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-div476" type="section" level="1" n="361">
          <pb o="220" file="0242" n="247" rhead="DE ECHO."/>
          <p>
            <s xml:id="echoid-s18865" xml:space="preserve">Quinta. </s>
            <s xml:id="echoid-s18866" xml:space="preserve">Linea recta ſonora, ſeu vocalis eſt, ſecundum quam vox in directum propagatur.</s>
            <s xml:id="echoid-s18867" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18868" xml:space="preserve">Quod pręterea ſonus in aperto, ac libero quoquouerſus per lineas diſſundatur, hiſce rationibus palam fiet;
              <lb/>
            </s>
            <s xml:id="echoid-s18869" xml:space="preserve">quarum prima fit ab experientia; </s>
            <s xml:id="echoid-s18870" xml:space="preserve">nam multo melius ad omnes plagas ſonum audimus, cum inter nos, & </s>
            <s xml:id="echoid-s18871" xml:space="preserve">ſo-
              <lb/>
            norum nihil directè interponitur, quod eius directæ ad nos productioni obſtet, quam cum quippiam interij-
              <lb/>
            citur. </s>
            <s xml:id="echoid-s18872" xml:space="preserve">Secunda, Echo ipſa idem manifeſtat, ipſa etenim nuſq; </s>
            <s xml:id="echoid-s18873" xml:space="preserve">reſonat, niſi vbi vox per lineam rectam à ſo-
              <lb/>
            noro ad reflectens procurrit, vnde poſtea reſilit. </s>
            <s xml:id="echoid-s18874" xml:space="preserve">Tertia, ſicuti in lumine, & </s>
            <s xml:id="echoid-s18875" xml:space="preserve">viſione in confeſſo eſt, rectas vn-
              <lb/>
            diq; </s>
            <s xml:id="echoid-s18876" xml:space="preserve">lineas dari oportere, quidni etiam in iono, & </s>
            <s xml:id="echoid-s18877" xml:space="preserve">voce? </s>
            <s xml:id="echoid-s18878" xml:space="preserve">Quarta, huius rei cauſa eſt, quod natura agit per li-
              <lb/>
            neas breuiſſimas, breuiſſimæ autem ſunt rectæ, ad quaſuis plagas extendantur.</s>
            <s xml:id="echoid-s18879" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18880" xml:space="preserve">Cæterum dixi (in loco aperto, aclibero) quod, vt vulgo notum eſt, ſonus, & </s>
            <s xml:id="echoid-s18881" xml:space="preserve">vox vel tenuiſſima per tu-
              <lb/>
            bos, & </s>
            <s xml:id="echoid-s18882" xml:space="preserve">canales, etiam curuos, ceu per ſon@ ductus, optimè defertur, ac longius quam in aperto propagatur.
              <lb/>
            </s>
            <s xml:id="echoid-s18883" xml:space="preserve">hac ratione in cænationibus concameratis, in quibus anguli caui parietum cont nuantur cauis angulis, qui
              <lb/>
            per fornicem diametraliter tranſcendunt ad oppoſitum angulum parietum, etiamſi quis ſubmiſſe loquatur
              <lb/>
            in vno parietum angulo, ore in angulum obuerſo, exauditur tamen ab altero. </s>
            <s xml:id="echoid-s18884" xml:space="preserve">in altero angulo oppoſito au-
              <lb/>
            ſcultante, nihil interim audientibus intermedijs. </s>
            <s xml:id="echoid-s18885" xml:space="preserve">id multis in locis licet experiri, ſed præcipuè celebr s eſt
              <lb/>
            Aula Sereniſs. </s>
            <s xml:id="echoid-s18886" xml:space="preserve">Ducis Mantuæ. </s>
            <s xml:id="echoid-s18887" xml:space="preserve">cauſa eſt, quia vox per angulum veluti per canalem vnita, & </s>
            <s xml:id="echoid-s18888" xml:space="preserve">clauſa, aſcendit
              <lb/>
            etiam per fornicis canalem, & </s>
            <s xml:id="echoid-s18889" xml:space="preserve">ad oppoſitum murorum angulum deſcendit vbi exauditur. </s>
