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-div498" type="section" level="1" n="377">
          <pb o="226" file="0248" n="253" rhead="DE ECHO."/>
        </div>
        <div xml:id="echoid-div499" type="section" level="1" n="378">
          <head xml:id="echoid-head397" style="it" xml:space="preserve">De Echo obliqua.</head>
          <p>
            <s xml:id="echoid-s19385" xml:space="preserve">QVemadmodum cùm in ſpeculum planum lineæ viſiuæ perpendiculariter accidunt, & </s>
            <s xml:id="echoid-s19386" xml:space="preserve">reflectuntur, ipfi
              <lb/>
            noſtram intuemur imaginem. </s>
            <s xml:id="echoid-s19387" xml:space="preserve">cum verò obliquè ei occurrunt, non ipſi ſed alius quiſpiam noſtam ima-
              <lb/>
            ginem intuetur. </s>
            <s xml:id="echoid-s19388" xml:space="preserve">pari ratione idem Echo accidit. </s>
            <s xml:id="echoid-s19389" xml:space="preserve">porrò hactenus de Echo quæ norm
              <unsure/>
            aliter reſona@
              <lb/>
            egimus, nunc nonnulla de ea, quæ ex obliquo repercuſſu, ab alio quam à ſonoro exaudiri ſolet.</s>
            <s xml:id="echoid-s19390" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div500" type="section" level="1" n="379">
          <head xml:id="echoid-head398" style="it" xml:space="preserve">Echum ab alio, quam à ſonoro audiri, cum vox parieti oblique occurrit.
            <lb/>
          Theorema XII.</head>
          <p>
            <s xml:id="echoid-s19391" xml:space="preserve">IN hac Echo præter ſonorum, neceſſarius eſt alius qui Echum exaudiat, vt in ſecunda figura. </s>
            <s xml:id="echoid-s19392" xml:space="preserve">ſit ſonorum
              <lb/>
            A. </s>
            <s xml:id="echoid-s19393" xml:space="preserve">cuius in parietem D B E. </s>
            <s xml:id="echoid-s19394" xml:space="preserve">oblique incidat, vti per lineam A B. </s>
            <s xml:id="echoid-s19395" xml:space="preserve">quę faciens angulum A B D. </s>
            <s xml:id="echoid-s19396" xml:space="preserve">deflectatur
              <lb/>
            ad audientem C. </s>
            <s xml:id="echoid-s19397" xml:space="preserve">faciens angulum C B E. </s>
            <s xml:id="echoid-s19398" xml:space="preserve">æqualem e
              <unsure/>
            lteri A B D. </s>
            <s xml:id="echoid-s19399" xml:space="preserve">iam experientia conſrat in tali caſu audien-
              <lb/>
            tem C. </s>
            <s xml:id="echoid-s19400" xml:space="preserve">audire Echum ipſius A. </s>
            <s xml:id="echoid-s19401" xml:space="preserve">A vero neutiquam. </s>
            <s xml:id="echoid-s19402" xml:space="preserve">cuius ratio ſuperius tacta eſt, quoniã ſcilicet natura agit
              <lb/>
            per lineas breuiſſimas; </s>
            <s xml:id="echoid-s19403" xml:space="preserve">omnium autem breuiſſimæ ſunt quæ faciunt prædictos angulos æquales, vti conſtat
              <lb/>
            per 1. </s>
            <s xml:id="echoid-s19404" xml:space="preserve">Theor. </s>
            <s xml:id="echoid-s19405" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s19406" xml:space="preserve">Diſtantia porrò ſonori à refiectente tantum eſſe oportet, vt binæ lineæ A B. </s>
            <s xml:id="echoid-s19407" xml:space="preserve">B C. </s>
            <s xml:id="echoid-s19408" xml:space="preserve">fi
              <lb/>
            mul non ſint maiores linea actionis.</s>
            <s xml:id="echoid-s19409" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div501" type="section" level="1" n="380">
          <head xml:id="echoid-head399" style="it" xml:space="preserve">Conſectarium.</head>
          <p>
