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-div229" type="section" level="1" n="148">
          <pb o="110" file="0130" n="134" rhead="De Mundi Fabrica,"/>
        </div>
        <div xml:id="echoid-div230" type="section" level="1" n="149">
          <head xml:id="echoid-head161" style="it" xml:space="preserve">Quantitas dierum artificialium. Cap. XV.</head>
          <p>
            <s xml:id="echoid-s11100" xml:space="preserve">PRimo conſiderandum eſt cur dies artificiales varij ſint in varijs terræ locis; </s>
            <s xml:id="echoid-s11101" xml:space="preserve">ſub æquatore enim vbi nihil
              <lb/>
            eleuatur polus perpetuum eſt æquinoctium; </s>
            <s xml:id="echoid-s11102" xml:space="preserve">in alijs vero locis vbi polus eleuatur magnam ſubeunt va-
              <lb/>
            rietatem, tum ſi inuicem comparentur dies eiuſdem eleuationis, tum etiam ſi cum diebus alterius eleuationis
              <lb/>
            conferantur. </s>
            <s xml:id="echoid-s11103" xml:space="preserve">in eadem enim eleuatione boreali dies lõgiſſimus eſt in tropico Cancri, poſtea decreſcunt vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s11104" xml:space="preserve">ad tropicum Capricorni, vbi nox lõgiſſima efficitur; </s>
            <s xml:id="echoid-s11105" xml:space="preserve">vt vulgo notum eſt. </s>
            <s xml:id="echoid-s11106" xml:space="preserve">in diuerſis autem eleuationibus hic
              <lb/>
            ordo ſeruatur, vt quanto maior eſt eleuatio poli. </s>
            <s xml:id="echoid-s11107" xml:space="preserve">tanto maior ſit dies longiſſima æſtiualis; </s>
            <s xml:id="echoid-s11108" xml:space="preserve">tantoq; </s>
            <s xml:id="echoid-s11109" xml:space="preserve">minor nox. </s>
            <s xml:id="echoid-s11110" xml:space="preserve">
              <lb/>
            hyemalis verò maxima. </s>
            <s xml:id="echoid-s11111" xml:space="preserve">cur autem hæc contingant, vt intelligas, conſiderandum eſt, Solem dum ab vno tro-
              <lb/>
            pico ad alterum accedit, deſcribere motu diurno circulos ferè 182. </s>
            <s xml:id="echoid-s11112" xml:space="preserve">inuicem paralellos: </s>
            <s xml:id="echoid-s11113" xml:space="preserve">quotidie videlices
              <lb/>
            vnum, quamuis reuera Sol non circulos, ſed ſpiras efficiat, vt alias diximus: </s>
            <s xml:id="echoid-s11114" xml:space="preserve">attamen ſine vllo errore, imò fa-
              <lb/>
            cilioris intelligentiæ cauſa, conſiderantur vt circuli. </s>
            <s xml:id="echoid-s11115" xml:space="preserve">hi igitur dicuntur circuli dierum naturalium, arcus ve-
              <lb/>
            ro ſiue portiones ipſorum ſupra horizontem extantes dicuntur arcus diurni dierum artificialium; </s>
            <s xml:id="echoid-s11116" xml:space="preserve">qui vero
              <lb/>
            infra horizontem arcus nocturni noctium artificialium. </s>
            <s xml:id="echoid-s11117" xml:space="preserve">in ſphæra autem materiali tres tantum horum cir-
              <lb/>
            culorum, ad vitandam confuſionem, ponuntur: </s>
            <s xml:id="echoid-s11118" xml:space="preserve">duo videlicet tropici, & </s>
            <s xml:id="echoid-s11119" xml:space="preserve">æquator. </s>
            <s xml:id="echoid-s11120" xml:space="preserve">cum igitur Sol motu diur-
              <lb/>
            no vniformiter moueatur, ſequitur vbi arcus diurni fuerint æquales nocturnis, dies noctibus pariter adæqua-
              <lb/>
            ri. </s>
            <s xml:id="echoid-s11121" xml:space="preserve">vbi vero maiores, vel minores fuerint, maiores pariter, ac minores fore dies noctibus. </s>
            <s xml:id="echoid-s11122" xml:space="preserve">Hinc ſequitur in
              <lb/>
            ſphæra recta perpetuum eſſe æquinoctium, quod ex materiali ſphæra ita conſtituta, vt poli mundi ſint in ho-
              <lb/>
            rizonte (quæ eſt ſphæræ rectæ conſtitutio) facile intelligi poteſt. </s>
            <s xml:id="echoid-s11123" xml:space="preserve">ex tali enim cõſtitutione apparet vtrum-
              <lb/>