            <s xml:id="echoid-s18890" xml:space="preserve">quod ſi in fornice
              <lb/>
            ſint anguli non caui, ſed conuexi, & </s>
            <s xml:id="echoid-s18891" xml:space="preserve">prominentes, ſeu adſit planum laqueare, vox illuc offendens, non vnita
              <lb/>
            pergit, ſed latè diſpergitur. </s>
            <s xml:id="echoid-s18892" xml:space="preserve">Porro huluſmodi vocum propagationes, cum non fiant per reflexionem, inſti-
              <lb/>
            tutæ tractationi cenſendæ ſunt alienæ.</s>
            <s xml:id="echoid-s18893" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18894" xml:space="preserve">Sexta. </s>
            <s xml:id="echoid-s18895" xml:space="preserve">Linea ſonora actiuitatis, actioniſuè, eſt ea ſecundum quam ſonus quam longiſſimè propagari po-
              <lb/>
            teſt. </s>
            <s xml:id="echoid-s18896" xml:space="preserve">dicitur etiam ſemidiameter ſphæræ actionis.</s>
            <s xml:id="echoid-s18897" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18898" xml:space="preserve">Septima. </s>
            <s xml:id="echoid-s18899" xml:space="preserve">Reflectens eſt omne corpus, quod ſonum modulatum, aut articulatum reflectere poteſt ad ip-
              <lb/>
            ſum ſonorum, ad aliumuè, quod nos aliquando, & </s>
            <s xml:id="echoid-s18900" xml:space="preserve">murum, & </s>
            <s xml:id="echoid-s18901" xml:space="preserve">parietem dicemus.</s>
            <s xml:id="echoid-s18902" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18903" xml:space="preserve">Octaua. </s>
            <s xml:id="echoid-s18904" xml:space="preserve">Sonora linea directa, ſeu incldens eſt ea, ſecundum quam ſonus primus ã ſonoro manans rectà in
              <lb/>
            obiectum aliquod corpus incidit.</s>
            <s xml:id="echoid-s18905" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18906" xml:space="preserve">Nona. </s>
            <s xml:id="echoid-s18907" xml:space="preserve">Linea vocalis reflexa eſt ea, ſecundum quam ſonus ad obiectum corpus colliſus reflectitur. </s>
            <s xml:id="echoid-s18908" xml:space="preserve">Quæ
              <lb/>
            omnia vt probè percipiantur, prænotandum eſt, quatuor eſſe, quæ eadem ratione per lineas incidentes, & </s>
            <s xml:id="echoid-s18909" xml:space="preserve">
              <lb/>
            reflexus explicari oporteat, lumen, & </s>
            <s xml:id="echoid-s18910" xml:space="preserve">viſionem; </s>
            <s xml:id="echoid-s18911" xml:space="preserve">ſonum, & </s>
            <s xml:id="echoid-s18912" xml:space="preserve">auditionem ſicuti enim perſpectiui in luminis
              <lb/>
            profuſione, & </s>
            <s xml:id="echoid-s18913" xml:space="preserve">reflexione conſiderant lineam radioſam, ſeu radium incidentem, & </s>
            <s xml:id="echoid-s18914" xml:space="preserve">reflexum in viſione pari-
              <lb/>
              <figure xlink:label="fig-0242-01" xlink:href="fig-0242-01a" number="127">
                <image file="0242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0242-01"/>
              </figure>
            ter concipiunt lineam incidentem, & </s>
            <s xml:id="echoid-s18915" xml:space="preserve">reflexam. </s>
            <s xml:id="echoid-s18916" xml:space="preserve">eadem ratione
              <lb/>
            par eſt in ſoni prolatione, & </s>
            <s xml:id="echoid-s18917" xml:space="preserve">reflexione lineas ſonoras, & </s>
            <s xml:id="echoid-s18918" xml:space="preserve">voca-
              <lb/>
            les ſtatuere, quarum aliæ ſint incidentes, aliæ reflexæ. </s>
            <s xml:id="echoid-s18919" xml:space="preserve">Earum
              <lb/>
