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-div475" type="section" level="1" n="360">
          <head xml:id="echoid-head379" xml:space="preserve">ECHOMETRIA
            <lb/>
          SIVE DE NATVRA ECHVS
            <lb/>
          GEOMETRICA TRACTATIO,
            <lb/>
          Publicè habita à quodam Academico.
            <lb/>
          PROLVSIO, ET OCCASIO COMMENTATIONIS.</head>
          <p>
            <s xml:id="echoid-s18807" xml:space="preserve">SVperiori Autumno, cum in ſcholis Halcyonia eſſent, relicta in vrbe Philoſophia, in ſubur-
              <lb/>
            banum relaxandi animi, acpurioris cæli captandi gratia conceſſeramus. </s>
            <s xml:id="echoid-s18808" xml:space="preserve">cumq; </s>
            <s xml:id="echoid-s18809" xml:space="preserve">ſimul non-
              <lb/>
            nulli ſuauioris Muſæ comites deambulatum iſſemus, accidit vt ex noſtris quidam Muſica,
              <lb/>
            ſimulq; </s>
            <s xml:id="echoid-s18810" xml:space="preserve">clariori voce præditus, carmen quoddam altius modularetur. </s>
            <s xml:id="echoid-s18811" xml:space="preserve">& </s>
            <s xml:id="echoid-s18812" xml:space="preserve">ecce tibi, carmen
              <lb/>
            idem, ex quadam ſatis remota turri, continuo pari ſuauitate recantatum excepimus. </s>
            <s xml:id="echoid-s18813" xml:space="preserve">primo
              <lb/>
            putatum eſt ſodalium aliquem inibi latentem ioculariter, ac blandè nobis illuſiſſe. </s>
            <s xml:id="echoid-s18814" xml:space="preserve">tandem
              <lb/>
            iterata, atque iterum relata modulatione, illa depræhenſa eſt,</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s18815" xml:space="preserve">-- quæ nec reticere loquenti,
              <lb/>
            Nec prior ipſa loqui didicit reſonabilis Echo:</s>
            <s xml:id="echoid-s18816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18817" xml:space="preserve">Pergratas noſtrarum vocum imagines reddidiſſe. </s>
            <s xml:id="echoid-s18818" xml:space="preserve">diutius igitur illius ſuauitate detenti, varij varios cantus
              <lb/>
            ei recinendos accinebamus. </s>
            <s xml:id="echoid-s18819" xml:space="preserve">cùm interim Geometria, quam ſimul cum reliqua Philoſophiæ familia in vrbe
              <lb/>
            reliqueramus, ſe nobis iterum comitem præbet, grateq; </s>
            <s xml:id="echoid-s18820" xml:space="preserve">ſuadet minimè inſtituto noſtro, relaxationiuè obeſ-
              <lb/>
            ſe, ſi latentem Echus naturam indagaremus; </s>
            <s xml:id="echoid-s18821" xml:space="preserve">quandoquidem id philoſophandi genus, iucundè per amæna
              <lb/>
            collium, & </s>
            <s xml:id="echoid-s18822" xml:space="preserve">vallium ambulationibus obiri poſſit. </s>
            <s xml:id="echoid-s18823" xml:space="preserve">Ego itaque veluti Pan alter, per ſaltus, per ſyluas, hac il-
              <lb/>
            lac vociferans Echum perſequi, & </s>
            <s xml:id="echoid-s18824" xml:space="preserve">captare; </s>
            <s xml:id="echoid-s18825" xml:space="preserve">ipſaque noſtris votis reſpondente, ipſi</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s18826" xml:space="preserve">-- pulſati colles clamore reſultant</s>
          </p>
          <p style="it">
            <s xml:id="echoid-s18827" xml:space="preserve">& </s>
            <s xml:id="echoid-s18828" xml:space="preserve">-- gemitu nemus omne remugit.</s>
            <s xml:id="echoid-s18829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18830" xml:space="preserve">Perſequebar, inquam, captabamque, contemplabar videlicet locorum reſonantium poſitionem, figuram,
              <lb/>
            qualitatem, quæ hanc vocis imaginem effinxiſſent. </s>
            <s xml:id="echoid-s18831" xml:space="preserve">atque ni fallor, Panos inſtar Echum depræhendi, natu-
              <lb/>
            ram eius videlicet, cauſaſque perueſtigaui. </s>
            <s xml:id="echoid-s18832" xml:space="preserve">Pan enim, vti tradunt Mythologi, fuit vir doctus, qui primus
              <lb/>
            Echus cauſam inueſtigauit, ductuſque ſuauitate noſcendi, diu collibus, montibuſque quaſi Echum perſe-
              <lb/>
            quens oberrauit. </s>
            <s xml:id="echoid-s18833" xml:space="preserve">vnde ipſum eam deperijſſe vetus fabula emanauit. </s>
            <s xml:id="echoid-s18834" xml:space="preserve">quæ igitur tunc temporis de hoc vocis
              <lb/>
            fimulacro, Geometriæ ope commentati ſumus, ea nunc in medium allata, non iniucunda fore ſperamus.