            que tropicum, æquatorem, ac proinde reliquos omnes Solis paralellos ibi conceptos, bifariam ab horizonte
              <lb/>
            diuidi, ac propterea arcus diurnos, ac nocturnos eſſe æquales. </s>
            <s xml:id="echoid-s11124" xml:space="preserve">in ſphæris vero obliquis vſq; </s>
            <s xml:id="echoid-s11125" xml:space="preserve">ad poli eleuatio-
              <lb/>
            nem gr. </s>
            <s xml:id="echoid-s11126" xml:space="preserve">66 {1/2}. </s>
            <s xml:id="echoid-s11127" xml:space="preserve">quoniã horizon ſecat omnes paralellos, excepto æquatore, inæqualiter, ita vt omnes arcus diur-
              <lb/>
            ni, qui ſunt ab æquatore ad polum eleuatum, maiores ſint nocturnis: </s>
            <s xml:id="echoid-s11128" xml:space="preserve">reliqui vero ad polum occultum vltra
              <lb/>
            æquatorem, ſint minores nocturnis (quod in materiali ſphæra obliquè conſtituta apparebit) ſequitur maio-
              <lb/>
            res eſſe dies verſus polum eleuatum quam verſus depreſſum. </s>
            <s xml:id="echoid-s11129" xml:space="preserve">quorum cauſa eſt polorum infra aut ſupra ho-
              <lb/>
            rizontem eleuatio, ac depreſſio. </s>
            <s xml:id="echoid-s11130" xml:space="preserve">hinc ſequitur in noſtra ſphæra, cui boreus polus eleuatur, dies æſtiuos hyber-
              <lb/>
            nis maiores eſſe; </s>
            <s xml:id="echoid-s11131" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s11132" xml:space="preserve">inter æſtiuos, eos cæteris maiores eſſe, qui tropico Cancri, vbi dies fit maximus, propio-
              <lb/>
            res fuerint. </s>
            <s xml:id="echoid-s11133" xml:space="preserve">cuius contrarium accidit in parte auſtrali. </s>
            <s xml:id="echoid-s11134" xml:space="preserve">notandum etiam arcus diurnos boreales eſſe æquales
              <lb/>
            arcubus nocturnis auſtralibus; </s>
            <s xml:id="echoid-s11135" xml:space="preserve">& </s>
            <s xml:id="echoid-s11136" xml:space="preserve">è contra. </s>
            <s xml:id="echoid-s11137" xml:space="preserve">lam vero vbi polus eleuatur præcisè gr. </s>
            <s xml:id="echoid-s11138" xml:space="preserve">66 {1/2}. </s>
            <s xml:id="echoid-s11139" xml:space="preserve">ac propterea tropi-
              <lb/>
            cus vnus totus ſupra horizontem emergit: </s>
            <s xml:id="echoid-s11140" xml:space="preserve">alter vero totus deprimitur, ita tamen vt horizontẽ in vnico pun-
              <lb/>
            cto tangant, ſequetur tam diem, quam noctem maximam conſtare hor. </s>
            <s xml:id="echoid-s11141" xml:space="preserve">24. </s>
            <s xml:id="echoid-s11142" xml:space="preserve">percurrente videlicet Sole tropi-
              <lb/>
            cos. </s>
            <s xml:id="echoid-s11143" xml:space="preserve">In eleuatiori vero ſphæra, quam gr. </s>
            <s xml:id="echoid-s11144" xml:space="preserve">66 {1/2} tam dies quam noctes conſtabunt hor. </s>
            <s xml:id="echoid-s11145" xml:space="preserve">pluſquam 24. </s>
            <s xml:id="echoid-s11146" xml:space="preserve">Demum
              <lb/>
            in ſphæra paralella, ſiue præcisè ſub polo, e@ it tam dies, quam nox, ſex menſium. </s>
            <s xml:id="echoid-s11147" xml:space="preserve">Porrò & </s>
            <s xml:id="echoid-s11148" xml:space="preserve">hoc non præter-
              <lb/>
            eundum, quod eodem tempore æquinoctium fit omnibus habitatoribus vbique terrarum; </s>
            <s xml:id="echoid-s11149" xml:space="preserve">quoniam in omni
              <lb/>
            ſphæræ conſtitutione excepta paralella, æquator ſecatur bifariam ab horizonte, vnde ai
              <unsure/>
            cus ipſius diurnus
              <lb/>
            æqualis ſemper eſt nocturno. </s>
            <s xml:id="echoid-s11150" xml:space="preserve">Extremo in ſphęra obliqua bini dies artificiales ab alterutro ſolſtitiorum æquè
              <lb/>
            remoti æquales ſunt. </s>
            <s xml:id="echoid-s11151" xml:space="preserve">quæ omnia inſpecta materiali ſphæra, eaq; </s>
            <s xml:id="echoid-s11152" xml:space="preserve">varijs habitatoribus accommodata, perſpi-
