Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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52
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ſeparatim oſtendit, aut vtens diuerſis demonſtrationibus, vna pro æquila
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tero, altera pro Iſoſcele, tertia pro Scaleno, oſtendens, quod
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vnumquodq;
">vnumquodque</
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illorum habet tres angules æquales duobus rectis angulis; iſte nondum no
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uit triangulum omne habere talem affectionem, niſi modo ſophiſtico, quia
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non cognoſcit hanc affectionem illis
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cõpetere
">competere</
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propter naturam illam com
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munem trianguli, cui primo, & per ſe competit; & neque vniuerſaliter co
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gnoſcit triangulum omne eſſe tale, etiam ſi nullum aliud reperiatur trian
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gulum, præter illud æquilaterum, vel illud Iſoſceles, vel illud Scalenum, de
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quibus ſeparatim
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abbr
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demõſtrauit
">demonſtrauit</
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, & ſecundum numerum, ideſt de vnoquoque,
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quatenus eſt vnum numero. </
s
>
<
s
id
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">non nouit autem ſecundum ſpeciem, idest fecun
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dum naturam, & formam communem illis tribus indiuiduis, quæ eſt natu
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ra trianguli. </
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<
s
id
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s.000958
">hoc autem eſſe exemplum primi erroris manifeſtè conuincitur,
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tum ex verbis illis, quando nihil ſit ſuperius, præter ſingulare, tum ex hu
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ius textus verbis illis
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(Singulum triangulum)
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& ex illis
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italics
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(Niſi ſecundum nume
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rum)
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ideſt, niſi de vno, quod ſit vnum numero. </
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<
s
id
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s.000959
">propterea nos de ſingulari
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triangulo omiſſa Zabarellæ ſententia explicauimus tandem in confirma
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tionem noſtræ expoſitionis in hæc tria errata illud non omittendum, ſatius
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eſſe dicere, Ariſt. attuliſſe pro tribus erratis tria exempla ordine retrogra
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do, quàm, quod facit Zabarella, primum eſſe pro tertio, ſecundum pro pri
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mo, tertium verò pro ſecundo; eo enim modo, Ariſt. confuſionem nulla ra
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tione, imò contra omnem rationem imponimus.</
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31</
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<
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">Textu 14. continet quidem quædam mathematica, ſed ferè eadem cum
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ſuperioribus, quæ quia tum ex prædictis facile intelligi poſſunt, tum quia
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benè ab expoſitoribus explicantur, ne actum agamus, prætermittimus.</
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32</
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<
s
id
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">Tex. 20.
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(Niſi magnitudines numeri ſint)
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hoc eſt, niſi magnitudines ſint di
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feretæ, ita vt cadant ſub numerum, vt ſi linea quæpiam diuidatur in partes
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decem, vel duodecim, tunc euadit quantitas diſcreta, ſiue numerus. </
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<
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id
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s.000966
">& tunc
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linea numerus eſt. </
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<
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id
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">idem de ſuperficie, ac ſolido intelligendum.</
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33</
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<
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">Ibidem
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(Propter hoc Geometriæ non licet monſtrare, quod contrariorum vna
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eſe ſcientia, ſed neque quod duo cubi cubus)
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quo ad verba illa, duo cubi cubus,
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quæ ad nos pertinent, vult Ariſt. docere, quod non debet Geometra oſten
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dere numerorum affectiones (per cubos enim intelligit numeros quoſdam
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ſic dictos, vt paulo poſt oſtendam) vt ſi quis vellet geometricè oſtendere id,
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quod oſtenditur in 4. noni Elem. ſcilicet, ſi cubus numerus cubum numerum
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multiplicauerit, productus numerus erit pariter cubus. </
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<
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id
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">nonnulli latinorum
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perperam textum hunc expoſuerunt putantes reperiri ſolummodo cubos
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geometricos, at Euclides definit. </
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<
s
id
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">19. ſeptimi, ſic arithmeticum cubum de
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finit, cubus numerus eſt, qui ſub tribus numeris æqualibus continetur, qua
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lis eſt. </
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<
s
id
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s.000973
">8. qui eſt ad inſtar cubi geometrici, & continetur ſub tribus binarijs
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multiplicatis inuicem, quæ multiplicatio ſic inſtituitur, exponuntur tres bi
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narij, 2, 2, 2, primus ducitur in ſecundum, & producitur.
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<
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">4. qui eſt numerus quadratus huius figuræ,
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, deinde
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tertius binarius ducitur in prædictum quadratum 4. & pro
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ducitur 8. qui dicitur cubus, quia ſi intelligantur duo qua
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ternarij, vnus ſupra alterum, vt in præſenti figura refe
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runt cubicam figuram, cuius tam longitudo, quam </
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