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-div241" type="section" level="1" n="158">
          <pb o="121" file="0143" n="148" rhead="Liber Decimus."/>
        </div>
        <div xml:id="echoid-div242" type="section" level="1" n="159">
          <head xml:id="echoid-head171" style="it" xml:space="preserve">De Horis. Cap. XVII.</head>
          <p>
            <s xml:id="echoid-s11795" xml:space="preserve">CVm iam de annis, de diebus, de crepuſculis ſatis dictum ſit, ſupereſt vt de horis etiam nonnulla adiunga-
              <lb/>
            mus, nam ex profeſſo de horis tractare pertinet ad tractatum de Horologijs: </s>
            <s xml:id="echoid-s11796" xml:space="preserve">hora enim eſt pars vigeſi-
              <lb/>
            ma quarta diei naturalis. </s>
            <s xml:id="echoid-s11797" xml:space="preserve">Horæ Aſtronomicæ ſunt partes diei Aſtronomici, qui incipit a meridie, atque in
              <lb/>
            meridiem deſinit. </s>
            <s xml:id="echoid-s11798" xml:space="preserve">Horæ Babylonicæ, ſiue ab ortu, ſunt partes diei Babylonici incipientis ab ortu Solis, at-
              <lb/>
            que in eundem ortum deſinentis. </s>
            <s xml:id="echoid-s11799" xml:space="preserve">Horæ Italicæ ſiue ab occaſu, ſunt partes diei more Italorum, incipientis ab
              <lb/>
            occaſu Solis, vſque ad alterum occaſum perdurantis. </s>
            <s xml:id="echoid-s11800" xml:space="preserve">Horæ antiquæ erant partes duodecimæ tam diei quam
              <lb/>
            noctis artificialis, de quibus ſcriptum eſt in Euangelio, nonne 12. </s>
            <s xml:id="echoid-s11801" xml:space="preserve">ſunt horæ diei. </s>
            <s xml:id="echoid-s11802" xml:space="preserve">ſit ergo problema primum
              <lb/>
            de horis Italicis.</s>
            <s xml:id="echoid-s11803" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div243" type="section" level="1" n="160">
          <head xml:id="echoid-head172" style="it" xml:space="preserve">Quota ſit hora Italica interdiu ex Sphæra materiali indagare.</head>
          <p>
            <s xml:id="echoid-s11804" xml:space="preserve">HAbeas primo gradum Solis in eclyptica pro oblata die; </s>
            <s xml:id="echoid-s11805" xml:space="preserve">deinde ſphæra Aſtronomicè conſtituta, pri-
              <lb/>
            mum mobile ſic motu diurno conuerte, vt gradus Solis ad Solem ipſum collucentem directè aſpiciat;
              <lb/>
            </s>
            <s xml:id="echoid-s11806" xml:space="preserve">quod exactè fiet ſi vmbra Zodiaci tota ceciderit in concauum partis Zodiaci oppoſitæ, ita vt torum illud con-
              <lb/>
            cauum exactè obumbretur. </s>
            <s xml:id="echoid-s11807" xml:space="preserve">tunc nota gradum æquatoris tangentem horizontem occiduum. </s>
            <s xml:id="echoid-s11808" xml:space="preserve">dein verte pri-
              <lb/>
            mum mobile donec gradus Solis horizontem occiduum attingat, atque iterum nota gradum æquatoris, qui
              <lb/>
            eundem horizontem tangi. </s>
            <s xml:id="echoid-s11809" xml:space="preserve">numera iam gradus æquatoris inter hos duos gradus interceptos, eoſq; </s>
            <s xml:id="echoid-s11810" xml:space="preserve">in tẽpus,
              <lb/>
            ſeu horas conuerte, numerumque horarum inuentum deme à 24. </s>
            <s xml:id="echoid-s11811" xml:space="preserve">ſic enim relinquitur numerus horarum ab
              <lb/>
            occaſu, ſeu Italicarum tunc temporis elapſarum.</s>
            <s xml:id="echoid-s11812" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div244" type="section" level="1" n="161">
          <head xml:id="echoid-head173" style="it" xml:space="preserve">Qua hora Italica Sol oriatur, ſit meridies, & medianox.</head>
          <p>
            <s xml:id="echoid-s11813" xml:space="preserve">1 TEmpus diurnum, vti diximus ſupra in tractatu de quantitate dierum artificialium, prius inuentum
              <lb/>
            de me à 24. </s>
            <s xml:id="echoid-s11814" xml:space="preserve">ſic enim relinquetur tempus nocturnum, ideſt, numerus horarum noctis, quibus elapſis
              <lb/>
            Soloritur.</s>
            <s xml:id="echoid-s11815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11816" xml:space="preserve">2 Deme tempus ſemidiurnum à 24. </s>
            <s xml:id="echoid-s11817" xml:space="preserve">reſiduus enim numerus eſt numerus horarum, quibus exactis meri-
              <lb/>
            dies eſt.</s>
            <s xml:id="echoid-s11818" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11819" xml:space="preserve">3 lam dimidium temporis nocturni, ideſt, dimidium numeri horarum nocturnarum exhibebit horam
              <lb/>
            mediæ noctis.</s>
            <s xml:id="echoid-s11820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11821" xml:space="preserve">Cæterum quod ad alia horarum genera attinet, ne ſim longior, facilè fuerit cuique ſtudioſo eadem inda-
              <lb/>
            gare, quæ de Italicis modo ſunt indagata.</s>
            <s xml:id="echoid-s11822" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div245" type="section" level="1" n="162">
          <head xml:id="echoid-head174" style="it" xml:space="preserve">Cur Solis illuminationes per quæuis foramina ingredientes rotunda
            <lb/>
          appareant. Cap. X V III.</head>
          <p>
            <s xml:id="echoid-s11823" xml:space="preserve">SEquitur iam, vt admirabile quiddam de Solis illuminatione elucidemus, qua ratione videlicet fieri poſ-
              <lb/>
            ſit, vt Solis illuminationes quæ per foramina tectorum, aut feneſtrarum anguloſa, ac valdè irregularia il-
              <lb/>
            labuntur, perpetuo inuita foraminis figura, in oppoſitis planis, aut ouales, aut rotundæ appareant. </s>
            <s xml:id="echoid-s11824" xml:space="preserve">huic pul-
              <lb/>
            cherrimæ quæſtioni, quæ ſuperiorum philoſophantiũ ingenia mirè vexauit, alias in opere de locis Mathem.
