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-div198" type="section" level="1" n="128">
          <p>
            <s xml:id="echoid-s9421" xml:space="preserve">
              <pb o="96" file="0116" n="120" rhead="De Mundi Fabrica,"/>
            que 38. </s>
            <s xml:id="echoid-s9422" xml:space="preserve">abiectis 30.</s>
            <s xml:id="echoid-s9423" xml:space="preserve">′ ſuperſunt 8. </s>
            <s xml:id="echoid-s9424" xml:space="preserve">dies pro ætate ***, quam ſupra inuenimus eſſe tantum 7. </s>
            <s xml:id="echoid-s9425" xml:space="preserve">quæ diſcrepantia in-
              <lb/>
            de oritur, quia hæ duæ regulæ ſunt ciuiles, & </s>
            <s xml:id="echoid-s9426" xml:space="preserve">populares, non omnino Aſtronomicæ, & </s>
            <s xml:id="echoid-s9427" xml:space="preserve">propterea ætatem ***,
              <lb/>
            non omnino exactè exhibent: </s>
            <s xml:id="echoid-s9428" xml:space="preserve">ſequuntur enim medium motum *** non verum.</s>
            <s xml:id="echoid-s9429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9430" xml:space="preserve">Sciendum etiaminitio anni incipere nouas epactas, ac nouum aureum, numerum; </s>
            <s xml:id="echoid-s9431" xml:space="preserve">ideſt, ad primam Ia-
              <lb/>
            nuarij diem.</s>
            <s xml:id="echoid-s9432" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9433" xml:space="preserve">Ratio huius vulgaris regulæ, quam ſolum apud Ioan. </s>
            <s xml:id="echoid-s9434" xml:space="preserve">Lucidum vidi, hæc eſt. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">Primo in duobus primis
              <lb/>
            menſibus Ianuarij, & </s>
            <s xml:id="echoid-s9436" xml:space="preserve">Februarij computantur tantum dies epactæ currentis, & </s>
            <s xml:id="echoid-s9437" xml:space="preserve">dies menſis, quia epactæ per-
              <lb/>
            tinent ad primam anni lunationem, & </s>
            <s xml:id="echoid-s9438" xml:space="preserve">dies menſis pariter ſunt dies lunę; </s>
            <s xml:id="echoid-s9439" xml:space="preserve">vt in allato exemplo ad diem 18. </s>
            <s xml:id="echoid-s9440" xml:space="preserve">Ia-
              <lb/>
            nuarij; </s>
            <s xml:id="echoid-s9441" xml:space="preserve">computo dies 18. </s>
            <s xml:id="echoid-s9442" xml:space="preserve">quia eos Luna acquiſciuit a principio anni vſq; </s>
            <s xml:id="echoid-s9443" xml:space="preserve">ad 18. </s>
            <s xml:id="echoid-s9444" xml:space="preserve">diem; </s>
            <s xml:id="echoid-s9445" xml:space="preserve">computo etiam epactam
              <lb/>
            12. </s>
            <s xml:id="echoid-s9446" xml:space="preserve">quia totidem dies habebat Luna in principi
              <unsure/>
            o anni. </s>
            <s xml:id="echoid-s9447" xml:space="preserve">quando ſumma excedit 30. </s>
            <s xml:id="echoid-s9448" xml:space="preserve">abijcitur 30. </s>
            <s xml:id="echoid-s9449" xml:space="preserve">quæ eſt inte-
              <lb/>
            gra lunatio, & </s>
            <s xml:id="echoid-s9450" xml:space="preserve">accipitur exceſſus pro ætate ***, quæritur enim ætas Lunæ, omiſſis integris lunationibus. </s>
            <s xml:id="echoid-s9451" xml:space="preserve">in his
              <lb/>
            duobus menſibus non computantur Calendæ, quia hi duo menſes ſimul efficiunt duas integras lunationes,
              <lb/>
            ideſt, dies 59. </s>
            <s xml:id="echoid-s9452" xml:space="preserve">eſt enim prima lunatio dierum 30. </s>
            <s xml:id="echoid-s9453" xml:space="preserve">ſecunda vero dierum 29. </s>
            <s xml:id="echoid-s9454" xml:space="preserve">qui ſimul pariter efficiunt 59. </s>
            <s xml:id="echoid-s9455" xml:space="preserve">in re-
              <lb/>
            liquis 10. </s>
            <s xml:id="echoid-s9456" xml:space="preserve">menſibus, computantur etiam Calendæ eorum, ideſt, pro ſingulis dies 1. </s>
            <s xml:id="echoid-s9457" xml:space="preserve">quia à Martio inci
              <unsure/>
            uſiuè in-
              <lb/>
            cipiendo ſinguli mẽſes ſuperant lunationem vnam vno die, qui etiam in ætatem lunationum præteritarum,
              <lb/>
            computari debent. </s>
            <s xml:id="echoid-s9458" xml:space="preserve">Exempli gr. </s>
            <s xml:id="echoid-s9459" xml:space="preserve">hoc anno 1616. </s>
            <s xml:id="echoid-s9460" xml:space="preserve">die 13. </s>
            <s xml:id="echoid-s9461" xml:space="preserve">Martij; </s>
            <s xml:id="echoid-s9462" xml:space="preserve">pro ætate Lunæ indaganda computabam 31.