            autem productio melius figuræ huius exemplo percipietur. </s>
            <s xml:id="echoid-s18920" xml:space="preserve">in
              <lb/>
            qua ſonorum ſit vbi A. </s>
            <s xml:id="echoid-s18921" xml:space="preserve">corpus autem ſonum reflectens ſit paries
              <lb/>
            C B D. </s>
            <s xml:id="echoid-s18922" xml:space="preserve">dum igitur ſonus ab A. </s>
            <s xml:id="echoid-s18923" xml:space="preserve">quaquauerſum diffunditur, in
              <lb/>
            oppoſitum parietem impingit. </s>
            <s xml:id="echoid-s18924" xml:space="preserve">in qua vocis diffuſione licebit
              <lb/>
            concipere innumeras lineas, quarum tres tantum hic depingun-
              <lb/>
            tur A B. </s>
            <s xml:id="echoid-s18925" xml:space="preserve">A C. </s>
            <s xml:id="echoid-s18926" xml:space="preserve">A D. </s>
            <s xml:id="echoid-s18927" xml:space="preserve">ſecundum quas vox parieti incidit, ideoq;
              <lb/>
            </s>
            <s xml:id="echoid-s18928" xml:space="preserve">lineæ incidentiæ dicuntur, harum omnium vna A B. </s>
            <s xml:id="echoid-s18929" xml:space="preserve">propriè eſt
              <lb/>
            parieti perpendicularis, ſeu normalis, quia ad angulos rectos ei
              <lb/>
            accidit. </s>
            <s xml:id="echoid-s18930" xml:space="preserve">reliquę omnes, quales ſunt A C. </s>
            <s xml:id="echoid-s18931" xml:space="preserve">A D. </s>
            <s xml:id="echoid-s18932" xml:space="preserve">eidem obliquè oc-
              <lb/>
            currunt. </s>
            <s xml:id="echoid-s18933" xml:space="preserve">licebit pariter innumeras lineas à pariete reflexas ima-
              <lb/>
            ginari, quæ totidẽ incidentibus reſpondeant: </s>
            <s xml:id="echoid-s18934" xml:space="preserve">harum hic tantum
              <lb/>
            tres depinguntur; </s>
            <s xml:id="echoid-s18935" xml:space="preserve">C F. </s>
            <s xml:id="echoid-s18936" xml:space="preserve">reflexa ipſius A C. </s>
            <s xml:id="echoid-s18937" xml:space="preserve">B A. </s>
            <s xml:id="echoid-s18938" xml:space="preserve">reflexa ipſius
              <lb/>
            A B. </s>
            <s xml:id="echoid-s18939" xml:space="preserve">normalis; </s>
            <s xml:id="echoid-s18940" xml:space="preserve">normales enim in ſe ipſas reciprocantur: </s>
            <s xml:id="echoid-s18941" xml:space="preserve">D E. </s>
            <s xml:id="echoid-s18942" xml:space="preserve">
              <lb/>
            tandem reflexa ipſius A D. </s>
            <s xml:id="echoid-s18943" xml:space="preserve">vbi notandum eſt, lineam reflexam obliquam ſemper reflecti in partem alteram,
              <lb/>
            ſeu directè oppoſitam ſuæ incidentis, ita vtambæ, & </s>
            <s xml:id="echoid-s18944" xml:space="preserve">incidens, & </s>
            <s xml:id="echoid-s18945" xml:space="preserve">roflexa poſſint eſſe in eadem plana ſuperfi-
              <lb/>
            cie, quæ tranſiret per lineam normalem A B. </s>
            <s xml:id="echoid-s18946" xml:space="preserve">necnon per lineas incidentes A C. </s>
            <s xml:id="echoid-s18947" xml:space="preserve">A D. </s>
            <s xml:id="echoid-s18948" xml:space="preserve">faceretque in pariete
              <lb/>
            lineam G C B D H. </s>
            <s xml:id="echoid-s18949" xml:space="preserve">hæc de ſonoris lineis, nunc de angulis earundem.</s>
            <s xml:id="echoid-s18950" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18951" xml:space="preserve">Decima. </s>
