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.</s>
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              75</s>
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              <s id="s.001258">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.</s>
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              EX TOPICIS.
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              Ex Primo Libro.
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              76</s>
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              <s id="s.001263">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.</s>
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              77</s>
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              <s id="s.001266">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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              </s>
              <s id="s.001267">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. </s>
              <s id="s.001268">Primus
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              Architas Tarentinus, vt eſt apud Por­
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              phirium in harmonicis Ptolæmei, & Zarlinum pag. </s>
              <s id="s.001269">58. complem. </s>
              <s id="s.001270">muſica­
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              lium, ait, ſi virga celerius feriat aerem, gigni motum celeriorem in aere,
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                <expan abbr="atq;">atque</expan>
              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. </s>
              <s id="s.001271">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. </s>
              <s id="s.001272">hæc ille. </s>
              <s id="s.001273">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. </s>
              <s id="s.001274">ab hac ſententia poſteriores Muſici non recelſ
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              ſerunt, vt videre eſt apud Zarlinum.</s>
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              <s id="s.001275">In quo poſtea conſiſtat ratio acuti anguli, explicat
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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. </s>
              <s id="s.001276">Demum explicat, cur nam gladius dicatur acutus,
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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.</s>
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