OCR Text |
Show -. -4 3 s· . . . ' lJe efJ}g;' His cnirrt'przhabids, pa1af!1 eft ex 3., J) 6'j ~heore~atibus, EchuJU...p. notlras· voces att·crnatu·ramcfie ;~fitq\le:ex· qpoltbet panetc Echum audJCc: potcrimu~ •• . A dato·q.U<Jlibet pl'ano pariete c cbum,: obli~uam_ elicere~ . : · ProhlemA· I ll. S Ollqrum , ~-A~dle~siil:~lilerfisp~riCti$-p-al'reS'vtriilque ab~ant, it~. vt vterque ~bltqu6 pl'rfc.cem medtllm,net't'lolf.qUantum 6en poteft ad: aoguloS'zquale¥ afi!i~i:a·nf;: fi·cuci· lecunda h~~~~~dj_cat; Ybi ex ~onoro · A, linca·Sonora. ~B,!ih patJetem DB E·,, obhqu~ mctdcns· reflecbtur ad. Aadientem· C, ger-linealn' B'C, fiuntque angnl'f. itttidcntaz A B D,& rcflc .. xionis-C BE z~altt;· qu·ate per 1 1~ Theoro-AhditbS in C,audtet Echur~ipfius A:., hoc cft"audict v·&c·cm ~ius.u;f.exam.• & potcrit aliquando etiam. audir~ prim!riam.;.- . l!odenrmodo ficile.crie Jtclium fccundariam} tcrtiariam, &c. ex Thcoo· conftrucrc o• ecbum:circu(artMc6nflruert •. TrobL IV. ' A D haAc:pUJClicrrimam conftruB:ionefll opus eft' duob.us ptanis paric•} Il. tibus invtic~m· paral.Je:ll~is magnis, fatifque inuictm dift:antibus ... · in horum alte'tius f'~ncftris Sonortlm timul di atijs auditoribus collocandi: funt: Sonorut'll".qurdem in medio, ahj vcro auditores ~irca ipfum in gyru •. alter auten'l'·l'aries erit pro Refiedenr:e.quibus paratis, (ex:dicti&.ad J.dc• finic •. ) vox Sonori non foJum normal iter incidet in oppofirum R"efleetcn!p~ fed etiam circunquaquc oblique, & in eadem diltantu ;tnormali,ideft, ad' finiftram, ad dextera, {urfum, dcorfum zqne long~ a perpcndiculari.qua· re edam· oblique refleftentur per plurimas~ lineas in diuetfas partes per' angulos zqualcs aogulis incidentium~ vndc & act priorem murum rcuer• teocu·r, in quo Sqnorum, & ahj circa ipfum a.udientes fiti funt.-.Jinea· igitur· norma lis rcu(rtctur ad ipfum Sonorurn ;: ali~ vero ad alios auditores ip-:fum fntiStlonge circund.antes ~~· ac·proinde 1j omoes propri;ts Edius c.rau .... dic:~r~ vt pat~t ex Confe~ario Theor.Jl .. & par tim intelligi porctt·eJtfigu•. ra ctufdem; aq qua Gcurt dhas· Ed\us dextram, & finifibtm al:feodtm so-. noro A', ad· aud itore~ C, H~f d~pingtmus ;· fie etiam innunteras alras ex pJll" ~imi!t pnnct'is eiufdc::rrt pat ic t·is circa D, in eund'em or be' cum B, E·,ficis,con .. · ~ipc:re de?emus ~efle.X!a~· a_d,.a ios audicorcs c:irea: ipfum !f., in circulusu Ja fcnctlns altcnus panetJS' 1mul cum; ~, fonoroi· conftitutosit' , De lebo, ~ - ·· I • • I . - , , J,ili~ llil !in"Dri; ~114 cum ~i~s.1ineil-~:~$gnli ; ~j 'B.ffletlcns ....