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-div480" type="section" level="1" n="363">
          <pb o="222" file="0244" n="249" rhead="DE ECHO."/>
        </div>
        <div xml:id="echoid-div481" type="section" level="1" n="364">
          <head xml:id="echoid-head383" style="it" xml:space="preserve">Echo reſonat ex planis, quibus ſonus per lineam normalem occurrit. Theorema III.</head>
          <p>
            <s xml:id="echoid-s19080" xml:space="preserve">ID primo docet obſeruatio, vt in pręcedenti prima figura, ſi ſonorũ in A. </s>
            <s xml:id="echoid-s19081" xml:space="preserve">ſit in eo fitu ad parietem C B D.
              <lb/>
            </s>
            <s xml:id="echoid-s19082" xml:space="preserve">vt vox per lineam A B. </s>
            <s xml:id="echoid-s19083" xml:space="preserve">delata, normaliter offenſet ad parietem in B. </s>
            <s xml:id="echoid-s19084" xml:space="preserve">eadem vox articulata repercutitur ad
              <lb/>
            idem A. </s>
            <s xml:id="echoid-s19085" xml:space="preserve">ſi vero ſit in tali ſitu, vnde vox obliquè tantum in murum incidat, vox non reuertitur ad idem A. </s>
            <s xml:id="echoid-s19086" xml:space="preserve">
              <lb/>
            quod præterea ratio ſuadet, cum enim probatum ſi@ reflexionem hanc fieri per angulos æquales angulis in-
              <lb/>
            cidentiæ; </s>
            <s xml:id="echoid-s19087" xml:space="preserve">angulis autem incidentiæ ſint recti, ſequitur angulos etiam reflexionis eſſe rectos, ac propterea vo-
              <lb/>
            cem à muro reflecti per eandem lineam, per quam muro incidit, hacq; </s>
            <s xml:id="echoid-s19088" xml:space="preserve">ratione ad ipſum A. </s>
            <s xml:id="echoid-s19089" xml:space="preserve">ſonorum reuer-
              <lb/>
            ti. </s>
            <s xml:id="echoid-s19090" xml:space="preserve">Porrò quamuis ex innumeris lineis, quæ ex A. </s>
            <s xml:id="echoid-s19091" xml:space="preserve">ad parietem tendunt, vna tantum Geometricè loquendo
              <lb/>
            normalis ſit, vti A B. </s>
            <s xml:id="echoid-s19092" xml:space="preserve">cæteræ tamen ei propiores ſecundum ſenſum, pro normalibus aſſumi debent, vt om-
              <lb/>
            nes ſimul ad Echum efficiendam ſufficiant; </s>
            <s xml:id="echoid-s19093" xml:space="preserve">omnes enim ſimul aerem circa ſonorum A. </s>
            <s xml:id="echoid-s19094" xml:space="preserve">exiſtentem commo-
              <lb/>
            uent. </s>
            <s xml:id="echoid-s19095" xml:space="preserve">Ea propter exiſtimo paruam eſſe muri partem, quæ reaſpe reflectit ad ſonorum A. </s>
            <s xml:id="echoid-s19096" xml:space="preserve">quod etiam obſer-
              <lb/>
            uationi conguit; </s>
            <s xml:id="echoid-s19097" xml:space="preserve">ſæpius enim obſeruaui exiguos parietes, vti tripedales, aut modicas rupes, humanas voces
              <lb/>
            perbellè ementiri. </s>
            <s xml:id="echoid-s19098" xml:space="preserve">Quod ſi Echo exaudiretur tantum per lineas reflexas a reflectente ad aures ſonori ipſum
              <lb/>
            reflectẽs exiguum admodum euaderet, eius ſcilicet latitudinis, quæ æqualis eſſet dimidio interuallo aurium
              <lb/>
            audientis, quod ſic oſtendo. </s>
            <s xml:id="echoid-s19099" xml:space="preserve">ſit in ſequenti figura linea B C. </s>
            <s xml:id="echoid-s19100" xml:space="preserve">interuallum aurium, medium eius A. </s>
            <s xml:id="echoid-s19101" xml:space="preserve">reflectens
              <lb/>
              <figure xlink:label="fig-0244-01" xlink:href="fig-0244-01a" number="129">
