Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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teriali; plures autem eſſe in primo elem. </
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<
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ris addita. </
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<
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id
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">Notandum hic
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quoq;
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cauſam eſſe natura ſua diſtinctam ab effe
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ctu, non ſecus ac potentia ab actu; nam ex eo, quòd poſſit aliquid diuidi in
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partes æquales aliquibus, ſequitur illud totum eſſe actu æquale alteri, & eſt
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à priori, quia partes natura prius ſunt toto, cùm ſint ipſius cauſa. </
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<
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dum hic etiam parallelam illam, qua angulus diuiditur, duci ad
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mediũ
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de
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monſtrationis indagandum, nequaquam verò ipſam eſſe medium, & idcir
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cò demonſtrationem hanc non eſſe per extrinſeca, niſi velis minorem
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pro-poſitionẽ
">pro
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poſitionem</
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per extrinſeca oſtendi, quòd libenter concedimus, cùm iſtud de
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monſtrationi nihil deroget. </
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<
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id
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">Eſt autem per intrinſecam, propriam, & adæ
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quatam cauſam illius æqualitatis, partes enim reſpectu totius ſunt tales.
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</
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<
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id
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">eſt igitur potiſſima demonſtratio, quòd erat demonſtrandum.</
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<
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">Poſtquam Euclides hanc primam propoſitionis partem demonſtrauit,
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oſtendit alteram. </
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">ſ. </
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">omne triangulum habere tres, &c. </
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<
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">quoniam partes duo
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rum rectorum ſunt æquales tribus angulis illis. </
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<
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id
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s.005309
">quod medium pariter eſt à
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cauſa materiali, à partibus ad totum. </
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<
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">Vide huius explicationem tex. 23.
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1. Poſter. vbi etiam videbis eam poſſe demonſtrari modo Pythagoreorum,
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abſque vlla diuiſione, ſed per partes actu exiſtentes. </
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<
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id
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">hoc dico propter eos,
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qui per haſce diuiſiones timent, ne non inueniatur medium á priori. </
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<
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">ſed vt
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deponant penitus hunc ſcrupulum, ſciant in huiuſmodi demonſtrationibus,
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quibus aliquid ęquale alteri adhibita diuiſione demonſtratur, ſępè accide
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re, vt non diuidatur, niſi vnus terminorum ęqualitatis, quare ex parte in
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diuiſi ęqualitas cauſabitur à partibus actu pręcedentibus, &
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conſtituẽtibus
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totum; quod videre eſt in
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vtraq;
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parte huius. </
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<
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">32. ſecundum Euclidem, & in
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47. primi elem. </
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<
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">& alijs plurimis.</
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<
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">Sed primò Piccolom. ex Proclo obijcit hęc
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(Quando enim eo, quòd extrin
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ſecus angulus duobus internis, & oppoſitis æqualis est, oſtenditur triangulum ha
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bere tres angulos æquales duobus rectis, quomodo à cauſa eſt
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demõstratio
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hæc? </
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<
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ne medium certum ſignum est? </
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<
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neq;
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externo exiſtente angulo cùm interni
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exiſtant, duobus rectis æquales ſunt; eſt. </
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<
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">n. </
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<
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">triangulum latere etiam non producto)
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Pergit deinde Proclus demonſtrare primam Euclidìs demonſtrationem eſſe
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per cauſam, & proinde veram demonſtrationem, quòd Piccolomin. in ſua
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citatione callidè videtur reticuiſſe. </
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<
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">Ad
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obiectionẽ
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reſpondeo primò. </
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<
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">angu
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lum externum in Euclidiana demonſtratione minimè extraneum eſſe, quia
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in hac ſecunda parte aſſumitur pro ſubiecto demonſtrationis, ideſt pro par
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te duorum rectorum, ipſe enim cum angulo ſibi deinceps facit duos angulos
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rectos, quibus tres anguli trianguli probantur ęquales: quod Proclus
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nõ
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vi
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detur vidiſſe. </
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<
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id
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">Secundò, ſi hęc Euclidiana illi
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nõ
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probatur, accipiat de eadem
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re Pythagoricam, quę abſque angulo externo, & ab
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vlla diuiſione probat
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intentum; & erit omnis ſublata dubitatio. </
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<
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">Tertiò, ſi conuincerent aduer
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farij, quòd nequaquam faciunt, hanc non eſſe à priori, ſequitur ne propte
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rea reliquas omnes eſſe ei ſimiles, vt ipſi inferre conantur? </
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<
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.
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</
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<
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">Secundò, obijcies, paſſionem hanc, habere tres angulos, &c. </
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<
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">non recipro
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cari cum triangulo, ſeu non eſſe ſecundum quod ipſum, vt aiunt Logici: re
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peritur enim figura quędam pręter triangulum, vt patet apud Proclum, quę </
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