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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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div221" type="section" level="1" n="142">
          <p>
            <s xml:id="echoid-s10639" xml:space="preserve">
              <pb o="106" file="0126" n="130" rhead="De Mundi Fabrica,"/>
            propè Perigæum, quia ſcilicet ibi remotior, quam hic, quæ enim propriora ſunt maiora apparent.</s>
            <s xml:id="echoid-s10640" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10641" xml:space="preserve">Porrò Hipparchus, ac poſtea Ptolemæus exiſtimarunt loci Apogæi in Zodiaco eſſe ſtabilem, eſſeq; </s>
            <s xml:id="echoid-s10642" xml:space="preserve">in par-
              <lb/>
            te 5 {1/2}. </s>
            <s xml:id="echoid-s10643" xml:space="preserve">Geminorum, ſed aliter a ſuccedentibus Aſtronomis Albategnio, Arzahele, Copernico, ac Tychone
              <lb/>
            depræhenſum eſt; </s>
            <s xml:id="echoid-s10644" xml:space="preserve">illud ſcilicet in ſignorum conſequentia tardè promoueri: </s>
            <s xml:id="echoid-s10645" xml:space="preserve">ita vt hac tempeſtate 6. </s>
            <s xml:id="echoid-s10646" xml:space="preserve">Cancri
              <lb/>
            gradui ſupponatur, ſinguliſq; </s>
            <s xml:id="echoid-s10647" xml:space="preserve">annis 45″. </s>
            <s xml:id="echoid-s10648" xml:space="preserve">tantum ſecundis promoueatnr. </s>
            <s xml:id="echoid-s10649" xml:space="preserve">vnde facilè eſt cognoſcere, quan to
              <lb/>
            annorum interuallo, totum Zodiacũ recurrat
              <unsure/>
            . </s>
            <s xml:id="echoid-s10650" xml:space="preserve">ſi enim omnia eclypticæ ſecũdę ſecunda, quę ſunt 1,296,000, ″.
              <lb/>
            </s>
            <s xml:id="echoid-s10651" xml:space="preserve">diuiſerimus per 45″. </s>
            <s xml:id="echoid-s10652" xml:space="preserve">motum, ſcilicet annuum, prodibit in quotiente numerus annorum quæſitus; </s>
            <s xml:id="echoid-s10653" xml:space="preserve">videlicet
              <lb/>
            28′800′. </s>
            <s xml:id="echoid-s10654" xml:space="preserve">quibus Apogæum totum Zodiacum abſoluat.</s>
            <s xml:id="echoid-s10655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div223" type="section" level="1" n="143">
          <head xml:id="echoid-head155" style="it" xml:space="preserve">De Apogæiloco, & Eccentricitate inuenienda. Cap. IX.</head>
          <p>
            <s xml:id="echoid-s10656" xml:space="preserve">QVoniam Solis motus, quamuis ſit inæqualis, nõ tamen ſenſu ea inæqualitas percipitur, ac proinde neq;
              <lb/>
            </s>
            <s xml:id="echoid-s10657" xml:space="preserve">in quo Zodiaci loco ſit tardiſſimus, & </s>
            <s xml:id="echoid-s10658" xml:space="preserve">conſequenter non patet ſenſu vbinam ſit Apogæum; </s>
            <s xml:id="echoid-s10659" xml:space="preserve">ideo Ptole-
              <lb/>
            mæus vt illud perſcrutaretur, ſic ex ſuis obſeruationibus ratiocinatus eſt. </s>
            <s xml:id="echoid-s10660" xml:space="preserve">Primo, quia tempus ab Ariete ad
              <lb/>
            Libram, maius eſt reliquo tempore, ideo neceſſe fuit Apogæum eſſe in ſemicirculo boreali Zodiaci; </s>
            <s xml:id="echoid-s10661" xml:space="preserve">pariter
              <lb/>
            quia in primo eius quadrante, ideſt, ab Ariete ad Cancrum, tardior erat Sol, quam in altero à Cancro ad Li-
              <lb/>
            bram, ibi enim inſumebat dies 94 {1/2}. </s>
            <s xml:id="echoid-s10662" xml:space="preserve">hic vero 92 {1/2}. </s>
            <s xml:id="echoid-s10663" xml:space="preserve">ideo concluſit Apogæum neceſſario verſari in primo qua-
              <lb/>
            drante. </s>
            <s xml:id="echoid-s10664" xml:space="preserve">ex his cæpit figura conſtruere, cuius auxilio reliqua exactè conſecutus eſt. </s>
            <s xml:id="echoid-s10665" xml:space="preserve">ſit eclyptica circa centrum
              <lb/>
              <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a" number="84">
                <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01"/>
              </figure>
            E. </s>
            <s xml:id="echoid-s10666" xml:space="preserve">in qua puncta quatuor Cardinalia ſint A B G D A. </s>
            <s xml:id="echoid-s10667" xml:space="preserve">punctum
              <lb/>
            vernale. </s>
            <s xml:id="echoid-s10668" xml:space="preserve">B. </s>
            <s xml:id="echoid-s10669" xml:space="preserve">ſolſtitiale. </s>