__. . _ -- ... .J . EchHm conflruert. . Probl~m~ v. ·' :. , ' • t ' - . ' . r A LocoSonorin,etirereaam ,diftantia~ . non maiorem femilfe tine~ rl'. aaioais eiufdep): mer.it:e e'•am ab eodem loco verfus eandem parterq minimam Rcfic¢tenci~ ditl~ciarn, videli~~c pa~us geometricos 14, plus minus. atq~e inter vcnunq~P. ter~'nu~ c~n~rue Reft~ctens aliq~od efupcriortbus , . to lieu t~(n,:o pcrpe~d~~~r1 ad hneam acttooJs. man•fe. ftun, eoim ettex Theor • .J .J. ~ I! chum i9~e ·a~dit~fl) iri.Czterum fi dift:an· ci~ fuerit 11-, p~tfuu~, eric J;ch9 mppo.fyliabC&);Ji +1,1~ilfy.Uabaj ij 7o,fcre, ~.ifyllaba , &,, . · · ~ ' ' . . ' .Bchum po[yphonam tonftruere: _Proble~4 V Ji ' : : ' (' . . , I' • ' 1 • ~ J ... ... • ,.. P RimG in plaoitie qu~piam ratis mag!l~· elig~;ar lo~u~ ~nortl po~~e ex przeedenti Pro~h cq~&rua\)turJ?ltJ:ra-a.d eum Jqe.unt R.eflectencia, cum diuerfis ae calibus ab eo· di(iantijs f't pririlurrl., feu qt~od ei prop ius &nit, Il"Chum mflnofyllabam·refor:tA fcc}lq~ull\quodJerc d~plo dilt ~b~e. dilfyllabarn: tertium quod qulli·:triplo aberit, tr.lfyllab1q1. & lie deinccp. ptout libL1eric'l!chum effi :f.-ereTmJrnerofiorcm.~rca~ ~gi~ul"· t~qpliq.ap Ecnu~ c.onftitucnt; quot ipfa eruot It';fiect!llti-a; r:epecencquc fig gula v~~ m.,,ean< ieMque fyll.a~am, contihaJ.o poA: alte_ram, tot~cs qu~~ ipfa (~nt; vt c:~ dcmontlratis ·cooftat. Pottro B.eflect~ntia hac ratione,&: ordi~c conftrufra...,. Echum cffieieot, vt ~x ipfa conftructione p~tet, pory,honam qu_id em , fed monofyllabam: quaouis enill).feC,:uodum poffic repetere duas fyll a bas, & tertium tres;&c.quia taruen prilltllm vnam caoc.gm rcdere potdl,idco neceife eft, tcliqua ei .t<:commodati, vc vnarn eand~~~~uc.·c:um eo. pari.ter refonent.·quod 6 velimtlS Echum po~yphonam ,diffyl.l.abam, qua: fcilicct Yerbum diffy:abum referat; cont\ruendu!ll eft ex pr~ced- Probl. primum Reflecteas, quoJ'ficdi:ffyll~blt1l1, cuius diftantia edt, fere 46,palfuum. fe· cundum vero cui us di!lancia lie paulo minor quam d\lpla pra:cedentis ,_ & reliqua e 1dem ratione. 6 Yero veli mus Echum trify!Iabam, au::· tctrafy·l- ·lablm, eamconftruernus ex przcedenti Probl. propQrtionaliter ad pi~- dich._,. · ~ · · ., ·· · , · Ex quibus patet, 6 ~priori ferie Reflectentium, auferancur ea , qu~ numero icrtpari" ffi~iuu-tur.iJqfl, primum, tertium, &c.·imparia,ea qtu: rolinqu~nt.LJr.,tff~etura ellc Echurn polyphonam dilfyllabam, & c. Porro pro.num~~QJl..efl e<!entiurn erjt Echo aut diphona , . aut triphona, autretr> 3phQ!l.a, pentaphona, &e. Seienclurn pr~terea po1fe ha:c Ref'c:Cier.ti'\-1 ~rio.ordine collocari, idelt,aut omnia fecund ttm eandem hori~onris pia. ~ KKk gam |