, dies enim decreſcunt à Cancro ad Capricornum, crepuſcula vero à
              <lb/>
            Cancro ad dimidium ferè Libræ. </s>
            <s xml:id="echoid-s11252" xml:space="preserve">vnde iterum vſq; </s>
            <s xml:id="echoid-s11253" xml:space="preserve">ad Capricornum augentur. </s>
            <s xml:id="echoid-s11254" xml:space="preserve">idem fit in altero Zodiaci ſe-
              <lb/>
            micirculo aſcendente à Capricorno ad Cancrum. </s>
            <s xml:id="echoid-s11255" xml:space="preserve">Porro crepuſculum duplex eſt, matutinum, & </s>
            <s xml:id="echoid-s11256" xml:space="preserve">veſperti-
              <lb/>
            num. </s>
            <s xml:id="echoid-s11257" xml:space="preserve">quorum quantitas indagari poterit ex ſphæra materiali, cui additus ſit circulus crepuſculinus; </s>
            <s xml:id="echoid-s11258" xml:space="preserve">de
              <lb/>
            quo lib. </s>
            <s xml:id="echoid-s11259" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11260" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11261" xml:space="preserve">11. </s>
            <s xml:id="echoid-s11262" xml:space="preserve">dictum eſt, eum infra horizontem deprimi gr. </s>
            <s xml:id="echoid-s11263" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11264" xml:space="preserve">eique æquidiſtare. </s>
            <s xml:id="echoid-s11265" xml:space="preserve">poſito enim Solis
              <lb/>
            gradu diei propoſito in circulo crepuſculino, ſiue orientali, ſiue occidentali, numerentur æquatoris gradus,
              <lb/>
            qui aſcendunt ſupra horizontem, dum Sol a circulo crepuſculi ad horizontem aſcendit. </s>
            <s xml:id="echoid-s11266" xml:space="preserve">ij enim dabunt ho-
              <lb/>
            ras, necnon ſemiſſes, & </s>
            <s xml:id="echoid-s11267" xml:space="preserve">quadrantes earum, quibus duratio, ſeu quantitas crepuſculi computatur, eo videlicet
              <lb/>
            modo quo antea dierum quantitatem computare docuimus, v.</s>
            <s xml:id="echoid-s11268" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11269" xml:space="preserve">in eleuatione poli gr. </s>
            <s xml:id="echoid-s11270" xml:space="preserve">45. </s>
            <s xml:id="echoid-s11271" xml:space="preserve">Sole in primo gra-
              <lb/>
            du Cancri exiſtente, pono hunc grad. </s>
            <s xml:id="echoid-s11272" xml:space="preserve">in circulo crepuſculi, eumq; </s>
            <s xml:id="echoid-s11273" xml:space="preserve">vſque ad horizontem promoueo, nume-
              <lb/>
            roq; </s>
            <s xml:id="echoid-s11274" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s11275" xml:space="preserve">æquatoris interim ſupra horizontem emergentes, ideſt, quia aſcendunt ſupra horizontem, dum
              <lb/>
            Sol a circulo crepuſculi ad horizontẽ aſcendit; </s>
            <s xml:id="echoid-s11276" xml:space="preserve">quos reperio eſſe ferè gr. </s>
            <s xml:id="echoid-s11277" xml:space="preserve">40. </s>
            <s xml:id="echoid-s11278" xml:space="preserve">eos diuido per 15. </s>
            <s xml:id="echoid-s11279" xml:space="preserve">prouenit quo-
              <lb/>
            tiens 2. </s>
            <s xml:id="echoid-s11280" xml:space="preserve">& </s>
            <s xml:id="echoid-s11281" xml:space="preserve">remanent 10. </s>
            <s xml:id="echoid-s11282" xml:space="preserve">gradus, ex quibus infero crepuſculum illius diei, in ea eleuatione, durare hor. </s>
            <s xml:id="echoid-s11283" xml:space="preserve">duas, cũ
              <lb/>
            duabus tertijs horarum, gradus enim 10. </s>
            <s xml:id="echoid-s11284" xml:space="preserve">in motu diurno efficiunt {2/3}. </s>
            <s xml:id="echoid-s11285" xml:space="preserve">horæ, vel ſic, quotiens eſt 2 {10/15}. </s>
            <s xml:id="echoid-s11286" xml:space="preserve">ſiue 2 {2/3}. </s>
            <s xml:id="echoid-s11287" xml:space="preserve">er-
              <lb/>
            go crepuſculi quantitas eſt horarum 2 {2/3}. </s>
            <s xml:id="echoid-s11288" xml:space="preserve">vel ſic, ex Tabula conuerſionis grad. </s>