              <lb/>
            </s>
            <s xml:id="echoid-s18835" xml:space="preserve">quæ vt ordine tradantur, opus eſt more Mathematicorum, nonnulla præmittere, ac primò definitiones
              <lb/>
            aliquot, quarum prima erit ipſius Echus nominis Etymon, nomina enim teſte Platonis Cratylo, quædam
              <lb/>
            ſunt perbreues rerum definitiones.</s>
            <s xml:id="echoid-s18836" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div476" type="section" level="1" n="361">
          <head xml:id="echoid-head380" style="it" xml:space="preserve">DEFINITIONES.</head>
          <p>
            <s xml:id="echoid-s18837" xml:space="preserve">PRima erit ipſius nominis definitio, ſeu Etymologia. </s>
            <s xml:id="echoid-s18838" xml:space="preserve">Echo Græcè dicitur Hχω, à verbo Hχεω, ideſt, re-
              <lb/>
            ſono, vnde Latinis aptè redditus reſonantia. </s>
            <s xml:id="echoid-s18839" xml:space="preserve">Poetæ Latini eam modo Echo, modo imaginem vocis ap-
              <lb/>
            pellat, ſic Virg. </s>
            <s xml:id="echoid-s18840" xml:space="preserve"># Saxa ſonant, vociſque offenſa reſultat imago,
              <lb/>
            Philoſophis vox reflexa, repercuſſa, reciproca etiam dicitur. </s>
            <s xml:id="echoid-s18841" xml:space="preserve">hinc ad ipſius definitionem commodius iam
              <lb/>
            tranſire licebit.</s>
            <s xml:id="echoid-s18842" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18843" xml:space="preserve">Secunda. </s>
            <s xml:id="echoid-s18844" xml:space="preserve">Echo enim nihil aliud eſt, quam vocis articulatæ, aut modulatæ ſonus reflexus, hoc videlicet
              <lb/>
            modo, cum vox noſtra prolata, ac motuaeris quoquouerſus delata, obiecto directè corpori plano, cauo-
              <lb/>
            ue, ac ſatis læuigato occurrens, inde pilæ inſtar ad noſmet reucrtitur. </s>
            <s xml:id="echoid-s18845" xml:space="preserve">vbi diſtinguendum eſt inter Bom-
              <lb/>
            bum, & </s>
            <s xml:id="echoid-s18846" xml:space="preserve">Echum.</s>
            <s xml:id="echoid-s18847" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18848" xml:space="preserve">Tertia. </s>
            <s xml:id="echoid-s18849" xml:space="preserve">Bombus enim eſt quidem ſonus reflexus, ſed ob defectum alicuius circumſtantiæ, ex ijs, quæ ne-
              <lb/>
            @eſſariæ ſunt ad Echum perſiciendam, confusſus, & </s>
            <s xml:id="echoid-s18850" xml:space="preserve">inarticulatus. </s>
            <s xml:id="echoid-s18851" xml:space="preserve">Echo autem propriè eſt, quæ vocesarti-
              <lb/>
            culatas, aut modulatas diſtinctè reſtituit. </s>
            <s xml:id="echoid-s18852" xml:space="preserve">Cuius naturam, vt melius perſcrutemur, animaduertimus non ſo-
              <lb/>
            lum communi Phy ſiologia, ſed præterea opus eſſe eam legibus Geometriæ, atq; </s>
            <s xml:id="echoid-s18853" xml:space="preserve">adeo linearibus demonſtra-
              <lb/>
            tionibus ſubijcere. </s>
            <s xml:id="echoid-s18854" xml:space="preserve">more videlicet opticorum, qui viſionis, atq; </s>
            <s xml:id="echoid-s18855" xml:space="preserve">illuminationis naturam per lineas, & </s>
            <s xml:id="echoid-s18856" xml:space="preserve">angu-
              <lb/>
            los optimè ſolent explicare. </s>
            <s xml:id="echoid-s18857" xml:space="preserve">quod ſi id cuipiam nouum, ac mirum videatur, non tamen impoſſibile videri
              <lb/>
            debet, eum enim hæc reſonantia fiat per reflexionem, reflexio autem omnis fiat per lineas, & </s>
            <s xml:id="echoid-s18858" xml:space="preserve">angulos meri-
              <lb/>
            to eam lineis, & </s>
            <s xml:id="echoid-s18859" xml:space="preserve">angulis reſerendam eſſe duximus. </s>
            <s xml:id="echoid-s18860" xml:space="preserve">ſed in primis exponendæ ſunt ſequentes deſinitiones.</s>
            <s xml:id="echoid-s18861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18862" xml:space="preserve">Quarta. </s>
            <s xml:id="echoid-s18863" xml:space="preserve">Sonorum, ſiue canorum nobis hic eſt omne corpus ſonum, aut vocem primam emittens.</s>
            <s xml:id="echoid-s18864" xml:space="preserve"/>
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