Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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punctum, & rectum; etenim ſecundum quod linea, & triangulo, ſecundum quod
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triangulum duo recti: etenim per ſe triangulum duobus rectis æquale. </
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<
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">Vniuerſale
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autem eſt tunc, quando in quolibet, & primo monſtratur, vt duos rectos habere,
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figuræ eſt vniuerſale, quamuis eſt monſtrare de figura, quod duos rectos habet,
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ſed non de qualibet figura,
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vtitur qualibet figura monstrans, quadrangulum
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enim figura a quidem est, non habet autem duobus rectis æquales. </
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<
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">Aequicrus verò
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habet quidem
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quodcunq;
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duobus rectis æquales, ſed non primò, ſed triangulum
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prius. </
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<
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id
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">quod igitur quoduis primum monſtratur duos rectos habens, aut
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quodcunq;
">quodcunque</
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aliud, huic primo ineſt vniuerſale, & demonstratio de hoc vniuerſaliter eſt, de alijs
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verò quodammodo, non per ſe,
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de æquicrure eſt vniuerſaliter, ſed in plus)
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pro
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quorum intelligentia neceſſaria ſunt ea, quæ primo Priorum ſecto 3. cap. 1.
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ſcripſimus. </
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<
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id
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">deinde memineris figuram vniuerſaliorem eſſe triangulo, & tri
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angulum vniuerſalius æquicrure. </
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">quando ait (vt duos rectos habere) vult
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dicere, habere duos angulos rectos non actu, ſed potentia; quæ affectio eſt
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trianguli, quia, vt ſuperius diximus, habet tres angulos æquales duobus
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rectis angulis: quæ proprietas vniuerſaliter, & primò competit triangulo.
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</
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<
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">non autem figuræ, quia figura eſt vniuerſalior. </
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iſoſceli, quia iſoſceles eſt
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reſtrictius triangulo. </
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">omittimus reliqua ſingillatim exponere, tum quia ſa
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tis clara ſunt, tum quia ab interpretibus benè explicantur.</
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26</
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<
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">Tex. 13.
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(Si quis igitur monſtrauerit, quod rectæ
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nõ
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coincidunt, videbitur
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vtiq;
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huius eſſe demonstratio, eo quod in omnibus eſt rectis; non eſt autem: ſi quidem
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non quoniam ſic æquales, fit hoc, ſed ſecundum quod
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æquales)
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pro
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ponit tres errores, qui circa demonſtrationem de vniuerſali contingunt,
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quos omnes Geometricis exemplis illuſtrat; affert autem primo pro tertio
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errore duo exempla, quorum primum in præmiſſis verbis continetur,
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atq;
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ex 28. primi Elem. deſumitur, quam propterea primo loco exponendam
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cenſui. </
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<
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">Quando igitur duæ rectæ conſtitu
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tæ fuerint, vt A B, C D, in quas alia recta,
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vt G F, incidens, faciat duos angulos in
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ternos, reſpectu rectarum A B, C D, & ad
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eaſdem partes rectæ E F, vt ſunt ex parte
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ſiniſtra anguli A G H, C H G; exparte ve
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rò dextra B G H, D H G; ſi
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inquã
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linea E F,
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fecerit duos illos angulos ex parte ſiniſtra ſimul ſumptos, æquales duobus
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rectis angulis, vel duos ex parte dextra pariter æquales duobus rectis, pro
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bat Euclides rectas A B, C D, non concurrere, ſiue parallelas eſſe. </
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<
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quia linea E F, poteſt facere aliquando prædictos angulos non
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tantũ
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æqua
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les duobus rectis, verum etiam rectos, quo etiam modo
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cædem
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lineæ eſſe parallelæ, vt in ſequenti figura, cum ſint anguli A G I, C I G, re
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cti, probabitur de rectis A B, C D, æquidiſtan
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tia. </
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nemus; ſi quis igitur monſtrauerit, quod rectæ
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A B, C D, nunquam coincidunt, etiamſi in infi
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nitum producantur, ſeu quod ſunt æquidiſtantes,
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quando anguli prædicti interni ſunt duo recti,
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videbitur
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huius eſſe demonſtratio de vniuerſali per ſe, & de primo </
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