            <s xml:id="echoid-s10670" xml:space="preserve">G. </s>
            <s xml:id="echoid-s10671" xml:space="preserve">Autumnale. </s>
            <s xml:id="echoid-s10672" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10673" xml:space="preserve">hyemale. </s>
            <s xml:id="echoid-s10674" xml:space="preserve">primus qua-
              <lb/>
            drans eſt A B. </s>
            <s xml:id="echoid-s10675" xml:space="preserve">in quo concluſit eſſe Apogæum, & </s>
            <s xml:id="echoid-s10676" xml:space="preserve">conſequenter
              <lb/>
            centrum eccentrici, in hac parte, v.</s>
            <s xml:id="echoid-s10677" xml:space="preserve">g.</s>
            <s xml:id="echoid-s10678" xml:space="preserve">vbi F. </s>
            <s xml:id="echoid-s10679" xml:space="preserve">ex quo deſcriptus ſit
              <lb/>
            eccentricus T K Q R. </s>
            <s xml:id="echoid-s10680" xml:space="preserve">duabus ecly pticæ diametris A G. </s>
            <s xml:id="echoid-s10681" xml:space="preserve">B D. </s>
            <s xml:id="echoid-s10682" xml:space="preserve">pa-
              <lb/>
            ralellæ ducantur duæ eccẽtrici diametri N Q. </s>
            <s xml:id="echoid-s10683" xml:space="preserve">X R. </s>
            <s xml:id="echoid-s10684" xml:space="preserve">tandem du-
              <lb/>
            cta per vtrumq; </s>
            <s xml:id="echoid-s10685" xml:space="preserve">centrum linea E F H. </s>
            <s xml:id="echoid-s10686" xml:space="preserve">erit Apogæi linea; </s>
            <s xml:id="echoid-s10687" xml:space="preserve">eritq;
              <lb/>
            </s>
            <s xml:id="echoid-s10688" xml:space="preserve">H. </s>
            <s xml:id="echoid-s10689" xml:space="preserve">locus Apogæi in Zodiaco. </s>
            <s xml:id="echoid-s10690" xml:space="preserve">quem vt vna cum E F. </s>
            <s xml:id="echoid-s10691" xml:space="preserve">eccentrici-
              <lb/>
            tate cognoſceret, ſic perrexit rationari. </s>
            <s xml:id="echoid-s10692" xml:space="preserve">cum conſtet Solem obi-
              <lb/>
            re quadrantem A B. </s>
            <s xml:id="echoid-s10693" xml:space="preserve">d ebus 94 {1/2}. </s>
            <s xml:id="echoid-s10694" xml:space="preserve">eodemq; </s>
            <s xml:id="echoid-s10695" xml:space="preserve">etiam tempore nam-
              <lb/>
            bulet arcum eccentric T K. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">æquali, ac medio motu, conſtetque
              <lb/>
            quantum ſingulis diebus motu æquali proficiat, conſtabit etiam
              <lb/>
            quantum diebus 94 {1/2}. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">proficiat in eccentrico, hoc eſt, quantus ſit
              <lb/>
            arcus T K. </s>
            <s xml:id="echoid-s10698" xml:space="preserve">fuitq; </s>
            <s xml:id="echoid-s10699" xml:space="preserve">graduum 93.</s>
            <s xml:id="echoid-s10700" xml:space="preserve">9′. </s>
            <s xml:id="echoid-s10701" xml:space="preserve">ſimili modo reperit arcum ec-
              <lb/>
            centrici K L. </s>
            <s xml:id="echoid-s10702" xml:space="preserve">eſſe gradus 91.</s>
            <s xml:id="echoid-s10703" xml:space="preserve">11″. </s>
            <s xml:id="echoid-s10704" xml:space="preserve">ergo totus arcus T K L. </s>
            <s xml:id="echoid-s10705" xml:space="preserve">notus
              <lb/>
            fuit; </s>
            <s xml:id="echoid-s10706" xml:space="preserve">vnde & </s>
            <s xml:id="echoid-s10707" xml:space="preserve">T X. </s>
            <s xml:id="echoid-s10708" xml:space="preserve">dimidium eius cognitum. </s>
            <s xml:id="echoid-s10709" xml:space="preserve">quia vero X N. </s>
            <s xml:id="echoid-s10710" xml:space="preserve">eſt
              <lb/>
            quadrans eccentrici notus, ideo ſi auferatur ab arcu T X. </s>
            <s xml:id="echoid-s10711" xml:space="preserve">noto,
              <lb/>
            notus relinquetur arcus T N. </s>
            <s xml:id="echoid-s10712" xml:space="preserve">gr.</s>
            <s xml:id="echoid-s10713" xml:space="preserve">2.</s>
            <s xml:id="echoid-s10714" xml:space="preserve">10′. </s>
            <s xml:id="echoid-s10715" xml:space="preserve">ſimiliter ex arcu T K.</s>
            <s xml:id="echoid-s10716" xml:space="preserve">iam
              <lb/>
            noto, ablato T X. </s>
            <s xml:id="echoid-s10717" xml:space="preserve">pariter noto, notus relinquitur K X. </s>
            <s xml:id="echoid-s10718" xml:space="preserve">59. </s>