                <image file="0244-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-01"/>
              </figure>
            ſit D E. </s>
            <s xml:id="echoid-s19102" xml:space="preserve">æquale ipſi A B. </s>
            <s xml:id="echoid-s19103" xml:space="preserve">vel A C. </s>
            <s xml:id="echoid-s19104" xml:space="preserve">medium eius
              <lb/>
            ſit F. </s>
            <s xml:id="echoid-s19105" xml:space="preserve">ſitque linea A F. </s>
            <s xml:id="echoid-s19106" xml:space="preserve">ipſi normalis. </s>
            <s xml:id="echoid-s19107" xml:space="preserve">iam intel-
              <lb/>
            ligatur linea vocalis incidens, & </s>
            <s xml:id="echoid-s19108" xml:space="preserve">r@flexa ſimul
              <lb/>
            A D B. </s>
            <s xml:id="echoid-s19109" xml:space="preserve">ad aurem B. </s>
            <s xml:id="echoid-s19110" xml:space="preserve">pariter ad aurem C. </s>
            <s xml:id="echoid-s19111" xml:space="preserve">ſit linea
              <lb/>
            vocalis incidens, & </s>
            <s xml:id="echoid-s19112" xml:space="preserve">reflexa A E C. </s>
            <s xml:id="echoid-s19113" xml:space="preserve">erũt enim an
              <lb/>
            guli ad D. </s>
            <s xml:id="echoid-s19114" xml:space="preserve">& </s>
            <s xml:id="echoid-s19115" xml:space="preserve">E. </s>
            <s xml:id="echoid-s19116" xml:space="preserve">incidentiæ, & </s>
            <s xml:id="echoid-s19117" xml:space="preserve">reflexioni
              <unsure/>
            s æqua-
              <lb/>
            les, quare totum reflectens D F E. </s>
            <s xml:id="echoid-s19118" xml:space="preserve">non amplius
              <lb/>
            patebit quam D E. </s>
            <s xml:id="echoid-s19119" xml:space="preserve">quod ex ſuppoſitione a qua-
              <lb/>
            le eſt ipſi A B. </s>
            <s xml:id="echoid-s19120" xml:space="preserve">dimidio aurium interſtitio. </s>
            <s xml:id="echoid-s19121" xml:space="preserve">Ve-
              <lb/>
            rum quia hæc vocis reflexa propagatur videtur
              <lb/>
            indigere adhuc maiori aeris commotione, cu-
              <lb/>
            ius certa quãtitas ignoratur, ideo difficile quo-
              <lb/>
            que erit reflectentis paruitatem determinare.</s>
            <s xml:id="echoid-s19122" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19123" xml:space="preserve">Cæterum cum hæc reflexio à B. </s>
            <s xml:id="echoid-s19124" xml:space="preserve">ad A. </s>
            <s xml:id="echoid-s19125" xml:space="preserve">in prima figura neceſſario fiat per lineam B A. </s>
            <s xml:id="echoid-s19126" xml:space="preserve">& </s>
            <s xml:id="echoid-s19127" xml:space="preserve">alias ei propiores,
              <lb/>
            manifeſtum euadit vocalem hanc reflexionem fieri per lineas reflexas, quæ ſint eædem cum incidentibus,
              <lb/>
            ſicuti reflexa B A. </s>
            <s xml:id="echoid-s19128" xml:space="preserve">eſt eadem cum incidente A B. </s>
            <s xml:id="echoid-s19129" xml:space="preserve">& </s>
            <s xml:id="echoid-s19130" xml:space="preserve">præterea fieri per angulos reflexionis, angulis inciden-
              <lb/>
            tiæ æquales; </s>
            <s xml:id="echoid-s19131" xml:space="preserve">ſic in figura angulis incidentiæ A B C. </s>
            <s xml:id="echoid-s19132" xml:space="preserve">A B D. </s>
            <s xml:id="echoid-s19133" xml:space="preserve">æquales ſunt angult reflexion@s C B A. </s>
            <s xml:id="echoid-s19134" xml:space="preserve">D B A.