              <lb/>
            cua fiunt.</s>
            <s xml:id="echoid-s11153" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11154" xml:space="preserve">Reliquum eſt docere qua ratione inueſtigetur quãtitas diei, ac noctis artificialis in quauis poli eleuatione-
              <lb/>
            Primo igitur ex materiali ſphæra accurate cõſtructa, quales eſſe ſolent æneæ, ſic; </s>
            <s xml:id="echoid-s11155" xml:space="preserve">vbi eleuatio poli non tran-
              <lb/>
            ſcendit gr. </s>
            <s xml:id="echoid-s11156" xml:space="preserve">66 {1/2}. </s>
            <s xml:id="echoid-s11157" xml:space="preserve">ſiue vbi horizon ſecat omnes Solis paralellos, hanc quantitatem reperies. </s>
            <s xml:id="echoid-s11158" xml:space="preserve">Eleuato ſupra ho-
              <lb/>
            rizontem polo iuxta loci exigentiam, pone gradum Zodiaci quem Sol occupat, eo die, cuius quantitatem
              <lb/>
            quæris in horizonte orientali. </s>
            <s xml:id="echoid-s11159" xml:space="preserve">quo ibi manente nota illum æquatoris gradum, qui pariter orientalem hori-
              <lb/>
            zontem tangit; </s>
            <s xml:id="echoid-s11160" xml:space="preserve">poſtea primum mobile motu diurno reuolue, donec grad. </s>
            <s xml:id="echoid-s11161" xml:space="preserve">ille Solis ad occiduum horizontem
              <lb/>
            perueniat; </s>
            <s xml:id="echoid-s11162" xml:space="preserve">tandem numera gradus æquatoris ab illa nota ſupra horizontem exortos, nam ſingulæ graduum
              <lb/>
            quindenæ ſingulas horas effici
              <unsure/>
            unt. </s>
            <s xml:id="echoid-s11163" xml:space="preserve">vnde, & </s>
            <s xml:id="echoid-s11164" xml:space="preserve">ſemiſſes, & </s>
            <s xml:id="echoid-s11165" xml:space="preserve">quadrantes horarũ facile dignoſces. </s>
            <s xml:id="echoid-s11166" xml:space="preserve">idem circa quan-
              <lb/>
            titatem noctium obſeruandum eſt. </s>
            <s xml:id="echoid-s11167" xml:space="preserve">ſit exempli gr. </s>
            <s xml:id="echoid-s11168" xml:space="preserve">in noſtra poli eleuatione gr. </s>
            <s xml:id="echoid-s11169" xml:space="preserve">45. </s>
            <s xml:id="echoid-s11170" xml:space="preserve">inueſtiganda qnantitas diei
              <lb/>
            maximi, quando ſcilicet Sol eſt in primo gra. </s>
            <s xml:id="echoid-s11171" xml:space="preserve">Cancri, ad diem 22. </s>
            <s xml:id="echoid-s11172" xml:space="preserve">Iunij. </s>
            <s xml:id="echoid-s11173" xml:space="preserve">pono igitur primum Cancri gradum
              <lb/>
            in horizonte ortiuo, notoq; </s>
            <s xml:id="echoid-s11174" xml:space="preserve">ſimul æquatoris punctum ſimul cooriens; </s>
            <s xml:id="echoid-s11175" xml:space="preserve">poſtea ſphæræ primum mobile iuxta
              <lb/>
            diurnam conuerſionem conuerto, donec idem primus gradus Cancri horizontem occiduum attingat; </s>
            <s xml:id="echoid-s11176" xml:space="preserve">de-
              <lb/>
            mum manente ſic ſphæra numero grad. </s>
            <s xml:id="echoid-s11177" xml:space="preserve">omnes æquatoris in hac motione exortos, interceptos ſcilicet inter
              <lb/>
            notam in æquatore factam, & </s>
            <s xml:id="echoid-s11178" xml:space="preserve">horizontẽ orientalem. </s>
            <s xml:id="echoid-s11179" xml:space="preserve">reperioq; </s>
            <s xml:id="echoid-s11180" xml:space="preserve">gradus f rè 232 {1/2}. </s>
            <s xml:id="echoid-s11181" xml:space="preserve">quos diuido per 15. </s>
            <s xml:id="echoid-s11182" xml:space="preserve">& </s>
            <s xml:id="echoid-s11183" xml:space="preserve">pro-
              <lb/>
            uenit quotiens pariter 15. </s>
            <s xml:id="echoid-s11184" xml:space="preserve">reſiduiq; </s>
            <s xml:id="echoid-s11185" xml:space="preserve">ſunt gr. </s>
            <s xml:id="echoid-s11186" xml:space="preserve">ferè 7 {1/2}. </s>
