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-div234" type="section" level="1" n="152">
          <p>
            <s xml:id="echoid-s11503" xml:space="preserve">
              <pb o="114" file="0136" n="141" rhead="De Mundi Fabrica,"/>
            rati quæat. </s>
            <s xml:id="echoid-s11504" xml:space="preserve">ſic enim paratum erit inſtrumentum, quo ad omnes poli eleuationes, necnon ad omnes Zodiaci
              <lb/>
            gradus, ſeu ad quodlibet anni tempus, magna facilitate æque, aciucunditate inuenire poterimus tria hæc,
              <lb/>
            a cum ſemidiurnum, arcum ſeminocturnum, & </s>
            <s xml:id="echoid-s11505" xml:space="preserve">crepuſculi quantitatem, vt exemplo patebit. </s>
            <s xml:id="echoid-s11506" xml:space="preserve">vtautem faci-
              <lb/>
            lius intelligamus horum rationem debemus concipere totum hoc inſtrumentum collocatum eſſe aſtronomi-
              <lb/>
            cè, hoc videlicet modo; </s>
            <s xml:id="echoid-s11507" xml:space="preserve">ipſe meridianus debet meridiano mundi congruere, acproinde erigi perpendicu-
              <lb/>
            lariter ad horizontem; </s>
            <s xml:id="echoid-s11508" xml:space="preserve">& </s>
            <s xml:id="echoid-s11509" xml:space="preserve">linea A C, ipſi horizonti æquidiſtare, & </s>
            <s xml:id="echoid-s11510" xml:space="preserve">quadrans diuiſus in gr. </s>
            <s xml:id="echoid-s11511" xml:space="preserve">90. </s>
            <s xml:id="echoid-s11512" xml:space="preserve">vergere ad po-
              <lb/>
            lum noſtrum arcticum. </s>
            <s xml:id="echoid-s11513" xml:space="preserve">poſtea polus Z, partis mobilis eleuetur ad quamuis propoſitam poli eleuationem;
              <lb/>
            </s>
            <s xml:id="echoid-s11514" xml:space="preserve">in qua poſitione erit inſtrumentum iſtud aſtronomicè collocatum. </s>
            <s xml:id="echoid-s11515" xml:space="preserve">vnde melius eius rationem intelligere
              <lb/>
            poterimus; </s>
            <s xml:id="echoid-s11516" xml:space="preserve">præſer@im ſi concipiamus eius ſemicirculos erectos perpendiculariter ad meridianum; </s>
            <s xml:id="echoid-s11517" xml:space="preserve">ex qua
              <lb/>
            poſitione ſequitur eos eſſe ſemicirculos orientales, cum in parte orientali conſtituantur. </s>
            <s xml:id="echoid-s11518" xml:space="preserve">ſed vt eius vſus pa-
              <lb/>
            teſcat, demus exemplum. </s>
            <s xml:id="echoid-s11519" xml:space="preserve">ſint in ſphæra recta inuenienda prædicta tria, ad initia Cancri, Capricorni, Arie-
              <lb/>
            tis, & </s>
            <s xml:id="echoid-s11520" xml:space="preserve">Libræ. </s>
            <s xml:id="echoid-s11521" xml:space="preserve">applico igitur polum vtrumque T Z, horizonti, in quo ſitu obfirmata parte mobili, accipio
              <lb/>
            duo puncta S y, in quibus duo ſila ſecant diametrum Q R, Capricorni. </s>
            <s xml:id="echoid-s11522" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s11523" xml:space="preserve">ex his duobus punctis duco duas
              <lb/>
            perpendiculares S T, γ λ, vſque ad ſemicirculum eiuſdem Capricorni in punctis T λ. </s>
            <s xml:id="echoid-s11524" xml:space="preserve">aſſumo itaque arcum
              <lb/>
            T λ, ab eis interceptum eumque quot horas ac minuta contineat expendo; </s>
            <s xml:id="echoid-s11525" xml:space="preserve">ſunt enim hi ſemicirculi diuiſi in
              <lb/>
            horas, & </s>
            <s xml:id="echoid-s11526" xml:space="preserve">hora vna ſaltem oportet ſit diuiſa in quatuor partes æquales; </s>
