Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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168</
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<
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">Ibidem
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(Si igitur circumducas ſemicirculŭm, in quo A, circa diametrum in qua
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G K P, que à G, K, reflexæ ad id in quo M; in omnibus planis ſimiliter ſe habebunt,
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& æqualem facient angulum, qui K M G, & quem etiam facient angulum, quæ
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K P, & P M, ſuper eam, quæ G P, ſemper æqualis erit. </
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<
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id
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">Trianguli igitur ſuper eam,
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quæ G P, æquales ei, qui G M P. conſiſtunt. </
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<
s
id
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">horum autem perpendiculares ad idem
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ſignum cadent eius, quæ G P, & æquales erunt, cadunt ad
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grc
">ω,</
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centrum ergò circuli
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<
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ſemicirculus autem, qui circa M N, abſectus eſt ab horizonte)
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hac vltima
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textus parte concludit Iridis portionem ſupra horizontem aſtro
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abbr
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oriẽte
">oriente</
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exi
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ſtentem eſſe ſemicirculum, hoc modo; ſi igitur imaginatione circumducas
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ſemicirculum, in quo A, circa diametrum horizontis G K P, in hac circum
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uolutione duæ lineæ G M, M K, in omnibus planis conſtitui poſſibilibus cir
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ca prædictam diametrum, quæ ſupra etiam fieri à triangulis infinitis dixi
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mus, ſucceſſiuè erunt; ſiue percurrent ſimiliter omnia illa plana, & facient
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vbique angulum Iridis K M G, eundem: pariter duæ lineæ K P, P M, facient
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vndique eundem angulum K P M. quare omnia triangula in predictis planis
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imaginata, &
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abbr
="
cõſtituta
">conſtituta</
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ſuper linea G P, ſimilia ipſi G M P, & æqualia erunt;
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ſi igitur ab angulis ipſorum, in quibus M, ductæ ſint perpendiculares ad la
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tus G P, omnes cadent in idem punctum
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vt in figura;
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abbr
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quarũ
">quarum</
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vna erit M
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grc
">ω,</
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quæ tamen cæteras omnes repreſentabit,
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abbr
="
eisq́
">eisque</
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>
; omnibus in volutatione axis
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G K
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coincidit; erunt autem omnes æquales, quandoquidem ſunt trian
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gulorum æqualium. </
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<
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abbr
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eruntq́
">eruntque</
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; in eodem eiuſdem circuli plano, & punctum
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">ω,</
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erit centrum ipſius. </
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<
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id
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">ſimilia dicta ſunt in Halone. </
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<
s
id
="
s.002123
">Cum ergò ipſius centrum
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<
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grc
">ω</
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, ſit in diametro horizontis G K
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P O, manifeſtum fit portionem eius, quæ
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ſupra horizontem eminet, eſſe ſemicirculum, qui in figura notatur lineis
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L M N. </
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<
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id
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">Atque hoc accidit Sole, vel Luna in horizonte exiſtentibus; quod
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erat primo loco demonſtrandum.</
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<
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">Porrò ſciendum poſſe nos breuius polum prædictum inuenire, ſi nimirum
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ad M, ducatur M P, faciens angulum K P M, æqua
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lem angulo G M K, per 23. primi, erunt enim duo
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triangula
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abbr
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æquiãgula
">æquiangula</
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>
G P M, K P M, angulus enim
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P, eſt communis, angulus verò M K P, eſt æqualis
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duobus G, & G M K, per 32. primi, ergo etiam
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duobus ad M, ſiue toti G M P, & reliquus K M P,
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reliquo, quare per 4.6. latera circa angulos æqua
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les proportionalia erunt, & omologa G M, ad M K, ita G P, ad P M, quæ
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æqualibus angulis ſubtenduntur. </
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<
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abbr
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eaſdẽ
">eaſdem</
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autem proprietates habebant etiam
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triangula Ariſt. in figura, de qua paulò ante dicebam. </
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<
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(Quæ ali
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bi quam in ſemicirculo constituuntur)
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ſunt perperam in antiqua tranſlatione
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tranſlata, nam Græcè ſic,
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transferenda
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eſſent, quæ in alio circuli loco concurrunt.</
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169</
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<
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(Iterum ſit horizon quidem in quo A C. oriatur autem ſupra hunc G,
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axis autem ſit nunc in quo G P. </
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<
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">Polus autem circuli, in quo P, erit ſub horizonte eo, in quo A C, eleuato puncto,
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in quo G. in eadem autem & polus, & centrum circuli, & terminantis nunc ortum,
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eſt enim iſte, in quo G P. </
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<
s
id
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">Quoniam autem ſupra diametrum, quæ A C, quod K G,
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centrum vtique erit ſub horizonte priori eius, in quo A C, in linea K P, in quo
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