Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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66
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hanc formam, dimidium duorum rectorum eſt rectus, angulus in ſemicir
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culo eſt dimidium duorum
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rectorũ
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, ergo angulus in ſemicirculo eſt rectus.
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</
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<
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<
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">adeò vt hæc ſit demonſtratio omnibus numeris abſoluta per cauſam mate
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rialem, vt benè ſentit Ariſt. </
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<
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">Reliqua ad logicum pertinent, etiamſi per cha
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racteres more mathematicorum exponantur.</
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72</
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">Tex. 24.
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(Vt propter quid reſonat? </
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Iris? </
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">omnia enim hæc idem problemata ſunt genere, omnia enim ſunt refractio, ſed
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ſpecie altera)
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propter quid reſonat? </
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<
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">ſcilicet echo; propter quid apparet?
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</
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<
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">dicit cauſam echo, imaginis in ſpeculo, & iridis
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in nubibus eſſe eandem; nimirum refractionem; quamuis tres illæ refractio
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nes, ſeu; vt melius loquamur, reflexiones differant ſpecie ab inuicem, illa
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enim eſt repercuſſio vocis; hæc reflexio ſpeciei viſibilis ex corpore terſo;
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iſta
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deniq;
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radiorum Solis ex nube rorida in ſtato angulo repercuſſus. </
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">qua
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ratione autem iſta omnia fiant, longum eſſet exponere, & ab intelligentia
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huius loci fortè alienum. </
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<
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">Illud tamen non prætereundum, quod ſi propriè
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cum Perſpectiuis loqui velimus, dicendum eſſe, omnia illa eſſe reflexionem,
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non refractionem. </
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<
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id
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">nam reflexio eſt, quando linea viſualis, per quam fertur
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ſpecies in aliquod corpus terſum, impingit, ex quo deinde ad oculos refle
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ctitur. </
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<
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">refractio tunc eſt, quando ſpecies obiecti viſibilis tranſit per media
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diuerſæ craſſitiei., vt quando ſpecies lapilli per aquam primùm, deinde per
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aerem means ad oculum peruenit; tunc enim linea, per quam ſpecies pro
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greditur, frangitur in confinio aquæ, & aeris, ita vt ſpecies non per vnicam
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lineam rectam, ſed per fractam, ſeu refractam in confinio illo, oculis tan
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dem accidat.</
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(Quoniam Luna deficit)
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non intelligit defectum illum, qui
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eclypſis appellatur, ſed ilium, quo paulatim lumen Lunæ minus oculis no
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ſtris apparet: decreſcente enim Luna ſolent humida augeri.</
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73</
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<
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">Tex. 25.
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(Vt propter quid, & permutatim proportionale? </
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<
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">& c.
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) quod quan
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titates, quæ ſunt proportionales, ſint etiam alternatim, ſeu permutatim
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proportionales explicatum eſt ad tex. 13. primi Poſter. quæ etiam neceſſa
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ria ſunt ad hunc locum benè intelligendum. </
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<
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quod ea, quæ ſunt proportionalia, ſint etiam permutatim proportionalia,
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eſt quoddam innominatum, de quo ibi dictum eſt, quod cum conueniat li
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neis, & numeris, & tamen ſeparatim de vtriſque illa paſſio demonſtretur,
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quærit cuinam primò, & per ſe conueniat hæc paſſio, eſſe permutatim pro
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portionale; ſcilicet quidnam ſit illud innominatum; in quo deinde commu
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nicent lineæ, & numeri, vt inde habeant eſſe etiam permutatim propor
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tionalia.</
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74</
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<
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">Ibidem (
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Hic quidem fortaſſe proportionaliter habere latera, & angulos
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) vult
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indicare, in quonam conſiſtat ſimilitudo inter duas figuras rectilineas geo
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metricas, quam ſimilitudinem Euclides definit. </
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<
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les figuræ rectilíneæ ſunt; quæ & angulos ſingulos, ſingulis angulis æquales
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habent,
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etiam latera, quæ circa angulos æquales ſunt proportionalia.
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<
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">vt ſi duo triangula appoſita habeant angulos æquales,
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angulũ
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A, angulo D:
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angulum B, angulo E. angulum C, angulo F. & præterea latera, quæ ſunt </
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