            <s xml:id="echoid-s10719" xml:space="preserve">min-
              <lb/>
            hinc Ptolemæus ex doctrina chordarum, vel ſinuum, propoſitum aſſequutus eſt, nos autem facilitatis cauſa
              <lb/>
            idem practicè ſic obtinebimus. </s>
            <s xml:id="echoid-s10720" xml:space="preserve">primo deſcribatur eccentricus vt in præcedenti figuræ, ex centro F. </s>
            <s xml:id="echoid-s10721" xml:space="preserve">ductiſq; </s>
            <s xml:id="echoid-s10722" xml:space="preserve">
              <lb/>
            diametris Q N. </s>
            <s xml:id="echoid-s10723" xml:space="preserve">X R. </s>
            <s xml:id="echoid-s10724" xml:space="preserve">ad angulos rectos, diuiſus erit in quatuor quadrantes. </s>
            <s xml:id="echoid-s10725" xml:space="preserve">deinde ſumatur arcus N T. </s>
            <s xml:id="echoid-s10726" xml:space="preserve">gr.</s>
            <s xml:id="echoid-s10727" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10728" xml:space="preserve">
              <lb/>
            10′. </s>
            <s xml:id="echoid-s10729" xml:space="preserve">arcus vero X K. </s>
            <s xml:id="echoid-s10730" xml:space="preserve">min.</s>
            <s xml:id="echoid-s10731" xml:space="preserve">59′. </s>
            <s xml:id="echoid-s10732" xml:space="preserve">& </s>
            <s xml:id="echoid-s10733" xml:space="preserve">per puncta T K. </s>
            <s xml:id="echoid-s10734" xml:space="preserve">ducantur duæ A T G. </s>
            <s xml:id="echoid-s10735" xml:space="preserve">B K D. </s>
            <s xml:id="echoid-s10736" xml:space="preserve">diametris eccentrici paralel-
              <lb/>
            læ; </s>
            <s xml:id="echoid-s10737" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s10738" xml:space="preserve">ex earum communi puncto E. </s>
            <s xml:id="echoid-s10739" xml:space="preserve">deſcribatur eclyptica A B G D. </s>
            <s xml:id="echoid-s10740" xml:space="preserve">tandem per vtrumque centrum E F. </s>
            <s xml:id="echoid-s10741" xml:space="preserve">
              <lb/>
            ducatur linea E F H. </s>
            <s xml:id="echoid-s10742" xml:space="preserve">quæ erit Apogæi linea, tranſibit enim per eccentrici Apogæum 1. </s>
            <s xml:id="echoid-s10743" xml:space="preserve">indicabitq; </s>
            <s xml:id="echoid-s10744" xml:space="preserve">in ecly-
              <lb/>
            ptica eius locũ in K. </s>
            <s xml:id="echoid-s10745" xml:space="preserve">hæc figura ſic conſtructa habebit veras proportiones, atq; </s>
            <s xml:id="echoid-s10746" xml:space="preserve">eaſdem quas haberet magna
              <lb/>
            figura quam in mundo concipimus. </s>
            <s xml:id="echoid-s10747" xml:space="preserve">diuiſa itaq; </s>
            <s xml:id="echoid-s10748" xml:space="preserve">eccentrici ſemid. </s>
            <s xml:id="echoid-s10749" xml:space="preserve">F I
              <unsure/>
            . </s>
            <s xml:id="echoid-s10750" xml:space="preserve">in partes 60. </s>
            <s xml:id="echoid-s10751" xml:space="preserve">æquales, apparebit auxilio
              <lb/>
            circini eccentricitatem E F. </s>
            <s xml:id="echoid-s10752" xml:space="preserve">conſtare ex duabus ex illis ſexageſimis ac medietate ferè. </s>
            <s xml:id="echoid-s10753" xml:space="preserve">quare proportio ſemi-
              <lb/>
            diametri ad eccentricitatem eſt ſicuti 24. </s>
            <s xml:id="echoid-s10754" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s10755" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s10756" xml:space="preserve">ſimiliter circini beneficio cognoſcemus arcum A H. </s>
            <s xml:id="echoid-s10757" xml:space="preserve">eſſe
              <lb/>
            gr.</s>
            <s xml:id="echoid-s10758" xml:space="preserve">65 {1/2}.</s>
            <s xml:id="echoid-s10759" xml:space="preserve">ideſt, Apogæum eſſe in gr.</s>
            <s xml:id="echoid-s10760" xml:space="preserve">5 {1/2}. </s>
            <s xml:id="echoid-s10761" xml:space="preserve">Geminorum, Perigæum autem in oppoſito loco. </s>
            <s xml:id="echoid-s10762" xml:space="preserve">Atque hæc perſcru-
              <lb/>
            tanda erant.</s>
            <s xml:id="echoid-s10763" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10764" xml:space="preserve">Simili methodo idem Apogæum, noſtro æuo, ſtatuerunt in 6. </s>
            <s xml:id="echoid-s10765" xml:space="preserve">Cancri eccentricitatem vero partium 2. </s>
            <s xml:id="echoid-s10766" xml:space="preserve">9′.