            <s xml:id="echoid-s11187" xml:space="preserve">quare pronuncio diem hunc maximam conſtare ex horis
              <lb/>
            15 {1/2}. </s>
            <s xml:id="echoid-s11188" xml:space="preserve">quia quotiens eſt 15. </s>
            <s xml:id="echoid-s11189" xml:space="preserve">quæ efficiunt hor. </s>
            <s xml:id="echoid-s11190" xml:space="preserve">15. </s>
            <s xml:id="echoid-s11191" xml:space="preserve">& </s>
            <s xml:id="echoid-s11192" xml:space="preserve">ſuperſunt gr. </s>
            <s xml:id="echoid-s11193" xml:space="preserve">7 {1/2}. </s>
            <s xml:id="echoid-s11194" xml:space="preserve">qui dimidiam dant hor. </s>
            <s xml:id="echoid-s11195" xml:space="preserve">vel ex Tabula con-
              <lb/>
            uerſionis graduum, &</s>
            <s xml:id="echoid-s11196" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11197" xml:space="preserve">æquatoris in horas, &</s>
            <s xml:id="echoid-s11198" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11199" xml:space="preserve">reperio primo è regione gr. </s>
            <s xml:id="echoid-s11200" xml:space="preserve">230. </s>
            <s xml:id="echoid-s11201" xml:space="preserve">hor. </s>
            <s xml:id="echoid-s11202" xml:space="preserve">15. </s>
            <s xml:id="echoid-s11203" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11204" xml:space="preserve">20′. </s>
            <s xml:id="echoid-s11205" xml:space="preserve">deinde è re-
              <lb/>
            gione gr. </s>
            <s xml:id="echoid-s11206" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11207" xml:space="preserve">reperio hor.</s>
            <s xml:id="echoid-s11208" xml:space="preserve">0
              <unsure/>
            @3′. </s>
            <s xml:id="echoid-s11209" xml:space="preserve">Tandem è regione gr. </s>
            <s xml:id="echoid-s11210" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s11211" xml:space="preserve">ideſt, 30. </s>
            <s xml:id="echoid-s11212" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11213" xml:space="preserve">reperio c--;</s>
            <s xml:id="echoid-s11214" xml:space="preserve">2′. </s>
            <s xml:id="echoid-s11215" xml:space="preserve">Quorum ſumma efficiunt
              <lb/>
            h. </s>
            <s xml:id="echoid-s11216" xml:space="preserve">15 30′. </s>
            <s xml:id="echoid-s11217" xml:space="preserve">ſiue h. </s>
            <s xml:id="echoid-s11218" xml:space="preserve">15 {1/2}. </s>
            <s xml:id="echoid-s11219" xml:space="preserve">vt prius.</s>
            <s xml:id="echoid-s11220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11221" xml:space="preserve">Vbi vero polus eleuatur gr. </s>
            <s xml:id="echoid-s11222" xml:space="preserve">66 {1/2}. </s>
            <s xml:id="echoid-s11223" xml:space="preserve">vbi ſcilicet tropicus vnus tangit horizontem, totuſq; </s>
            <s xml:id="echoid-s11224" xml:space="preserve">ſupra eum emergit;
              <lb/>
            </s>
            <s xml:id="echoid-s11225" xml:space="preserve">alter è contrario tangens horizontem totus deprimitur, in tali inquam habitatione dies maximus, & </s>
            <s xml:id="echoid-s11226" xml:space="preserve">nox ma-
              <lb/>
            xima erunt 24. </s>
            <s xml:id="echoid-s11227" xml:space="preserve">horarum. </s>
            <s xml:id="echoid-s11228" xml:space="preserve">In maiore poſtea
              <unsure/>
            e
              <unsure/>
            le
              <unsure/>
            uatione vbi tropici non tangunt horizontem, dies maiores
              <lb/>
            ſunt hor. </s>
            <s xml:id="echoid-s11229" xml:space="preserve">24. </s>
            <s xml:id="echoid-s11230" xml:space="preserve">& </s>
            <s xml:id="echoid-s11231" xml:space="preserve">alicubi continent etiam menſes totos; </s>
            <s xml:id="echoid-s11232" xml:space="preserve">vt igitur ibi quantitas horum dierum continuorum re-
              <lb/>
            periatur ex ſphæra materiali, eleuato polo ad datam altitudinem, oportet diligenter notare arcum </s>
          </p>
        </div>
      </text>
    </echo>
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