              <lb/>
            </s>
            <s xml:id="echoid-s9463" xml:space="preserve">dies menſis; </s>
            <s xml:id="echoid-s9464" xml:space="preserve">item 12. </s>
            <s xml:id="echoid-s9465" xml:space="preserve">pro epacta, quia pertinent ad lunationes hactenus elapſas. </s>
            <s xml:id="echoid-s9466" xml:space="preserve">computo tandem 1. </s>
            <s xml:id="echoid-s9467" xml:space="preserve">pro Ca-
              <lb/>
            lendis Martij quia Martius habet dies 31. </s>
            <s xml:id="echoid-s9468" xml:space="preserve">quibus vno die ſuperat lunationem ſibi reſpondentem, quæ eſt 30. </s>
            <s xml:id="echoid-s9469" xml:space="preserve">
              <lb/>
            dierum. </s>
            <s xml:id="echoid-s9470" xml:space="preserve">omnibus ſimul computatis fit ſumma dierum 44. </s>
            <s xml:id="echoid-s9471" xml:space="preserve">abiectis 30. </s>
            <s xml:id="echoid-s9472" xml:space="preserve">ſuperſunt 14. </s>
            <s xml:id="echoid-s9473" xml:space="preserve">dies ætatis Lunę. </s>
            <s xml:id="echoid-s9474" xml:space="preserve">Vbi con-
              <lb/>
            ſiderandum eſt, quod tacite omittuntur omnes integræ lunationes a principio anni, vſque ad oblatui
              <unsure/>
            n diem
              <unsure/>
              <lb/>
            exactæ; </s>
            <s xml:id="echoid-s9475" xml:space="preserve">vna ſcilicet pro ſingulis menſibus, ſeu pro quolibet menſe. </s>
            <s xml:id="echoid-s9476" xml:space="preserve">Computantur tandem Calendæ, quia vl-
              <lb/>
            tra integras Lunas, quilibet menſis exhibet dies vnum amplius ad Lunam pertinentem. </s>
            <s xml:id="echoid-s9477" xml:space="preserve">ſuntque hæ Calen-
              <lb/>
            dæ, tanquam epactæ quædam partiales menſium præterit
              <unsure/>
            orum; </s>
            <s xml:id="echoid-s9478" xml:space="preserve">ex quibus paulatim conflatur epacta ſeq. </s>
            <s xml:id="echoid-s9479" xml:space="preserve">an-
              <lb/>
            ni. </s>
            <s xml:id="echoid-s9480" xml:space="preserve">quamuis autem ſin tantumt 10. </s>
            <s xml:id="echoid-s9481" xml:space="preserve">mẽſes vſq; </s>
            <s xml:id="echoid-s9482" xml:space="preserve">ad finem anni, aſtronomi tamen, qui has regulas ciuiles condi-
              <lb/>
            derunt, aſſumunt pro epacta 11. </s>
            <s xml:id="echoid-s9483" xml:space="preserve">ſic enim melius regulæ huius regulas conſeruatur.</s>
            <s xml:id="echoid-s9484" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9485" xml:space="preserve">Sciendum poſtremo, haſce regulas epactales, non exactè veram Lunæ etatem exhibere, ſed ſemper paulo
              <lb/>
            minorem vera, quia tamen exiguus eſt error, ideo in vulgus vtiles ſunt.</s>
            <s xml:id="echoid-s9486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9487" xml:space="preserve">4 Per Aſtronomicum calculum, & </s>
            <s xml:id="echoid-s9488" xml:space="preserve">quidem præciſius, quam per præcedentes vulgares regulas. </s>
            <s xml:id="echoid-s9489" xml:space="preserve">primo
              <lb/>
            igitur oportet ſcire, ad datum temporis inſtans, loca luminarium in Zodiaco, & </s>
            <s xml:id="echoid-s9490" xml:space="preserve">conſequẽtur quanta ſit elon-
              <lb/>
            gatio *** a ***, quam propoſ. </s>
            <s xml:id="echoid-s9491" xml:space="preserve">6. </s>
            <s xml:id="echoid-s9492" xml:space="preserve">inuenimus fuiſſe gr. </s>
            <s xml:id="echoid-s9493" xml:space="preserve">30. </s>
            <s xml:id="echoid-s9494" xml:space="preserve">quoniam vero Luna elongatur a Sole diario motu gr.
