Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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circa angulos æquales, v. g. circa an
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gulos A, & D, habeant proportiona
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lia, hoc eſt, vt latus A B, ad latus A C;
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ita ſit latus D E, ad latus D F; & ſic de
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lateribus alijs circa reliquos angulos
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æquales; erunt tunc prædicta duo tri
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angula ſimilia.</
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<
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">Ibidem (
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Vt extrinſecos æquales eſſe
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) ideſt extrinſecos angulos cuiuſuis fi
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guræ rectilineæ æquales eſſe quatuor rectis angulis: vide quæ ſcripſimus de
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hac re ad tex. 39. ſecundi Poſter. quæ huic pariter loco ſatisfaciunt.</
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EX TOPICIS.
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Ex Primo Libro.
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">Cap. 13. (
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Conſiderare, quod diameter est coſtæ incommenſurabilis
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) vide
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quæ de hac re ſcripſi lib. 1. Priorum ſecto 1. cap. 23.</
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">Eodem cap. (
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Similiter autem & acutum; non enim idem ſimpliciter
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in omnibus dicitur: nam vox acuta quidem velox (ſicut dicunt, qui ſe
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cundum numeros harmonici ſunt) angulus autem acutus, qui minor eſt recto; gla
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dius verò, qui eſt anguli acuti
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) affert tres ſpecies acuti, aliud dicens eſſe acu
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tum, quod eſt in voce acuta; aliud, quod eſt in angulo acuto: aliud denique,
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quod eſt in gladio acuto horum enim trium acumen diuerſo modo ſe habet.
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">nam acumen vocis, & ſoni ex celeritate motus, qua aer percuſſus impelli
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tur; grauitatem autem ex tarditate oriri tradiderunt antiqui Muſici om
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nes: quamuis non ex ſola celeritate, & tarditate, ſed ex alijs etiam cauſis
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oriri poſſe voluerint. </
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<
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Architas Tarentinus, vt eſt apud Por
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phirium in harmonicis Ptolæmei, & Zarlinum pag. </
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lium, ait, ſi virga celerius feriat aerem, gigni motum celeriorem in aere,
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hinc ſonum acutiorem reddi, experientia conſtat: ſi autem eadem vir
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ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam ſo
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num grauem, vt experientia docet. </
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<
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">Ptolæmeus deinde lib. 1. cap. 3. Harm.
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cum ex alijs, tum ex celeritate oriri ſonum acutum, grauem verò ex tardi
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tate aſſerit; vt ſi chorda eadem parum intenſa pulſetur, tardius aerem ver
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berat, & ideo grauiorem ſonum efficit: ſi autem magis intendatur, validius
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aerem pulſabit, & proinde citiorem motum illi imprimet, & propterea
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acutiorem ſonum reddet. </
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<
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">videmus etiam, quod cannæ organo
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rum maiores cum plus aeris moueant, & idcirco tardius, ſonum grauiorem
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emittunt, quàm cannæ graciliores, quæ quia parum aeris cient, & ideo ce
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lerius, ſonum acutum edunt. </
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<
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ſerunt, vt videre eſt apud Zarlinum.</
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definitionem
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ipſius, quæ eſt inter definitiones primi Elem. huiuſmodi, Angulus acutus
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eſt, qui minor recto eſt. </
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<
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quia nimirum habet angulum acutum ſuperficialem, ideſt, quem duæ ſuper
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ficies ſimul in acie gladij concurrentes efficiunt.</
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