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

List of thumbnails

< >
181
181 (154) 		182
182 (155)
183
183 (156) 		184
184 (157)
185
185 (158) 		186
186 (159)
187
187 (160) 		188
188 (161)
189
189 (162) 		190
190 (163)
< >
page |< < (230) of 300 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div516" type="section" level="1" n="391">
          <pb o="230" file="0252" n="257" rhead="DE ECHO."/>
        </div>
        <div xml:id="echoid-div518" type="section" level="1" n="392">
          <head xml:id="echoid-head411" style="it" xml:space="preserve">Dati ſonori lineam actionis reperire. Problema I.</head>
          <p>
            <s xml:id="echoid-s19684" xml:space="preserve">IDexperimẽto diſees, tanta eſt enim linea actionis, quanta eſt maxima diſtãtia, ex qua vox tua ab alio audiri
              <lb/>
            poterit. </s>
            <s xml:id="echoid-s19685" xml:space="preserve">vel abſq; </s>
            <s xml:id="echoid-s19686" xml:space="preserve">auxilio alterius, ſed tantũ auxilio ipſius Echus: </s>
            <s xml:id="echoid-s19687" xml:space="preserve">ſi enim a pariete tibi reſonã@e eouſq; </s>
            <s xml:id="echoid-s19688" xml:space="preserve">pau
              <lb/>
            l
              <unsure/>
            atim recedas donec vltimo Echũ exaudias, erit diſtadtia hæc dimidia lineę actionis, vt ex 6. </s>
            <s xml:id="echoid-s19689" xml:space="preserve">Theor. </s>
            <s xml:id="echoid-s19690" xml:space="preserve">apparet.</s>
            <s xml:id="echoid-s19691" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div519" type="section" level="1" n="393">
          <head xml:id="echoid-head412" style="it" xml:space="preserve">Dato quouis reflectente, & quouis ſonoro, locum reperire vnde ſonorum
            <lb/>
          ſibi Echum eliciat. Problema II.</head>
          <p>
            <s xml:id="echoid-s19692" xml:space="preserve">PRimò ſonorum conſtituendum eſt in eo loco, vnde vocalis eius linea normaliter teflectenti occurrat.
              <lb/>
            </s>
            <s xml:id="echoid-s19693" xml:space="preserve">Secundo, in tanta ab eo diſtantia, quæ maior non ſit ſemiſſe lineæ actionis inuentæ ex problem. </s>
            <s xml:id="echoid-s19694" xml:space="preserve">præce-
              <lb/>
            denti, nec minor 24. </s>
            <s xml:id="echoid-s19695" xml:space="preserve">paſſibus geometricis.</s>
            <s xml:id="echoid-s19696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19697" xml:space="preserve">His enim præhabitis, palam eſt ex 3. </s>
            <s xml:id="echoid-s19698" xml:space="preserve">5. </s>
            <s xml:id="echoid-s19699" xml:space="preserve">6. </s>
            <s xml:id="echoid-s19700" xml:space="preserve">Theorematibus, Echum noſtras voces alternaturam eſſe; </s>
            <s xml:id="echoid-s19701" xml:space="preserve">ſic-
              <lb/>
            que ex quolibet pariete Echum audire poterimus.</s>
            <s xml:id="echoid-s19702" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div520" type="section" level="1" n="394">
          <head xml:id="echoid-head413" style="it" xml:space="preserve">Adato quolibet plano pariete Echum obliquam elicere. Problema III.</head>
          <p>
            <s xml:id="echoid-s19703" xml:space="preserve">SOnorum, & </s>
            <s xml:id="echoid-s19704" xml:space="preserve">audiens in diuerſas parietis partes
              <unsure/>
            vtrinq; </s>
            <s xml:id="echoid-s19705" xml:space="preserve">abeant, ita vt vt vterq; </s>
            <s xml:id="echoid-s19706" xml:space="preserve">obliquè parietem mediũ,
              <lb/>
            necnon quantũ fieri poteſt ad angulos ęquales aſpici
              <unsure/>
            ant; </s>
            <s xml:id="echoid-s19707" xml:space="preserve">ſicuti ſecunda figura indicat; </s>
            <s xml:id="echoid-s19708" xml:space="preserve">vbi ex ſonoro A. </s>
            <s xml:id="echoid-s19709" xml:space="preserve">li-
              <lb/>
            nea ſonora A B. </s>
            <s xml:id="echoid-s19710" xml:space="preserve">in parietem D B E. </s>
            <s xml:id="echoid-s19711" xml:space="preserve">oblique incidens reflectitur ad audientem C. </s>
            <s xml:id="echoid-s19712" xml:space="preserve">per lineam B C. </s>
            <s xml:id="echoid-s19713" xml:space="preserve">fiuntq; </s>