              <lb/>
            </s>
            <s xml:id="echoid-s11825" xml:space="preserve">Ariſtotelis Geometricè reſpondimus; </s>
            <s xml:id="echoid-s11826" xml:space="preserve">nunc aliter, ſed facilius ex 10. </s>
            <s xml:id="echoid-s11827" xml:space="preserve">Keplero hac experientia ſatisfaciemus. </s>
            <s xml:id="echoid-s11828" xml:space="preserve">
              <lb/>
            Summo igitur laqueari affige corpus aliquod, verbi gratia, rotundam Tabellam, quæ Solem referat; </s>
            <s xml:id="echoid-s11829" xml:space="preserve">infra
              <lb/>
            quam in medio inter ipſam, & </s>
            <s xml:id="echoid-s11830" xml:space="preserve">pauimentum, ſit foramen aliquod, verbi gratia triangulare, iam ex aliquo
              <lb/>
            puncto peripheriæ rotundæ deſcendat filum, quod ſit ſolaris radij inſtar, per foramen illud tri
              <unsure/>
            angulare ad
              <lb/>
            pauimentum filum iſtud ſecus trianguli latera ab aliquo circumlatum, altero extremo inferiori ſignet in pa-
              <lb/>
            nimento veſtigium. </s>
            <s xml:id="echoid-s11831" xml:space="preserve">idemque fiat ex quatuor, aut quinque punctis eiuſdem peripheriæ, & </s>
            <s xml:id="echoid-s11832" xml:space="preserve">illico in pauimento
              <lb/>
            apparebunt quatuor, aut quinque triangula in orbem conſtituta. </s>
            <s xml:id="echoid-s11833" xml:space="preserve">ſicque ex omnibus illius pũctis omnia trian-
              <lb/>
            gula in pauimento delineata in gyrum conſtituta apparebunt; </s>
            <s xml:id="echoid-s11834" xml:space="preserve">ac propterea omnes ſimui rotundam quãdam
              <lb/>
            figuram efficiunt. </s>
            <s xml:id="echoid-s11835" xml:space="preserve">quanto autem foramen illud fuerit ſublimius, tanto citius triangula illa in rotundiorem
              <lb/>
            orbem ſeſe accommodabunt. </s>
            <s xml:id="echoid-s11836" xml:space="preserve">quod ſi foramen illud non ſit perpendiculariter ſub Tabella, ſed ad partem
              <lb/>
            vnam, ita vt filum per illud recta intrans obliquè pauimento accidat, tunc triangula illa ſeſe in oualem figurã
              <lb/>
            componunt. </s>
            <s xml:id="echoid-s11837" xml:space="preserve">ex hac igitur obſeruatione diligenter facta, & </s>
            <s xml:id="echoid-s11838" xml:space="preserve">conſiderata, variatiſq; </s>
            <s xml:id="echoid-s11839" xml:space="preserve">foraminibus ac Tabellæ
              <lb/>
            @guris, manifeſtè apparebit qua ratione ſua Sol illuminationes ſemper, aut rotundas efficiat, aut ouales, aut
              <lb/>
            cclypſis tempore eclypſatas.</s>
            <s xml:id="echoid-s11840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11841" xml:space="preserve">Hæc porro conſideratio, vt rectè perficiatur eo indiget principio, quod ſupra poſuimus, à quolibet vi-
              <lb/>
            delicet Solis puncto, lucem per lineas rectas quoquo verſus emicare; </s>
            <s xml:id="echoid-s11842" xml:space="preserve">ſic enim non ſolum à punctis periphe-
              <lb/>
            riæ, ſed a quolibet etiam ſolaris diſci puncto, radij per foramina ad rotundas illuminationes efficiendas
              <unsure/>
              <lb/>
            prodibunt.</s>
            <s xml:id="echoid-s11843" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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