            <s xml:id="echoid-s11527" xml:space="preserve">quæ erunt horæ quadrantes, quarum
              <lb/>
            ſingulæ continent horæ minuta 15′. </s>
            <s xml:id="echoid-s11528" xml:space="preserve">arcus enim T ω, eſt hora vna. </s>
            <s xml:id="echoid-s11529" xml:space="preserve">arcus ω λ, ſuperat quartam horæ partem,
              <lb/>
            ita vt ſit vna ferè tertia pars horæ; </s>
            <s xml:id="echoid-s11530" xml:space="preserve">quare in ſphæra recta crepuſculum tempore ſolſtitij erit hora 1. </s>
            <s xml:id="echoid-s11531" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11532" xml:space="preserve">19′. </s>
            <s xml:id="echoid-s11533" xml:space="preserve">
              <lb/>
            tantundem erit in altero tropico. </s>
            <s xml:id="echoid-s11534" xml:space="preserve">ſic ſemper faciendum eſt, ideſt, accipiendæ ſunt ſemper duæ perpendicu-
              <lb/>
            lares à punctis, in quibus diameter paralelli propoſiti, ſecatur a filis horizontis, & </s>
            <s xml:id="echoid-s11535" xml:space="preserve">crepuſculi, quæ lineæ pro-
              <lb/>
            ducantur vſque ad ſemicirculum eiuſdem paralelli, arcus enim inter ipſas interceptus dabit quantitatem
              <lb/>
            crepuſculi; </s>
            <s xml:id="echoid-s11536" xml:space="preserve">quod ſi perpendiculares ibi deſcriptæ, non præcisè per dicta puncta ſectionum tranſierint, aliæ
              <lb/>
            iuxta eas concipiendæ ſunt. </s>
            <s xml:id="echoid-s11537" xml:space="preserve">rurſus in eodem paralello, & </s>
            <s xml:id="echoid-s11538" xml:space="preserve">in eadem ſphæra recta arcus T Q, erit arcus diur-
              <lb/>
            nus, arcus vero λ R, erit nocturnus puræ, ſeu intempeſtæ noctis. </s>
            <s xml:id="echoid-s11539" xml:space="preserve">eodem modo in æquatore agendum eſt,
              <lb/>
            puncta ſectionum in diametro erunt A β, perpendiculares erunt A E, β δ, vſque ad ſemicirculum eiuſdem
              <lb/>
            æquatoris, intercipientes arcum E δ, qui continet horam vnam, & </s>
            <s xml:id="echoid-s11540" xml:space="preserve">quantam horæ partem, ideſt, min. </s>
            <s xml:id="echoid-s11541" xml:space="preserve">12′. </s>
            <s xml:id="echoid-s11542" xml:space="preserve">
              <lb/>
            Alterum exemplum, ſit in ſphæra paralella quærendum crepuſculum, &</s>
            <s xml:id="echoid-s11543" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11544" xml:space="preserve">pono igitur polum Z, in vertice,
              <lb/>
            ſeu in fine gr. </s>
            <s xml:id="echoid-s11545" xml:space="preserve">90. </s>
            <s xml:id="echoid-s11546" xml:space="preserve">ibique eo obfirmato, noto punctum in diametro eclypticæ, quod ſecatur à filo crepuſculo-
              <lb/>
            rum, à quo duco perpendicularem ipſi eclypticæ diametro, vſque ad ſemicirculum ipſius eclypticæ Q E N,
              <lb/>
            alteram perpendicularem duco a centro A, vbi ſecatur à linea ſeu filo horizontali, vſque ad eundem ſemi-
              <lb/>
            circulum eclypticæ; </s>
            <s xml:id="echoid-s11547" xml:space="preserve">arcus en im interceptus dabit quantitatem crepuſculi. </s>
            <s xml:id="echoid-s11548" xml:space="preserve">erit gr. </s>
            <s xml:id="echoid-s11549" xml:space="preserve">ferè 48. </s>
            <s xml:id="echoid-s11550" xml:space="preserve">quos eclypticæ
              <lb/>
            gradus motu propri
              <unsure/>
            o Sol percurrit totidem ferè diebus, quare huic habitationi primũ crepuſculum erit die-