              <lb/>
            </s>
            <s xml:id="echoid-s19135" xml:space="preserve">cum ſint ijdem re vera cum illis, ac proinde omnes ſint recti.</s>
            <s xml:id="echoid-s19136" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div483" type="section" level="1" n="365">
          <head xml:id="echoid-head384" style="it" xml:space="preserve">Muri plant quibus ſonus oblique tantum occurrit, non reflectunt Echum
            <lb/>
          ad ipſum ſonorum. Theorema IV.</head>
          <p>
            <s xml:id="echoid-s19137" xml:space="preserve">ID ex præmiſſis facilè deducitur, ſi enim omnes lineæ murum obliquè petunt, obliquè pariter, & </s>
            <s xml:id="echoid-s19138" xml:space="preserve">quidem
              <lb/>
            in auerſam partem excurrent; </s>
            <s xml:id="echoid-s19139" xml:space="preserve">quare omnis illa vox reflexa, neutiquam ad ſonorum reuertitur, ſed in
              <lb/>
            auerſam ab eo partem deflectet. </s>
            <s xml:id="echoid-s19140" xml:space="preserve">quod etiam experientia comprobat. </s>
            <s xml:id="echoid-s19141" xml:space="preserve">vt in ſuperiori ſecunda figura, ſit ſono-
              <lb/>
            rum A. </s>
            <s xml:id="echoid-s19142" xml:space="preserve">in eo ſitu ad murum D B E. </s>
            <s xml:id="echoid-s19143" xml:space="preserve">ſupra horizontem erectum, ad quem omnis linea vocalis obliquè ſatis
              <lb/>
            occurrat, vti facit@linea A E. </s>
            <s xml:id="echoid-s19144" xml:space="preserve">eius reflexa iuxta leges angulorum incidentiæ, & </s>
            <s xml:id="echoid-s19145" xml:space="preserve">reflexionis ſit B C. </s>
            <s xml:id="echoid-s19146" xml:space="preserve">palam eſt
              <lb/>
            Echum exaudiri ab altero. </s>
            <s xml:id="echoid-s19147" xml:space="preserve">quare ſi paries ſit adeo magnus, vt ei in orbem vox obliquè accidat, Echo pariter
              <lb/>
            in orbem exaudi ri poterit, ab auditoribus ſcilicet in orbem è regione muri conſtitutis.</s>
            <s xml:id="echoid-s19148" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div484" type="section" level="1" n="366">
          <head xml:id="echoid-head385" style="it" xml:space="preserve">Conſectarium.</head>
          <figure number="130">
            <image file="0244-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s19149" xml:space="preserve">HInc palam fit cur ædificia in edito ſita, ſonoro in planitie
              <lb/>
            conſtituto, non ei reſonent Echo. </s>
            <s xml:id="echoid-s19150" xml:space="preserve">ratio eſt quoniam omnes
              <lb/>
            lineæ a ſonoro ſurſum aſcendentes obliquè hiſce muris occurrunt,
              <lb/>
            ac proinde ſurſum verſum reflectuntur; </s>
            <s xml:id="echoid-s19151" xml:space="preserve">vnde tota illa vox, iuxta
              <lb/>
            leges angulorum incidentiæ, & </s>
            <s xml:id="echoid-s19152" xml:space="preserve">reflexionis in altum reuerbera-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s19153" xml:space="preserve">vtin hac ſequenti figura omnes lineæ ductæ a ſonoro A. </s>
            <s xml:id="echoid-s19154" xml:space="preserve">ad
              <lb/>
            murum E. </s>
            <s xml:id="echoid-s19155" xml:space="preserve">neceſſario ſurſum verſus E. </s>
            <s xml:id="echoid-s19156" xml:space="preserve">repelluntur; </s>
            <s xml:id="echoid-s19157" xml:space="preserve">debet enim
              <lb/>
            angulus reflexionis C B E. </s>
            <s xml:id="echoid-s19158" xml:space="preserve">eſſe æqualis angulo incidentiæ D B A.
              <lb/>
            </s>
            <s xml:id="echoid-s19159" xml:space="preserve">atque in partem auerſam, videlicet ſurſum vergere. </s>
            <s xml:id="echoid-s19160" xml:space="preserve">Eadem de
              <lb/>
            cauſa cliuus propugnaculorum ei ſonoro non reddit Echo, quod
              <lb/>
            exiſtit in horizontali planitie ſupra quam propugnaculum erigi-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s19161" xml:space="preserve">quoniam cum in oppoſitam parcem ſit inclinatum, videli-
              <lb/>
            cet in altum reuerberat. </s>
            <s xml:id="echoid-s19162" xml:space="preserve">hactenus de ſi@u inter ſonorum, & </s>
            <s xml:id="echoid-s19163" xml:space="preserve">refle
              <lb/>
            ctens, nunc de interuallo eorumdem.</s>
            <s xml:id="echoid-s19164" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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