            <s xml:id="echoid-s11289" xml:space="preserve">æquatoris in horas, &</s>
            <s xml:id="echoid-s11290" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11291" xml:space="preserve">quam
              <lb/>
            in cap. </s>
            <s xml:id="echoid-s11292" xml:space="preserve">de æquatore dedimus, è regione grad. </s>
            <s xml:id="echoid-s11293" xml:space="preserve">40. </s>
            <s xml:id="echoid-s11294" xml:space="preserve">reperio horas 2. </s>
            <s xml:id="echoid-s11295" xml:space="preserve">cum 40′. </s>
            <s xml:id="echoid-s11296" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11297" xml:space="preserve">minuta autem 40. </s>
            <s xml:id="echoid-s11298" xml:space="preserve">efficiunt
              <lb/>
            {2/3}. </s>
            <s xml:id="echoid-s11299" xml:space="preserve">horæ.</s>
            <s xml:id="echoid-s11300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11301" xml:space="preserve">Porrò hi gradus æquatoris coaſcendentes, ideo crepuſculi magnitudinem oſtendunt, quia ij ſimul cum
              <lb/>
            gr. </s>
            <s xml:id="echoid-s11302" xml:space="preserve">Solis oriuntur, & </s>
            <s xml:id="echoid-s11303" xml:space="preserve">occidunt, dum Sol crepuſculum tam matutinum quam veſpertinum, quę æqualia ſunt,
              <lb/>
            abſoluit.</s>
            <s xml:id="echoid-s11304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11305" xml:space="preserve">Nunc vero conſiderandum eſt varias reperiri crepuſculorum differentias, nam vbi paralellus Solis ſecat
              <lb/>
            & </s>
            <s xml:id="echoid-s11306" xml:space="preserve">horizontem, & </s>
            <s xml:id="echoid-s11307" xml:space="preserve">crepuſculinum, @bi fit crepuſculum, ſed nõ per totam noctem, vt in allato exemplo patuit,
              <lb/>
            vbi vero Solis paralellus ſecat tantum horizontem non autem crepuſculinum, ibi fit crepuſculum per totam
              <lb/>
            noctem. </s>
            <s xml:id="echoid-s11308" xml:space="preserve">Tertio vbi paralellus Solis neutrum ſecat ibi nullum accidit crepuſculũ ſed vel dies puros, vel nox
              <lb/>
            pura. </s>
            <s xml:id="echoid-s11309" xml:space="preserve">quod manifeſtè patebit ſi materialis ſphęra conſtituatur ad eleuationem poli gr. </s>
            <s xml:id="echoid-s11310" xml:space="preserve">66. </s>
            <s xml:id="echoid-s11311" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s11312" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s11313" xml:space="preserve">etiam ad ma-
              <lb/>
            i
              <unsure/>
            orem, v.</s>
            <s xml:id="echoid-s11314" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11315" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s11316" xml:space="preserve">70. </s>
            <s xml:id="echoid-s11317" xml:space="preserve">ibi enim erunt paralelli Solis, qui toti ſupra horizontem extabunt, ijque nullum dabunt
              <lb/>
            crepuſculum; </s>
            <s xml:id="echoid-s11318" xml:space="preserve">vnus vero ipſum tanget, qui nullum quoq; </s>
            <s xml:id="echoid-s11319" xml:space="preserve">crepuſculum dabit. </s>
            <s xml:id="echoid-s11320" xml:space="preserve">alij ſecabunt horizontem, ſed
              <lb/>
            non crepuſculinum, ijque exhibebunt crepuſculum per totam noctem. </s>
            <s xml:id="echoid-s11321" xml:space="preserve">alij tãdem vtrum
              <unsure/>
            q; </s>
            <s xml:id="echoid-s11322" xml:space="preserve">ſecabunt, qui cre-
              <lb/>
            puſculum partem noctis efficient. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">In ſphæra tandem obliquiſſima eleuationis gr. </s>
            <s xml:id="echoid-s11324" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s11325" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s11326" xml:space="preserve">ad ſphæram para-
              <lb/>
            lellam circulus, crepuſculi non ſecat omnes paralellos, quia plures infra ipſum exiſtunt, quos Sole percurren
              <lb/>
            te nox intempeſta orbi incumbit, &</s>
