Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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Ex Tertio Phyſicorum.
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93</
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<
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">Tex. 26.
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(Et hi quidem infinitum eſſe par; hoc enim compræhenſura, &
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ab impari terminatum tribuit ijs, quæ ſunt, infinitatem. </
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<
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">ſignum autem
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huius id eſſe, quod contingit in numeris, circumpoſitis enim Gnomoni
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bus circa vnum, & ſeorſum, aliquando quidem ſemper aliam fieri ſpe
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ciem, aliquando autem vnam)
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vt melius percipiantur ea, quæ ſequuntur, lege
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prius, quæ in cap. de Motu in poſt prædicamentis ſcripſi de Gnomone, ad
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ſimilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu
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meris Gnomones Arithmetici. </
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<
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">Pythagorici enim (à quibus iſta mutuatus
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eſt Ariſt. numeros impares ſolos appellabant Gnomones, eò quod in for
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mam normæ æquilateræ, ſiue Gnomonis conſtitui poſſint, vt patet in his
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nimirum in ternario, quinario, ſeptenario, & ſic de
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reliquis imparibus. </
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">pares autem numeri, quia ne
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queunt in figuram normæ æquilateræ diſponi, cum
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non habeant vnitatem pro angulo, & paria poſtea la
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tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, ſi di
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ſponatur ſic
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non refert Gnomonem, quia lateribus inęqualibus con
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ſtat;
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ſi hoc modo
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quia deeſt huic figuræ angularis vnitas, quæ
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illi neceſſaria eſt. </
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<
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">Pythagorici igitur dicebant, numerum parem ideò eſſe
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infinitum ipſum, quia videbant ipſum eſſe cauſam perpetuæ diuiſionis, cum
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quælibet res quanta ſit diuiſibilis bifariam, ideſt in duo ſecundum numerum
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parem, & ſubdiuiſibilis poſtea bifariam, & ſic in infinitum, vt de linea pro
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blematicè probatur in 10. primi Elem. quamuis theorematicè ſit axioma.
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</
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<
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">hunc porrò numerum parem dicebant terminatum eſſe ab impari, quia ori
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tur ex diuiſione cuiuſuis rei, quæ vna ſit, ſumentes vnitatem pro impari.
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<
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">ſignum præterea huius finitatis ab impari, & infinitatis à pari numero pro
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cedentis, aiunt eſſe Gnomones, numeros ſcilicet impares: Gnomones enim,
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ideſt impares numeri vnitati additi, producunt eandem perpetuò numero
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rum formam, videlicet quadratum: at verò è contrariò numeri pares vni
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tati additi, conflant perpetuò varias numerorum formas: quapropter vi
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dentur numeri impares eſſe finitatis cauſa; ſicut pares ex aduersò infinitatis
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principium. </
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<
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">quæ vt melius intelligas, declaranda eſt 26. propoſ. </
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<
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metices lordani, vbi iſtud idem demonſtrat, quæ eſt hæc. </
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<
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dine ſequantur impares, vt in ſequenti hac ſerie apparet 1. 3. 5. 7. 9. & c.
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ſi igitur vnitati addatur ternarius in Gnomo
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nis modum, vt vides in prima figura, produ
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cetur quaternarius numerus, qui eſt numerus
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quadratus (quid ſit quadratus numerus expli
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caui in Logicis tex. 9. primi Poſter.) etſi huic
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quaternario addatur ſequens impar, qui eſt
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quinarius in modum Gnomonis, vt in ſecunda
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figura, ſit numerus nouenarius, qui pariter eſt quadratus. </
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<
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addatur ſequens impar, nimirum ſeptenarius, conflabitur ſedenarius, qui
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numerus pariter quadratus eſt, vt in tertia figura, & hoc modo, ſi in </
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