              <lb/>
            rum 48. </s>
            <s xml:id="echoid-s11551" xml:space="preserve">ab initio Lib æ vſq; </s>
            <s xml:id="echoid-s11552" xml:space="preserve">ad gr. </s>
            <s xml:id="echoid-s11553" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11554" xml:space="preserve">Scorpij. </s>
            <s xml:id="echoid-s11555" xml:space="preserve">Rurſus a gr. </s>
            <s xml:id="echoid-s11556" xml:space="preserve">12. </s>
            <s xml:id="echoid-s11557" xml:space="preserve">Aquarij vſq; </s>
            <s xml:id="echoid-s11558" xml:space="preserve">ad Arietem, erit alterum crepu-
              <lb/>
            ſcuium dierum totidem 48. </s>
            <s xml:id="echoid-s11559" xml:space="preserve">quare in vniuerſum tempus crcpuſculi erit trium menſiũ, dierum ſex conſequen-
              <lb/>
            ter, nox pura erit reliquum ſex menſium, nimirum duorum menſium, dierum 24.</s>
            <s xml:id="echoid-s11560" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11561" xml:space="preserve">In eadem ſphæra paralella, licebit videre vnicum eſſe diem ſex menſium continuum, & </s>
            <s xml:id="echoid-s11562" xml:space="preserve">noctem pariter
              <lb/>
            vnam intempeſtam dnorum menſium, ac dierum 24. </s>
            <s xml:id="echoid-s11563" xml:space="preserve">duo vero crepuſcula ſingula dierum 48. </s>
            <s xml:id="echoid-s11564" xml:space="preserve">vnde ſequitur
              <lb/>
            eos habere diem artificialem, computatis crepuſculis, menſium 9. </s>
            <s xml:id="echoid-s11565" xml:space="preserve">dierum 6. </s>
            <s xml:id="echoid-s11566" xml:space="preserve">& </s>
            <s xml:id="echoid-s11567" xml:space="preserve">amplius. </s>
            <s xml:id="echoid-s11568" xml:space="preserve">pro exemplo autem
              <lb/>
            eleuationis polaris inter ſphæram rectam, & </s>
            <s xml:id="echoid-s11569" xml:space="preserve">paralellam, ſufficiat illud quod allatum eſt ſuperius in Ana-
              <lb/>
            lemmate particular.</s>
            <s xml:id="echoid-s11570" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11571" xml:space="preserve">Cæterum ex varia poſitione Analemmatis, ad varias poli eleuationes licebit magna cũ voluptate, quo di-
              <lb/>
            ximus modo, @@atim reperire non ſolum quantitatem dierum, noctium. </s>
            <s xml:id="echoid-s11572" xml:space="preserve">& </s>
            <s xml:id="echoid-s11573" xml:space="preserve">crepuſculorum; </s>
            <s xml:id="echoid-s11574" xml:space="preserve">ſed etiam diuerſi-
              <lb/>
            tat@m inter vnam habitationem, & </s>
            <s xml:id="echoid-s11575" xml:space="preserve">alteram; </s>
            <s xml:id="echoid-s11576" xml:space="preserve">nec non diuerſitatem currentem pertotum annum in eadem
              <lb/>
            ſphæra. </s>
            <s xml:id="echoid-s11577" xml:space="preserve">Apparebit primo in tropico Cãcri, ſemper maiora eſſe crepuſcula, quam in altero: </s>
            <s xml:id="echoid-s11578" xml:space="preserve">minima vero con-
              <lb/>
            tingere ci
              <unsure/>
            rca dimidiam L bram, & </s>
            <s xml:id="echoid-s11579" xml:space="preserve">Piſces; </s>
            <s xml:id="echoid-s11580" xml:space="preserve">dummodo eleuatio poli non tranſcendat gra. </s>
            <s xml:id="echoid-s11581" xml:space="preserve">66 {1/2}; </s>
            <s xml:id="echoid-s11582" xml:space="preserve">nam in maiori
              <lb/>
            eleuatione crepuſcula Capricorni decreſcunt, ac non ſolum mi
              <unsure/>
            nora euadunt, quam circa dimidiam Libram.
