Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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ex
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quinq;
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prædictis proportionibus, ſi ſimul coaluerint, ita vt ex eis vnus
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tantum ſonus efficiatur; ſonus ille erit concordans, & auribus gratus. </
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hæc eſt ſententia priſcorum præſertim Pythagoreorum, qui propterea di
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cebant non licere Muſico vltra quaternarium pertranſire, eò quod ſolæ pro
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portiones, vt diximus, numerorum quaternario contentorum, concordem,
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ac conſonantem concentum efficere poterant: quod vt adhuc melius per
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cipiamus, accipe exemplum. </
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<
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">Sint duæ chordæ
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A, & B, æqualis craſſitici, & æquè tenſæ. </
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<
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rum A, dupla ſit ipſius B, quia igitur corpora
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ſonantia ſunt in dupla proportione, erunt pa
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riter eorum ſoni in ratione dupla (vt patet ex
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principijs harmonicæ) hoc eſt,
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eorũ
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ſoni erunt,
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vt 2. ad 1. quia ſcilicet ſonus maioris chordæ A, erit duplus ad ſonum mi
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noris chordæ B. hoc eſt, erit, vt 2. ad 1. & propterea, ſi ſimul ambæ chordæ
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pulſentur, ſonus, quem ex duobus mixtum edent, conſonans,
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gratiſſi
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mus auribus noſtris perueniet. </
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<
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">huiuſmodi porrò conſonantia, quæ eſt in
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proportione dupla,
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omnium ſuauiſſima eſt, à græcis dicebatur Dia
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paſon. </
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hæc in præſentia ſufficiant, cum plura de his ad ſectionem pro
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blematum 19. quæ tota eſt de Muſica, dicenda ſint.</
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65</
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<
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">Tex. 2.
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(Vt quod omnis triangulus duobus rectis æquales habet)
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vide anno
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tata lib. 1. Priorum ſecto 3. cap. 1.</
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<
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(Definitiones verò apparent omnes ſupponentes, & accipientes
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ipſum quid eſt, vt Mathematicæ, quid vnitas, quid par, & impar)
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alludit ad de
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finitiones 7. Elem. vbi agitur de numeris. </
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dicuntur, luculentiſſimè patent conſideranti definitiones, & axiomata, quæ
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Mathematicis demonſtrationibus in omnibus ferè libris præmittuntur; ex
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quibus ſtatim demonſtrationes deriuantur.</
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<
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">Et paulo poſt
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(
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de plano figura, non enim eſt planum figura,
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fi
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gura planum)
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alludit ad definitiones planarum figurarum, qualis eſt circu
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lus, cuius definitio eſt inter definitiones primi Elem. 15. & eſt huiuſmodi:
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circulus eſt figura plana, ſub vnica linea comprehenſa, quæ periphæria ap
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pellatur, ad quam ab vno puncto eorum, quæ intra figuram ſunt poſita, ca
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dentes omnes rectæ lineæ inter ſe ſunt æquales: in qua quidem definitione
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non prædicatur planum de figura, nec figura de plano:
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enim planum,
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ſeu plana ſuperficies eſt figura ſecundum ſe, niſi terminetur;
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neq;
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figura eſt
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plana ſuperficies, cum plurimæ ſint figuræ curuæ, & præterea ſolidæ quam
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plurimæ.</
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(Quoniam monſtratum eſt Iſoſceles habere tres angulos æquales duo
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bus rectis, ſi id de omni triangulo monſtratum ſit)
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ex dictis lib. 1. Priorum ſecto
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3. cap. 1. petatur huius loci declaratio.</
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69</
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(Quid enim ſignificat triangulum, accipit Geometra)
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vt manifeſtum
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eſt in 20. definitione primi Elem.</
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70</
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<
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(Quod autem ſit, monstrat)
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vt perſpicuum eſt in prima
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tione</
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primi Elem. vbi triangulum æquilaterum conſtruit, & poſtea probat
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illud eſſe triangulum æquilaterum. </
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<
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nere triangulum in communi, cum inter definitiones ipſius </
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