              <lb/>
            </s>
            <s xml:id="echoid-s10767" xml:space="preserve">qualium ſemidiameter eſt 60.</s>
            <s xml:id="echoid-s10768" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10769" xml:space="preserve">Porrò ſciendum eſt eccentricitatem eſſe dimidium craſſitiei cæli Solis, quod patebit deſcriptis ex centro
              <lb/>
            mundi E. </s>
            <s xml:id="echoid-s10770" xml:space="preserve">duobus circulis, vno per Apogæum, altero per Perigæum tranſeunte, inter eos enim claudetur cæ-
              <lb/>
            li craſſities, quam duplam eſſe eccentricitatis circino comperies. </s>
            <s xml:id="echoid-s10771" xml:space="preserve">cum igitur nos ſuperius ſtatuerimus craſſi-
              <lb/>
            tiem illam eſſe ſemidiametros terræ 81. </s>
            <s xml:id="echoid-s10772" xml:space="preserve">erit eius ſemiſſis 40 {1/2}. </s>
            <s xml:id="echoid-s10773" xml:space="preserve">eccentricitas, ideſt, tantum diſtabit a terræ cen-
              <lb/>
            tro eccentrici centrum.</s>
            <s xml:id="echoid-s10774" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10775" xml:space="preserve">His igitur ſic conſtitutis, rurſus ad ſolarem motum redeamus. </s>
            <s xml:id="echoid-s10776" xml:space="preserve">primoq; </s>
            <s xml:id="echoid-s10777" xml:space="preserve">illud annotandum, diſtantiam lineę
              <lb/>
            medij motus in Zodiaco ab Apogeo dici Anomaliam Solis mediam, vt in priori ſigura pag. </s>
            <s xml:id="echoid-s10778" xml:space="preserve">105. </s>
            <s xml:id="echoid-s10779" xml:space="preserve">arcus Zodia-
              <lb/>
            ci D X. </s>
            <s xml:id="echoid-s10780" xml:space="preserve">erit Anomalia media. </s>
            <s xml:id="echoid-s10781" xml:space="preserve">Sol autem ab Apogæo in conſequentia recedit annuo tempore paulo minus,
              <lb/>
            quam ab æquinoctio, quia illud mobile eſt pariter in conſequentia; </s>
            <s xml:id="echoid-s10782" xml:space="preserve">quare tanto minus Sol annuatim reccdit
              <lb/>
            ab eo, quanto eſt ipſius Apogæi motus, nempe 45″. </s>
            <s xml:id="echoid-s10783" xml:space="preserve">Diſtantia vero inter lineam medij, & </s>
            <s xml:id="echoid-s10784" xml:space="preserve">veri motus, dicitur
              <lb/>
            æquatio, qualis eſt in eadem figura arcus X Z. </s>
            <s xml:id="echoid-s10785" xml:space="preserve">de qua poſtea fuſius. </s>
            <s xml:id="echoid-s10786" xml:space="preserve">Poſtremo illud quoq; </s>
            <s xml:id="echoid-s10787" xml:space="preserve">animaduerſione di-
              <lb/>
            gnum eſt, quod ſi Sol, hoc ſolo proprio motu in eccentrico moueretur, ideſt, ſi motu d
              <unsure/>
            iurno, ſeu primi </s>
          </p>
        </div>
      </text>
    </echo>
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