              <lb/>
            </s>
            <s xml:id="echoid-s11583" xml:space="preserve">& </s>
            <s xml:id="echoid-s11584" xml:space="preserve">Piſces; </s>
            <s xml:id="echoid-s11585" xml:space="preserve">ſed omnium breuiſſima eſſe poſſunt. </s>
            <s xml:id="echoid-s11586" xml:space="preserve">quod alij non videntur ammaduertiſi
              <unsure/>
            e, cum abſolute dicant
              <lb/>
            minima eſſe ad dimidiam Libram, & </s>
            <s xml:id="echoid-s11587" xml:space="preserve">Piſces quod præterea falſum eſt in ſphæra recta, in ea enim crepuſcu-
              <lb/>
            lum æquatoris minimum eſt omnium. </s>
            <s xml:id="echoid-s11588" xml:space="preserve">apparebit etiam falſum eſſe, quod dicunt crepuſculum Capricorni eſſe
              <lb/>
            ſemper maius crepuſculo æquatoris; </s>
            <s xml:id="echoid-s11589" xml:space="preserve">nam in ſphęris obliquiſſimis, vt modo diximus, eſt omnium minimum. </s>
            <s xml:id="echoid-s11590" xml:space="preserve">
              <lb/>
            Secundo apparebit, quanto magis eleuatur polus, tanto maiora euadere crepuſcula, quæ omni patebunt ex
              <unsure/>
              <lb/>
            conſideratione @patiorum, quæ includuntur inter lineam horizontis, & </s>
            <s xml:id="echoid-s11591" xml:space="preserve">lineam crepuſculi, & </s>
            <s xml:id="echoid-s11592" xml:space="preserve">duos diame-
              <lb/>
            tro tropicorum; </s>
            <s xml:id="echoid-s11593" xml:space="preserve">in toto enim eo ſpatio fit crepuſculum. </s>
            <s xml:id="echoid-s11594" xml:space="preserve">hoc autem ſpatium ſemper maius eſt in eleuator@
              <lb/>
            ſphæra, adeo vt maximum ſit in paralella. </s>
            <s xml:id="echoid-s11595" xml:space="preserve">qua in re conſideranda eſt diuina prouidentia, quæ vt incommo-
              <lb/>
            da ſphærarum borealiorum, aliquo bono, compenſaret, maiora eis crepuſcula, ideſt, maiorem lucis copiam
              <lb/>
            attribuit, quam reliquis auſtralioribus; </s>
            <s xml:id="echoid-s11596" xml:space="preserve">quod paradoxum vulgo putatur. </s>
            <s xml:id="echoid-s11597" xml:space="preserve">fic crepuſcula ſphæræ borealiſ@imæ,
              <lb/>
            ideſt, paralellæ, conſtant menſibus tribus, diebus 7. </s>
            <s xml:id="echoid-s11598" xml:space="preserve">& </s>
            <s xml:id="echoid-s11599" xml:space="preserve">amplius; </s>
            <s xml:id="echoid-s11600" xml:space="preserve">at crepuſcula ſphæræ rectæ ſimul ſumpta dies
              <unsure/>
              <lb/>
            tantum 39. </s>
            <s xml:id="echoid-s11601" xml:space="preserve">circiter continet. </s>
            <s xml:id="echoid-s11602" xml:space="preserve">Tertio conſtabit in nonnullis ſphæris aliquando eſſe diem continuum ſine cre-
              <lb/>
            puſcui
              <unsure/>
            o, & </s>
            <s xml:id="echoid-s11603" xml:space="preserve">nocte: </s>
            <s xml:id="echoid-s11604" xml:space="preserve">aliquando diem cum crepuſculo tantum, quia ibi crepuſculum durat tota nocte: </s>
            <s xml:id="echoid-s11605" xml:space="preserve">aliquan-
              <lb/>
            do diem, crepuſculum, & </s>
            <s xml:id="echoid-s11606" xml:space="preserve">noctem. </s>
            <s xml:id="echoid-s11607" xml:space="preserve">aliquando crepuſculum cõtinuum; </s>
            <s xml:id="echoid-s11608" xml:space="preserve">aliquando noctem puram continuam; </s>
            <s xml:id="echoid-s11609" xml:space="preserve">
              <lb/>
            aliquando crepuſculum, & </s>
            <s xml:id="echoid-s11610" xml:space="preserve">noctem ſimul. </s>
            <s xml:id="echoid-s11611" xml:space="preserve">exempli cauſa; </s>
            <s xml:id="echoid-s11612" xml:space="preserve">conſtituto Analemmate ad eleuationem gr. </s>
            <s xml:id="echoid-s11613" xml:space="preserve">86. </s>
            <s xml:id="echoid-s11614" xml:space="preserve">quiæ
              <lb/>
            video diametrum Cancri totum ſupra horizontem, agnoſco Sole cancrum percurrente eſſe diem cõtinuum
              <lb/>
            purum, abſque crepuſculo, ibidem quia diameter æquatoris partim ſupra horizontem, partim infra </s>
          </p>
        </div>
      </text>
    </echo>
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