Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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43
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G H D, appoſito
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vtiq;
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communi angulo B G H, erant primum, duo anguli
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E G B, B G H, maiores, quam ſint duo B G H, G H D, quia ſi inæqualibus
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æqualia addantur, tota erunt inæqualia, vt prius per 4, axioma: hoc loco
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communis angulus additur ſemel maiori angulo, & ſemel minori; & ideo
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totum illud, in quo eſt maior angulus, adhuc maius eſt altero toto, in quo
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minor angulus continetur. </
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<
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">at illi duo E G B, B G H, per 13. primi, ſunt
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æquales duobus rectis angulis, ergo duo
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quoq;
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recti erunt maiores duobus
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internis B G H, D H G, ſiue hi duo interni erunt minores duobus rectis.
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</
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">At quando hi duo interni ſunt minores duobus rectis, tunc lineæ A B, C D,
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ſunt concurrentes, ſi protrahantur ad partes prædictorum
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angulorũ
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. </
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P. Clauius luculenti, & hactenus deſiderata demonſtratione ad 28. primi
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demonſtrauit. </
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Atq;
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hoc pacto ex prima falſa ſuppoſitione, nimirum angu
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lum illum externum eſſe maiorem interno, & oppoſito; ſequitur falſum, ni
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mirum lineas parallelas concurrere.</
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">Præterea ſi ſupponamus aliam falſitatem, ſcilicet triangulum habere tres
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angulos maiores duobus rectis, ſequetur eadem iterum falſitas, ſcilicet pa
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rallelas coincidere, & probatur ſic; ſint enim
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triãguli
">trianguli</
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A B C, tres anguli maiores, quam duo
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recti anguli, & per punctum C, ducta ſit recta
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C D, parallela lateri B A. quia ergo angulus
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A, æqualis eſt angulo ſibi alterno A C D, per
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29. primi, & quia totalis angulus B C D, æqua
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lis eſt duobus angulis B C A, A C D, quos tanquam ſuas partes adæquatas
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continet, quorum alter, ſcilicet A C D, eſt æqualis angulo A. erit idem to
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talis angulus B C D, æqualis duobus angulis A, & A C B, trianguli propoſi
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ti. </
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">ergo totus iſte angulus B C D, ſimul cum reliquo
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triãguli
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angulo B. con
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ſtabit compoſitionem ex tribus angulis trianguli dati: & conſequenter ta
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lis compoſitio trium angulorum erit maior, quam ſint duo anguli recti. </
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quo ſequitur duas rectas B A, C D, ſuper quas cadit linea B C, faciens duos
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angulos internos, & ad eaſdem partes, ſcilicet A B D, maiores duobus re
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ctis non eſſe parallelas, ſed concurrentes (vt patet ex nuper citata demon
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ſtratione P. Clauij) quod falſum eſt. </
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<
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">& ſequitur ex ſecunda falſa ſuppoſitio
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ne. </
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15</
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<
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">Ex cap. 26.
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(Vt ſi A, duo recti, in quo autem P., triangulus, in quo vero C,
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ſenſibilis triangulus, ſuſpicari
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namq;
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poſſet aliquis non eſſe C, ſciens, quod omnis
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triangulus habet duos rectos: quare ſimul noſcet, & ignorabit idem. </
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<
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omnem triangulum, quod duobus rectis, non ſimplex eſt: ſed hoc quidem eo, quod
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vniuerſalem habet ſcientiam: illud autem eo, quod ſingularem. </
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<
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">ſic igitur, vt vni
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uerſale nouit C, quod duo recti; vt autem ſingulare non nouit, quare non habebit
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contrarias)
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vide, quæ diximus lib. 1. ſecto 3. cap. 1. ex quibus quidquid Ma
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thematicum eſt hic, clarum redditur. </
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">reliqua verò, quæ ad Logicum ſpe
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ctant, huius loci commentatores proſequuntur.</
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16</
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">Notandum hic cum eruditiſſimo Burana, Abductionem hanc, de qua in hoc
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cap. agitur eſſe vocem mathematicam,
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; Ariſt. quemadmodum multa
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alia à Mathematicis mutuatum ad omnes alias ſcientias tranſtuliſſe. </
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<
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