            <s xml:id="echoid-s19714" xml:space="preserve">an-
              <lb/>
            guli incidentiæ A B D. </s>
            <s xml:id="echoid-s19715" xml:space="preserve">& </s>
            <s xml:id="echoid-s19716" xml:space="preserve">reflexionis C B E. </s>
            <s xml:id="echoid-s19717" xml:space="preserve">æquales, quare per 12. </s>
            <s xml:id="echoid-s19718" xml:space="preserve">Theor. </s>
            <s xml:id="echoid-s19719" xml:space="preserve">audiens in C. </s>
            <s xml:id="echoid-s19720" xml:space="preserve">audiet Echum ipſius
              <lb/>
            A. </s>
            <s xml:id="echoid-s19721" xml:space="preserve">hoc eſt audiet vocem eius reflexam. </s>
            <s xml:id="echoid-s19722" xml:space="preserve">& </s>
            <s xml:id="echoid-s19723" xml:space="preserve">poterit aliquando etiam audire primariam.</s>
            <s xml:id="echoid-s19724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19725" xml:space="preserve">Eodem modò facilè erit Echum ſecundariam, tertiariam, &</s>
            <s xml:id="echoid-s19726" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19727" xml:space="preserve">ex Theor. </s>
            <s xml:id="echoid-s19728" xml:space="preserve">conſtruere.</s>
            <s xml:id="echoid-s19729" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div521" type="section" level="1" n="395">
          <head xml:id="echoid-head414" style="it" xml:space="preserve">Echum circularem construere. Problema IV.</head>
          <p>
            <s xml:id="echoid-s19730" xml:space="preserve">AD hanc pulcherrimam conſtructionẽ opus eſt duobus planis parietibus inuicem paralellis ſatis magnis,
              <lb/>
            ſatiſq; </s>
            <s xml:id="echoid-s19731" xml:space="preserve">inuicem diſtantibus. </s>
            <s xml:id="echoid-s19732" xml:space="preserve">in horum alterius feneſtris ſonorum ſimul cum alijs auditoribus collocandi
              <lb/>
            ſunt: </s>
            <s xml:id="echoid-s19733" xml:space="preserve">Sonorum quidem in medio, alij vero auditores circa ipium in gyrum. </s>
            <s xml:id="echoid-s19734" xml:space="preserve">alter autem paries erit pro re-
              <lb/>
            flectente. </s>
            <s xml:id="echoid-s19735" xml:space="preserve">quibus paratis (ex dictis ad 5. </s>
            <s xml:id="echoid-s19736" xml:space="preserve">definit.) </s>
            <s xml:id="echoid-s19737" xml:space="preserve">vox ſonori non ſolum normaliter incidet in oppoſitum re-
              <lb/>
            flectens, ſed etiam circumquaq; </s>
            <s xml:id="echoid-s19738" xml:space="preserve">obliquè, & </s>
            <s xml:id="echoid-s19739" xml:space="preserve">in eadem diſtantia a normali, ideſt, ad ſiniſtram, ad dexteram, ſu@
              <lb/>
            ſum, deorſum æquè longè à
              <unsure/>
            perpendiculari. </s>
            <s xml:id="echoid-s19740" xml:space="preserve">quare etiam obliquè reflectentur per plurimas lineas in diuer-
              <lb/>
            ſas partes per angulos æquales angulis incidentium, vnde & </s>
            <s xml:id="echoid-s19741" xml:space="preserve">ad priorem murum reuertentur, in quo ſonorũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s19742" xml:space="preserve">alij circa ipſum audientes ſiti ſunt. </s>
            <s xml:id="echoid-s19743" xml:space="preserve">linea igitur normalis reuertetur ad ipſum ſonorum; </s>
            <s xml:id="echoid-s19744" xml:space="preserve">aliæ verò ad alios
              <lb/>
            auditores ipfum ſatis longè circumdantes, ac proinde ij omnes proprias Echus exaudient. </s>
            <s xml:id="echoid-s19745" xml:space="preserve">vt patet ex Con-
              <lb/>
            ſectario Theor. </s>
            <s xml:id="echoid-s19746" xml:space="preserve">12. </s>
            <s xml:id="echoid-s19747" xml:space="preserve">& </s>
            <s xml:id="echoid-s19748" xml:space="preserve">partim intelligi poteſt ex figura eiuſdem; </s>
            <s xml:id="echoid-s19749" xml:space="preserve">in qua ſicuti duas Echus dextram, & </s>
            <s xml:id="echoid-s19750" xml:space="preserve">ſiniſtrã
              <lb/>
            ab eodem ſonoro A. </s>
            <s xml:id="echoid-s19751" xml:space="preserve">ad auditores C H. </s>
            <s xml:id="echoid-s19752" xml:space="preserve">depingimus; </s>