            <s xml:id="echoid-s19410" xml:space="preserve">HInc ſequitur Echum audiri poſſe ab audientibus in orbem ſitis, ſi enim adeo magnus ſit paries, vt ab eo
              <lb/>
            reflexiones fieri poſſint circumquaque, ideſt, a dextris, & </s>
            <s xml:id="echoid-s19411" xml:space="preserve">à ſiniſtris, ſupernè, & </s>
            <s xml:id="echoid-s19412" xml:space="preserve">infernè; </s>
            <s xml:id="echoid-s19413" xml:space="preserve">omnes autem
              <lb/>
            reflexionum anguli ſint inuicem æquales, manifeſtum eſt omnia puncta incidentie fore in peripheria circu-
              <lb/>
              <figure xlink:label="fig-0248-01" xlink:href="fig-0248-01a" number="134">
                <image file="0248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-01"/>
              </figure>
            li deſcripta in pariete, quare linea omnes
              <lb/>
            ref
              <unsure/>
            lexę, cum reflectantur ad conſimiles an-
              <lb/>
            gulos, erunt omnes in ſuperficie conica
              <lb/>
            reflexa, cuius baſis erit circulus, in cuius
              <lb/>
            circuli peripheria auditores poſiti omnes
              <lb/>
            Echum exaudient. </s>
            <s xml:id="echoid-s19414" xml:space="preserve">porrò ſi
              <unsure/>
            hæc fuſius ex-
              <lb/>
            plicare velim, intelligenda eſſet prius py-
              <lb/>
            ramis incidentiæ, more opticorum, cuius
              <lb/>
            vertex eſſet in A. </s>
            <s xml:id="echoid-s19415" xml:space="preserve">figuræ, baſis verò in pa-
              <lb/>
            riete E B D. </s>
            <s xml:id="echoid-s19416" xml:space="preserve">quæ baſis eſſet circulus cuius
              <lb/>
            centrum D. </s>
            <s xml:id="echoid-s19417" xml:space="preserve">circumferentia verò per B E.
              <lb/>
            </s>
            <s xml:id="echoid-s19418" xml:space="preserve">tranſiret, ex qua circumferentia reflecte-
              <lb/>
            rentur omnes lineæ efficientes reliquann
              <lb/>
            pyramidem reflexionis; </s>
            <s xml:id="echoid-s19419" xml:space="preserve">cuius baſis eſſet
              <lb/>
            orbis, in cuius peripheria auditores poſi-
              <lb/>
            ti varias Echus exaudirent. </s>
            <s xml:id="echoid-s19420" xml:space="preserve">quæ omnia eſſent eodem modo demonſtranda, quo demonſtrantur in tracta-
              <lb/>
            tu de figura Iridis. </s>
            <s xml:id="echoid-s19421" xml:space="preserve">Sed hæc fortè nimis breuiter.</s>
            <s xml:id="echoid-s19422" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div503" type="section" level="1" n="381">
          <head xml:id="echoid-head400" style="it" xml:space="preserve">Echum ſecundariam manifeſtare. Theorema XIII.</head>
          <p>
            <s xml:id="echoid-s19423" xml:space="preserve">SInt exempli gratia, duo reflectentia C S. </s>
            <s xml:id="echoid-s19424" xml:space="preserve">A B. </s>
            <s xml:id="echoid-s19425" xml:space="preserve">ab inuicem diſtantia ſaltem 25. </s>
            <s xml:id="echoid-s19426" xml:space="preserve">paſſus Geometricos, inui-
              <lb/>
            cemq; </s>
            <s xml:id="echoid-s19427" xml:space="preserve">non omnino paralella, ſed ad partes C A. </s>
            <s xml:id="echoid-s19428" xml:space="preserve">modicum diuergentia. </s>
            <s xml:id="echoid-s19429" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s19430" xml:space="preserve">linea actiuitatis paulo maior
              <lb/>