            <s xml:id="echoid-s18952" xml:space="preserve">Angulus incidentiæ lineæ obliquæ hic eſt quem facit linea obliquà incidens, cum linea in pa-
              <lb/>
            riete ducta à termino lineæ normalis per terminum lineæ obliquæ incidentis (qualis in præſenti figura eſt
              <lb/>
            linea B C G. </s>
            <s xml:id="echoid-s18953" xml:space="preserve">tranſit enim per B. </s>
            <s xml:id="echoid-s18954" xml:space="preserve">& </s>
            <s xml:id="echoid-s18955" xml:space="preserve">C. </s>
            <s xml:id="echoid-s18956" xml:space="preserve">terminos linearum A B. </s>
            <s xml:id="echoid-s18957" xml:space="preserve">A C. </s>
            <s xml:id="echoid-s18958" xml:space="preserve">talis eſt etiam linea B D H. </s>
            <s xml:id="echoid-s18959" xml:space="preserve">trannens
              <lb/>
            per terminos B D. </s>
            <s xml:id="echoid-s18960" xml:space="preserve">linearum A B. </s>
            <s xml:id="echoid-s18961" xml:space="preserve">A D.) </s>
            <s xml:id="echoid-s18962" xml:space="preserve">anguli igitur incidentiæ ſunt A C B. </s>
            <s xml:id="echoid-s18963" xml:space="preserve">A D B. </s>
            <s xml:id="echoid-s18964" xml:space="preserve">angulus incidentiæ
              <lb/>
            lineæ normalis eſt quem ipſa facit cum quauis linea in pariete ducta per ſuum terminum B. </s>
            <s xml:id="echoid-s18965" xml:space="preserve">qualis erit an-
              <lb/>
            gulus A B C. </s>
            <s xml:id="echoid-s18966" xml:space="preserve">& </s>
            <s xml:id="echoid-s18967" xml:space="preserve">A B D.</s>
            <s xml:id="echoid-s18968" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18969" xml:space="preserve">Vndecima. </s>
            <s xml:id="echoid-s18970" xml:space="preserve">Angulus reflexionis lineæ obliquæ is eſt, quem facit linea reflexa obliqua cum prædicta linea
              <lb/>
            in pariete: </s>
            <s xml:id="echoid-s18971" xml:space="preserve">tales ſunt anguli F C G. </s>
            <s xml:id="echoid-s18972" xml:space="preserve">E D H. </s>
            <s xml:id="echoid-s18973" xml:space="preserve">angulus reflexionis lineę normalis is eſt quem ipſa facit cum prę-
              <lb/>
            dicta linea, quales ſunt anguli C B A. </s>
            <s xml:id="echoid-s18974" xml:space="preserve">B D A. </s>
            <s xml:id="echoid-s18975" xml:space="preserve">notandum eſt angulum hunc reflexionis ſemper vergere ad
              <lb/>
            partem directè auerſam angulo incidentiæ, quoniam fit a linea reflexa, quæ vti ſupra notatnm eſt, illuc pa-
              <lb/>
            riter tendit. </s>
            <s xml:id="echoid-s18976" xml:space="preserve">porrò ex prænotatis facile eſt varias Echus diuiſiones; </s>
            <s xml:id="echoid-s18977" xml:space="preserve">acſpecies definire; </s>
            <s xml:id="echoid-s18978" xml:space="preserve">nam,</s>
          </p>
          <p>
            <s xml:id="echoid-s18979" xml:space="preserve">Duodecima, alia eſt normalis, & </s>
            <s xml:id="echoid-s18980" xml:space="preserve">reciproca, quæ ſcilieet reflectitur per eandem lineam: </s>
            <s xml:id="echoid-s18981" xml:space="preserve">alia vero obliqua,
              <lb/>
            quæ obliquè per diuerſam lineam a primaria reflectitur, quaſi & </s>
            <s xml:id="echoid-s18982" xml:space="preserve">ad alium auditorem, quam ad ſonorum. </s>
            <s xml:id="echoid-s18983" xml:space="preserve">hęc
              <lb/>
            autem aut fit per vnam tantum reflexionem, aut per plures.</s>
            <s xml:id="echoid-s18984" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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