              <lb/>
            </s>
            <s xml:id="echoid-s9495" xml:space="preserve">12′ 11′. </s>
            <s xml:id="echoid-s9496" xml:space="preserve">ſi prædicta elongatio diuidatur per hunc motum diarium, quotiens numerus indicabit quot diebus
              <lb/>
            anteceſſerit nouilunium, quare cum 12. </s>
            <s xml:id="echoid-s9497" xml:space="preserve">11′. </s>
            <s xml:id="echoid-s9498" xml:space="preserve">contineantur bis in 30. </s>
            <s xml:id="echoid-s9499" xml:space="preserve">neceſſe erit nouilunium præceſſiſſe duo-
              <lb/>
            bus diebus momẽtum temporis dati, Iulij die 16. </s>
            <s xml:id="echoid-s9500" xml:space="preserve">h. </s>
            <s xml:id="echoid-s9501" xml:space="preserve">1 {1/4}. </s>
            <s xml:id="echoid-s9502" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9503" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9504" xml:space="preserve">rurſus diuiſis 30. </s>
            <s xml:id="echoid-s9505" xml:space="preserve">per 12. </s>
            <s xml:id="echoid-s9506" xml:space="preserve">11′ ſuperſunt 338′. </s>
            <s xml:id="echoid-s9507" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9508" xml:space="preserve">
              <lb/>
            ea diuidenda erant per horariam elongationem Lunæ a Sole: </s>
            <s xml:id="echoid-s9509" xml:space="preserve">quæ ex diaria 12. </s>
            <s xml:id="echoid-s9510" xml:space="preserve">11′, facilè habetur, eſt enim. </s>
            <s xml:id="echoid-s9511" xml:space="preserve">
              <lb/>
            illius pars 24. </s>
            <s xml:id="echoid-s9512" xml:space="preserve">videlicet 30′. </s>
            <s xml:id="echoid-s9513" xml:space="preserve">27″. </s>
            <s xml:id="echoid-s9514" xml:space="preserve">diuiſis igiter 338′. </s>
            <s xml:id="echoid-s9515" xml:space="preserve">per 30′. </s>
            <s xml:id="echoid-s9516" xml:space="preserve">27'
              <unsure/>
            . </s>
            <s xml:id="echoid-s9517" xml:space="preserve">proueniũt ferè 11. </s>
            <s xml:id="echoid-s9518" xml:space="preserve">horæ ſcilicet, quibus præter
              <lb/>
            duos dies nouilunium anteceſſit tempus datum. </s>
            <s xml:id="echoid-s9519" xml:space="preserve">præceſſit igitur dies 2. </s>
            <s xml:id="echoid-s9520" xml:space="preserve">h. </s>
            <s xml:id="echoid-s9521" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9522" xml:space="preserve">quibus demptis ex dato tempo-
              <lb/>
            re diei 16. </s>
            <s xml:id="echoid-s9523" xml:space="preserve">h. </s>
            <s xml:id="echoid-s9524" xml:space="preserve">1 {1/4}. </s>
            <s xml:id="echoid-s9525" xml:space="preserve">p.</s>
            <s xml:id="echoid-s9526" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9527" xml:space="preserve">remanet dies 13. </s>
            <s xml:id="echoid-s9528" xml:space="preserve">h. </s>
            <s xml:id="echoid-s9529" xml:space="preserve">14 {1/4}. </s>
            <s xml:id="echoid-s9530" xml:space="preserve">p.</s>
            <s xml:id="echoid-s9531" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9532" xml:space="preserve">ideſt, duabus hor. </s>
            <s xml:id="echoid-s9533" xml:space="preserve">poſt mediam noctem, quæ interce
              <unsure/>
            -
              <lb/>
            dit inter diem 13. </s>
            <s xml:id="echoid-s9534" xml:space="preserve">& </s>
            <s xml:id="echoid-s9535" xml:space="preserve">14.</s>
            <s xml:id="echoid-s9536" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div200" type="section" level="1" n="129">
          <head xml:id="echoid-head141" style="it" xml:space="preserve">Aliter exactius.</head>
          <p>
            <s xml:id="echoid-s9537" xml:space="preserve">EX calculo ***, quem infra habebis, necnon ex calculo ***, habeas ad datum tempus mediam vtriuſq; </s>
            <s xml:id="echoid-s9538" xml:space="preserve">lon-
              <lb/>
            gitudinem ab æquinoctio atque hinc mediam *** a *** elongationem, quam per diurnam elongationem
              <lb/>
            mediam 12. </s>
            <s xml:id="echoid-s9539" xml:space="preserve">11′. </s>