            <s xml:id="echoid-s19753" xml:space="preserve">ſic etian, innumeras alias ex plurimis punctis eiuſdem
              <lb/>
            parietis circa D. </s>
            <s xml:id="echoid-s19754" xml:space="preserve">in eundem orbem cum B E. </s>
            <s xml:id="echoid-s19755" xml:space="preserve">ſitis, concipere debemus reflexas ad alios auditores circa ipſum
              <lb/>
            A. </s>
            <s xml:id="echoid-s19756" xml:space="preserve">in circulum in feneſtris parietis ſimul cum A. </s>
            <s xml:id="echoid-s19757" xml:space="preserve">ſonoro, conſtitutos.</s>
            <s xml:id="echoid-s19758" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div522" type="section" level="1" n="396">
          <head xml:id="echoid-head415" style="it" xml:space="preserve">Dato loco ſonori, vna cum eius linea actionis, eireflectus Echum conſtruere
            <lb/>
          Problema V.</head>
          <p>
            <s xml:id="echoid-s19759" xml:space="preserve">ALoco ſonori metire rectam diſtantiam noh maiorem ſemiſſe lineæ actionis eiuſddem: </s>
            <s xml:id="echoid-s19760" xml:space="preserve">metire etiam ab
              <lb/>
            eodem loco verſus eandem partem minimã reflectentis diſtantiam, videlicet paſſus geometricos 24. </s>
            <s xml:id="echoid-s19761" xml:space="preserve">plus
              <lb/>
            minus. </s>
            <s xml:id="echoid-s19762" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s19763" xml:space="preserve">inter vtrumq; </s>
            <s xml:id="echoid-s19764" xml:space="preserve">terminum cõſtrue reflectens aliquod è ſuperioribus, in ſitu tamen perpendiculari
              <lb/>
            ad lineam actionis. </s>
            <s xml:id="echoid-s19765" xml:space="preserve">manifeſtum enim eſt ex Theor. </s>
            <s xml:id="echoid-s19766" xml:space="preserve">3. </s>
            <s xml:id="echoid-s19767" xml:space="preserve">5. </s>
            <s xml:id="echoid-s19768" xml:space="preserve">6. </s>
            <s xml:id="echoid-s19769" xml:space="preserve">Echum inde auditum iri. </s>
            <s xml:id="echoid-s19770" xml:space="preserve">Cæterum ſi diſtantia
              <lb/>
            fererit 24. </s>
            <s xml:id="echoid-s19771" xml:space="preserve">paſſuum, erit Echo monoſyllaba; </s>
            <s xml:id="echoid-s19772" xml:space="preserve">ſi 48. </s>
            <s xml:id="echoid-s19773" xml:space="preserve">diſſyllaba; </s>
            <s xml:id="echoid-s19774" xml:space="preserve">ſi 70. </s>
            <s xml:id="echoid-s19775" xml:space="preserve">ferè triſyl@aba, &</s>
            <s xml:id="echoid-s19776" xml:space="preserve">c.</s>
            <s xml:id="echoid-s19777" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div523" type="section" level="1" n="397">
          <head xml:id="echoid-head416" style="it" xml:space="preserve">Echum polyphonam conſtruere. Problema VI.</head>
          <p>
            <s xml:id="echoid-s19778" xml:space="preserve">PRimo in planitie quapiam ſatis magna, eligatur locus ſonori; </s>
            <s xml:id="echoid-s19779" xml:space="preserve">poſtea ex præced. </s>
            <s xml:id="echoid-s19780" xml:space="preserve">Probl. </s>
            <s xml:id="echoid-s19781" xml:space="preserve">conſtruantur plu-
              <lb/>
            ra ad eum locum reflectentia, cum diuerſis ac talibus ab eo diſtantijs vt primũ, ſeu quod ei propius fuerit,
              <lb/>
            Echum mono@yllabam reſohet: </s>
            <s xml:id="echoid-s19782" xml:space="preserve">ſecundum quod ferè duplo diſtabit diſſyllabam: </s>
            <s xml:id="echoid-s19783" xml:space="preserve">tertium quod quaſi triplo
              <lb/>
            aberit, triſyllabam. </s>
            <s xml:id="echoid-s19784" xml:space="preserve">& </s>
            <s xml:id="echoid-s19785" xml:space="preserve">ſic deinceps prout libuerit Echum efficere numeroſiorem ea igitur totuplicem Echũ
              <lb/>
            conſtituent, quot ipſa erunt reflectentia; </s>
            <s xml:id="echoid-s19786" xml:space="preserve">repetentq; </s>
            <s xml:id="echoid-s19787" xml:space="preserve">ſingula vnã eandemq; </s>
            <s xml:id="echoid-s19788" xml:space="preserve">ſyllabam, continuò poſt </s>
          </p>
        </div>
      </text>
    </echo>
Impressum