            <s xml:id="echoid-s11327" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11328" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div232" type="section" level="1" n="151">
          <head xml:id="echoid-head163" style="it" xml:space="preserve">Aliter dierum, ac crepuſculorum quantitatem computare.</head>
          <p>
            <s xml:id="echoid-s11329" xml:space="preserve">ALiter poſſumus vna eademque opera dierum, noctium, & </s>
            <s xml:id="echoid-s11330" xml:space="preserve">crepuſculorum, quantitatem ex Analem-
              <lb/>
            mate reperire. </s>
            <s xml:id="echoid-s11331" xml:space="preserve">Eſt autem Analemma figura plana ex circulis, rectiſque lineis conſtans, referens ſphæ-
              <lb/>
            ræ circulos, axes, diametros, centra, &</s>
            <s xml:id="echoid-s11332" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11333" xml:space="preserve">vti eſt præſens, in qua circulus A E B H. </s>
            <s xml:id="echoid-s11334" xml:space="preserve">refert circulum meridia-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s11335" xml:space="preserve">f
              <unsure/>
            aciem eius orientalem. </s>
            <s xml:id="echoid-s11336" xml:space="preserve">C, eſt centrum mundi. </s>
            <s xml:id="echoid-s11337" xml:space="preserve">A B, diameter horizontis. </s>
            <s xml:id="echoid-s11338" xml:space="preserve">I K, diameter circuli
              <lb/>
            crepuſculorum, qui debet eſſe infra horizontem grad. </s>
            <s xml:id="echoid-s11339" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11340" xml:space="preserve">duo enim arcus A I, B K, per prima propoſ. </s>
            <s xml:id="echoid-s11341" xml:space="preserve">Ap-
              <lb/>
            par. </s>
            <s xml:id="echoid-s11342" xml:space="preserve">continent grad. </s>
            <s xml:id="echoid-s11343" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11344" xml:space="preserve">quanta videlicet eſt Solis depreſſio ſub horizonte ini@io crepuſculi matutini, & </s>
            <s xml:id="echoid-s11345" xml:space="preserve">fine
              <lb/>
            veſpert
              <unsure/>
            ini. </s>
            <s xml:id="echoid-s11346" xml:space="preserve">Arcus B P, eſt poli eleuatio pro data regione, v. </s>
            <s xml:id="echoid-s11347" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s11348" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s11349" xml:space="preserve">45. </s>
            <s xml:id="echoid-s11350" xml:space="preserve">totus eſt oppoſitus arcus A π. </s>
            <s xml:id="echoid-s11351" xml:space="preserve">linea
              <lb/>
            ergo π C P, eſt axis mundi. </s>
            <s xml:id="echoid-s11352" xml:space="preserve">P, polus nobis arcticus. </s>
            <s xml:id="echoid-s11353" xml:space="preserve">π, antarcticus. </s>
            <s xml:id="echoid-s11354" xml:space="preserve">linea C D, perpendicularis ipſi axi, erit
              <lb/>
            æquatoris diameter. </s>
            <s xml:id="echoid-s11355" xml:space="preserve">accipiatur deinde hinc inde ab æquatore maxima eclypticæ declinatio, ideſt, arcus con-
              <lb/>
            @inens gr. </s>
            <s xml:id="echoid-s11356" xml:space="preserve">23 {1/2}. </s>
            <s xml:id="echoid-s11357" xml:space="preserve">& </s>
            <s xml:id="echoid-s11358" xml:space="preserve">notentur punctis E G F H, quare duæ lineæ E F, G H. </s>
            <s xml:id="echoid-s11359" xml:space="preserve">erunt diametri tropicorum. </s>
            <s xml:id="echoid-s11360" xml:space="preserve">ſint igi-
              <lb/>
            tur, exempli gratia, in hac noſtra eleuatione poli gr. </s>
            <s xml:id="echoid-s11361" xml:space="preserve">45. </s>
            <s xml:id="echoid-s11362" xml:space="preserve">ad quam Alemma conſtruximus, inquirenda tria
              <lb/>
            prædicta, quando Soloccupat initium Cancri, ſiue quando Cancri tropicum percurrit; </s>
            <s xml:id="echoid-s11363" xml:space="preserve">quod ad 22. </s>
            <s xml:id="echoid-s11364" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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