            <s xml:id="echoid-s9540" xml:space="preserve">diuide, quotiens enim dabit dies, quibus medium nouil. </s>
            <s xml:id="echoid-s9541" xml:space="preserve">præceſſit datum tempus. </s>
            <s xml:id="echoid-s9542" xml:space="preserve">medium
              <lb/>
            noui
              <unsure/>
            l. </s>
            <s xml:id="echoid-s9543" xml:space="preserve">eſt coniunctio centri epicycli cum loco Solis medio. </s>
            <s xml:id="echoid-s9544" xml:space="preserve">habito temporis coniunctionis mediæ ☌, ad il-
              <lb/>
            lud computa æquationes tam ***, quam ***, ex quibus cognoſces quantum tempus mediæ ☌, diſtent vera lo-
              <lb/>
            ca luminarium. </s>
            <s xml:id="echoid-s9545" xml:space="preserve">ſi Luna Solem præcedit, i
              <unsure/>
            deſt ſi habet minorem diſtantiam ab æquinoctio, nondum facta eſt
              <lb/>
            vera ☌, ſeu nouil, conſidera igitur veram luminarium diſlantiam, ideſt, quot gradus diſtent, & </s>
            <s xml:id="echoid-s9546" xml:space="preserve">conijcere po-
              <lb/>
            teris quot horis poſt mediam ☌, futurum ſit verum nouilunium: </s>
            <s xml:id="echoid-s9547" xml:space="preserve">ſi vero Luna Solẽ ſequatur, iam ante mediã
              <unsure/>
              <lb/>
            ☌, præceſſit vera; </s>
            <s xml:id="echoid-s9548" xml:space="preserve">idque tot horis, quot diſtantia luminarium vera importare videris. </s>
            <s xml:id="echoid-s9549" xml:space="preserve">quia vera in ſuperiori
              <lb/>
            exemplo, tempore mediæ ☌, quæ fuit circa meridiem diei 13. </s>
            <s xml:id="echoid-s9550" xml:space="preserve">Luna ſequebatur per 3. </s>
            <s xml:id="echoid-s9551" xml:space="preserve">circiter gradus, quibus
              <lb/>
            Luna a Sole elongatur per horas ferè 6. </s>
            <s xml:id="echoid-s9552" xml:space="preserve">ideo verum nouilunium factum eſt die 13. </s>
            <s xml:id="echoid-s9553" xml:space="preserve">hora poſt merid. </s>
            <s xml:id="echoid-s9554" xml:space="preserve">18. </s>
            <s xml:id="echoid-s9555" xml:space="preserve">Præ-
              <lb/>
            terea quia Luna erat in ſuperiori parte epicycli propè apogæum, vbi reſpectu motus longitudinis, & </s>
            <s xml:id="echoid-s9556" xml:space="preserve">elon-
              <lb/>
            gationis a ***, propterea tardiſſima euadit, fit vt verum nouilunium adhuc prius acciderit; </s>
            <s xml:id="echoid-s9557" xml:space="preserve">videlicet circa.
              <lb/>
            </s>
            <s xml:id="echoid-s9558" xml:space="preserve">diei 31. </s>
            <s xml:id="echoid-s9559" xml:space="preserve">mediam noctem. </s>
            <s xml:id="echoid-s9560" xml:space="preserve">ex quibus etiam ætas *** conſtabit. </s>
            <s xml:id="echoid-s9561" xml:space="preserve">Verum iſta ſubtilius indagere, extra præfixas no-
              <lb/>
            bis metas nimis excurrit.</s>
            <s xml:id="echoid-s9562" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div201" type="section" level="1" n="130">
          <head xml:id="echoid-head142" style="it" xml:space="preserve">Inuenire tempus, ſeu horas, quibus noctu Luna luceat. Propoſ. VIII.</head>
          <p>
            <s xml:id="echoid-s9563" xml:space="preserve">HIc Aſtronomi loquuntur de horis inæqualibus, quibus olim Romani vtebantur, & </s>
            <s xml:id="echoid-s9564" xml:space="preserve">quibus tam æſtate,
              <lb/>
            quam hyeme; </s>
            <s xml:id="echoid-s9565" xml:space="preserve">tam diem, quam noctẽ, in 12. </s>
            <s xml:id="echoid-s9566" xml:space="preserve">horas diuidebant, quæ propterea dictæ ſunt inæquales, quia
              <lb/>
            pro varia diei, ac noct s magnitudine ipſæ quoque variæ erant. </s>
            <s xml:id="echoid-s9567" xml:space="preserve">Cum enim maximi erant dies, ipſæ quoque
              <lb/>
            maximæ erant; </s>
            <s xml:id="echoid-s9568" xml:space="preserve">cum minimi, minimæ. </s>
            <s xml:id="echoid-s9569" xml:space="preserve">ſemper tamen ſunt partes diei, vel noctis, duodecimæ de his in </s>
          </p>
        </div>
      </text>
    </echo>
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