            quam tripla prædictæ diſtantiæ, v.</s>
            <s xml:id="echoid-s19431" xml:space="preserve">g. </s>
            <s xml:id="echoid-s19432" xml:space="preserve">paſſuum 80. </s>
            <s xml:id="echoid-s19433" xml:space="preserve">ſonorum ſit S. </s>
            <s xml:id="echoid-s19434" xml:space="preserve">cuius linea prima ſonora S B. </s>
            <s xml:id="echoid-s19435" xml:space="preserve">feratur in pa-
              <lb/>
              <figure xlink:label="fig-0248-02" xlink:href="fig-0248-02a" number="135">
                <image file="0248-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-02"/>
              </figure>
            rietem A B. </s>
            <s xml:id="echoid-s19436" xml:space="preserve">recta. </s>
            <s xml:id="echoid-s19437" xml:space="preserve">reflectetur igitur ad S. </s>
            <s xml:id="echoid-s19438" xml:space="preserve">ſonorum, ex demonſtra-
              <lb/>
            tis, eique Echum reſonabit. </s>
            <s xml:id="echoid-s19439" xml:space="preserve">rurſus conſidero aliam lineam S I. </s>
            <s xml:id="echoid-s19440" xml:space="preserve">quæ
              <lb/>
            obliquè parieti A I B. </s>
            <s xml:id="echoid-s19441" xml:space="preserve">occurrat, quare reflectetur vltra in alterũ pa-
              <lb/>
            rietem in C. </s>
            <s xml:id="echoid-s19442" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s19443" xml:space="preserve">I C. </s>
            <s xml:id="echoid-s19444" xml:space="preserve">vnde iterum reflecti poterit ad A. </s>
            <s xml:id="echoid-s19445" xml:space="preserve">vbi ſit au-
              <lb/>
            ditor, per lineã C A. </s>
            <s xml:id="echoid-s19446" xml:space="preserve">quare ab audiente A. </s>
            <s xml:id="echoid-s19447" xml:space="preserve">exaudiri poterit: </s>
            <s xml:id="echoid-s19448" xml:space="preserve">eſt enim
              <lb/>
            tota linea S I C A. </s>
            <s xml:id="echoid-s19449" xml:space="preserve">75. </s>
            <s xml:id="echoid-s19450" xml:space="preserve">ex hypoth eſi paulò minor tota linea actionis
              <lb/>
            80. </s>
            <s xml:id="echoid-s19451" xml:space="preserve">igitur A. </s>
            <s xml:id="echoid-s19452" xml:space="preserve">exaudiet vocem ſonori S. </s>
            <s xml:id="echoid-s19453" xml:space="preserve">ei ſecũdò reflexam ex C. </s>
            <s xml:id="echoid-s19454" xml:space="preserve">erit
              <lb/>
            tamen Echo iſthæc diuerſa ab ea, quam percipit ſonorum S. </s>
            <s xml:id="echoid-s19455" xml:space="preserve">imò illa
              <lb/>
            tardior in ratione ſeſquialtera, nam eius diſtantia à ſonoro conſtat
              <lb/>
            tribus lineis S I. </s>
            <s xml:id="echoid-s19456" xml:space="preserve">I C. </s>
            <s xml:id="echoid-s19457" xml:space="preserve">C A. </s>
            <s xml:id="echoid-s19458" xml:space="preserve">diſl
              <unsure/>
            antia autem per quam recurrit Echo ad ipſum ſonorum conſtat tantum dua-
              <lb/>
            bus S B. </s>
            <s xml:id="echoid-s19459" xml:space="preserve">B S. </s>
            <s xml:id="echoid-s19460" xml:space="preserve">vnde patet propoſitum. </s>
            <s xml:id="echoid-s19461" xml:space="preserve">eodem modo Echum tertiariam in ratione dupla, &</s>
            <s xml:id="echoid-s19462" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19463" xml:space="preserve">ſimiles faci-
              <lb/>
            lè demonſtrabimus</s>
          </p>
        </div>
      </text>
    </echo>
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