Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000820">
                <pb pagenum="43" xlink:href="009/01/043.jpg"/>
              G H D, appoſito
                <expan abbr="vtiq;">vtique</expan>
              communi angulo B G H, erant primum, duo anguli
                <lb/>
              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
                <lb/>
              communis angulus additur ſemel maiori angulo, & ſemel minori; & ideo
                <lb/>
              totum illud, in quo eſt maior angulus, adhuc maius eſt altero toto, in quo
                <lb/>
              minor angulus continetur. </s>
              <s id="s.000821">at illi duo E G B, B G H, per 13. primi, ſunt
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              æquales duobus rectis angulis, ergo duo
                <expan abbr="quoq;">quoque</expan>
              recti erunt maiores duobus
                <lb/>
              internis B G H, D H G, ſiue hi duo interni erunt minores duobus rectis.
                <lb/>
              </s>
              <s id="s.000822">At quando hi duo interni ſunt minores duobus rectis, tunc lineæ A B, C D,
                <lb/>
              ſunt concurrentes, ſi protrahantur ad partes prædictorum
                <expan abbr="angulorũ">angulorum</expan>
              . </s>
              <s id="s.000823">quod
                <lb/>
              P. Clauius luculenti, & hactenus deſiderata demonſtratione ad 28. primi
                <lb/>
              demonſtrauit. </s>
              <s id="s.000824">
                <expan abbr="Atq;">Atque</expan>
              hoc pacto ex prima falſa ſuppoſitione, nimirum angu­
                <lb/>
              lum illum externum eſſe maiorem interno, & oppoſito; ſequitur falſum, ni­
                <lb/>
              mirum lineas parallelas concurrere.</s>
            </p>
            <p type="main">
              <s id="s.000825">Præterea ſi ſupponamus aliam falſitatem, ſcilicet triangulum habere tres
                <lb/>
              angulos maiores duobus rectis, ſequetur eadem iterum falſitas, ſcilicet pa­
                <lb/>
                <figure id="id.009.01.043.1.jpg" place="text" xlink:href="009/01/043/1.jpg" number="12"/>
                <lb/>
              rallelas coincidere, & probatur ſic; ſint enim
                <lb/>
                <expan abbr="triãguli">trianguli</expan>
              A B C, tres anguli maiores, quam duo
                <lb/>
              recti anguli, & per punctum C, ducta ſit recta
                <lb/>
              C D, parallela lateri B A. quia ergo angulus
                <lb/>
              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
                <lb/>
              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. </s>
              <s id="s.000826">ergo totus iſte angulus B C D, ſimul cum reliquo
                <expan abbr="triãguli">trianguli</expan>
              angulo B. con­
                <lb/>
              ſtabit compoſitionem ex tribus angulis trianguli dati: & conſequenter ta­
                <lb/>
              lis compoſitio trium angulorum erit maior, quam ſint duo anguli recti. </s>
              <s id="s.000827">ex
                <lb/>
              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
                <lb/>
              ſtratione P. Clauij) quod falſum eſt. </s>
              <s id="s.000828">& ſequitur ex ſecunda falſa ſuppoſitio­
                <lb/>
              ne. </s>
              <s id="s.000829">ex quibus textus Ariſt. videtur ſatis clarus.</s>
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            <p type="main">
              <s id="s.000830">
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              </s>
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            <p type="margin">
              <s id="s.000831">
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              15</s>
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            <p type="main">
              <s id="s.000832">Ex cap. 26.
                <emph type="italics"/>
              (Vt ſi A, duo recti, in quo autem P., triangulus, in quo vero C,
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              ſenſibilis triangulus, ſuſpicari
                <expan abbr="namq;">namque</expan>
              poſſet aliquis non eſſe C, ſciens, quod omnis
                <lb/>
              triangulus habet duos rectos: quare ſimul noſcet, & ignorabit idem. </s>
              <s id="s.000833">noſce enim
                <lb/>
              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. </s>
              <s id="s.000834">ſic igitur, vt vni­
                <lb/>
              uerſale nouit C, quod duo recti; vt autem ſingulare non nouit, quare non habebit
                <lb/>
              contrarias)
                <emph.end type="italics"/>
              vide, quæ diximus lib. 1. ſecto 3. cap. 1. ex quibus quidquid Ma­
                <lb/>
              thematicum eſt hic, clarum redditur. </s>
              <s id="s.000835">reliqua verò, quæ ad Logicum ſpe­
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              ctant, huius loci commentatores proſequuntur.</s>
            </p>
            <p type="main">
              <s id="s.000836">In cap. 31. de Abductione.</s>
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            <p type="margin">
              <s id="s.000838">
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              16</s>
            </p>
            <p type="main">
              <s id="s.000839">Notandum hic cum eruditiſſimo Burana, Abductionem hanc, de qua in hoc
                <lb/>
              cap. agitur eſſe vocem mathematicam,
                <expan abbr="camq́">eamque</expan>
              ; Ariſt. quemadmodum multa
                <lb/>
              alia à Mathematicis mutuatum ad omnes alias ſcientias tranſtuliſſe. </s>
              <s id="s.000840">eſſe </s>
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