Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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              <s id="s.005299">
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              teriali; plures autem eſſe in primo elem. </s>
              <s id="s.005300">conſtat ex appendice in fine ope­
                <lb/>
              ris addita. </s>
              <s id="s.005301">Notandum hic
                <expan abbr="quoq;">quoque</expan>
              cauſam eſſe natura ſua diſtinctam ab effe­
                <lb/>
              ctu, non ſecus ac potentia ab actu; nam ex eo, quòd poſſit aliquid diuidi in
                <lb/>
              partes æquales aliquibus, ſequitur illud totum eſſe actu æquale alteri, & eſt
                <lb/>
              à priori, quia partes natura prius ſunt toto, cùm ſint ipſius cauſa. </s>
              <s id="s.005302">Notan­
                <lb/>
              dum hic etiam parallelam illam, qua angulus diuiditur, duci ad
                <expan abbr="mediũ">medium</expan>
              de­
                <lb/>
              monſtrationis indagandum, nequaquam verò ipſam eſſe medium, & idcir­
                <lb/>
              cò demonſtrationem hanc non eſſe per extrinſeca, niſi velis minorem
                <expan abbr="pro-poſitionẽ">pro­
                  <lb/>
                poſitionem</expan>
              per extrinſeca oſtendi, quòd libenter concedimus, cùm iſtud de­
                <lb/>
              monſtrationi nihil deroget. </s>
              <s id="s.005303">Eſt autem per intrinſecam, propriam, & adæ­
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              quatam cauſam illius æqualitatis, partes enim reſpectu totius ſunt tales.
                <lb/>
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              <s id="s.005304">eſt igitur potiſſima demonſtratio, quòd erat demonſtrandum.</s>
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              <s id="s.005305">Poſtquam Euclides hanc primam propoſitionis partem demonſtrauit,
                <lb/>
              oſtendit alteram. </s>
              <s id="s.005306">ſ. </s>
              <s id="s.005307">omne triangulum habere tres, &c. </s>
              <s id="s.005308">quoniam partes duo­
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              rum rectorum ſunt æquales tribus angulis illis. </s>
              <s id="s.005309">quod medium pariter eſt à
                <lb/>
              cauſa materiali, à partibus ad totum. </s>
              <s id="s.005310">Vide huius explicationem tex. 23.
                <lb/>
              1. Poſter. vbi etiam videbis eam poſſe demonſtrari modo Pythagoreorum,
                <lb/>
              abſque vlla diuiſione, ſed per partes actu exiſtentes. </s>
              <s id="s.005311">hoc dico propter eos,
                <lb/>
              qui per haſce diuiſiones timent, ne non inueniatur medium á priori. </s>
              <s id="s.005312">ſed vt
                <lb/>
              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, &
                <expan abbr="conſtituẽtibus">conſtituentibus</expan>
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              totum; quod videre eſt in
                <expan abbr="vtraq;">vtraque</expan>
              parte huius. </s>
              <s id="s.005313">32. ſecundum Euclidem, & in
                <lb/>
              47. primi elem. </s>
              <s id="s.005314">& alijs plurimis.</s>
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              <s id="s.005315">Sed primò Piccolom. ex Proclo obijcit hęc
                <emph type="italics"/>
              (Quando enim eo, quòd extrin­
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              ſecus angulus duobus internis, & oppoſitis æqualis est, oſtenditur triangulum ha­
                <lb/>
              bere tres angulos æquales duobus rectis, quomodo à cauſa eſt
                <expan abbr="demõstratio">demonstratio</expan>
              hæc? </s>
              <s id="s.005316">non
                <lb/>
              ne medium certum ſignum est? </s>
              <s id="s.005317">etenim
                <expan abbr="neq;">neque</expan>
              externo exiſtente angulo cùm interni
                <lb/>
              exiſtant, duobus rectis æquales ſunt; eſt. </s>
              <s id="s.005318">n. </s>
              <s id="s.005319">triangulum latere etiam non producto)
                <emph.end type="italics"/>
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              Pergit deinde Proclus demonſtrare primam Euclidìs demonſtrationem eſſe
                <lb/>
              per cauſam, & proinde veram demonſtrationem, quòd Piccolomin. in ſua
                <lb/>
              citatione callidè videtur reticuiſſe. </s>
              <s id="s.005320">Ad
                <expan abbr="obiectionẽ">obiectionem</expan>
              reſpondeo primò. </s>
              <s id="s.005321">angu­
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              lum externum in Euclidiana demonſtratione minimè extraneum eſſe, quia
                <lb/>
              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
                <lb/>
              rectos, quibus tres anguli trianguli probantur ęquales: quod Proclus
                <expan abbr="nõ">non</expan>
              vi­
                <lb/>
              detur vidiſſe. </s>
              <s id="s.005322">Secundò, ſi hęc Euclidiana illi
                <expan abbr="nõ">non</expan>
              probatur, accipiat de eadem
                <lb/>
              re Pythagoricam, quę abſque angulo externo, & ab
                <expan abbr="q;">que</expan>
              vlla diuiſione probat
                <lb/>
              intentum; & erit omnis ſublata dubitatio. </s>
              <s id="s.005323">Tertiò, ſi conuincerent aduer­
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              farij, quòd nequaquam faciunt, hanc non eſſe à priori, ſequitur ne propte­
                <lb/>
              rea reliquas omnes eſſe ei ſimiles, vt ipſi inferre conantur? </s>
              <s id="s.005324">minimè
                <expan abbr="gentiũ">gentium</expan>
              .
                <lb/>
              </s>
              <s id="s.005325">quo logico iure ab vno particulari inferre volunt vniuerſale?</s>
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              <s id="s.005326">Secundò, obijcies, paſſionem hanc, habere tres angulos, &c. </s>
              <s id="s.005327">non recipro­
                <lb/>
              cari cum triangulo, ſeu non eſſe ſecundum quod ipſum, vt aiunt Logici: re­
                <lb/>
              peritur enim figura quędam pręter triangulum, vt patet apud Proclum, quę </s>
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