<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-2450</journal-id>
<journal-title><![CDATA[Diánoia]]></journal-title>
<abbrev-journal-title><![CDATA[Diánoia]]></abbrev-journal-title>
<issn>0185-2450</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Investigaciones Filosóficas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-24502022000200039</article-id>
<article-id pub-id-type="doi">10.22201/iifs.18704913e.2022.89.1903</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estilo polimodal en la demostración euclidiana]]></article-title>
<article-title xml:lang="en"><![CDATA[Polymodal Style in Euclidean Proof]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Seoane]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de la República Facultad de Humanidades y Ciencias de la Educación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Uruguay</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>67</volume>
<numero>89</numero>
<fpage>39</fpage>
<lpage>65</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-24502022000200039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-24502022000200039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-24502022000200039&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Una demostración matemática puede exponerse mediante el empleo secuencial de diversas modalidades o formatos expresivos; diremos que en tal caso se usa un estilo polimodal. Euclides se sirva de este recurso, pero ¿cuál podría ser la motivación subyacente? Esta cuestión interroga por una posible lógica, no por la hipótesis históricamente correcta -aunque la interrogante pueda, en algún caso, resultar útil al historiador-. Una respuesta inicialmente razonable podría apuntar a razones estéticas y pedagógicas. Sin embargo, la explotación metodológica del contraste entre estructura y expresión muestra las limitaciones de tal hipótesis: la modalidad expresiva, en determinadas circunstancias, resulta impuesta por la estructura de la prueba. El objetivo principal de este artículo es, en esencia, proveer una comprensión inicial del estilo polimodal en Euclides.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract A mathematical proof can be presented using, sequentially, various expressive modalities; we will say that in such a case it uses a polymodal style. Euclid uses this resource, but what could be understood as the underlying motivation? Such a question asks for a possible logic, not for the historically correct hypothesis -although this question may, in some cases, be useful to the historian. An initially plausible answer could point to aesthetic and pe- dagogical reasons. However, the methodological exploitation of the contrast between structure and expression shows the limitations of such a hypothesis: the expressive modality, in certain circumstances, is imposed by the structure of the proof. The main purpose of this article is therefore to provide an initial understanding of the polymodal style in Euclid.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[razonamiento geométrico]]></kwd>
<kwd lng="es"><![CDATA[Euclides]]></kwd>
<kwd lng="es"><![CDATA[expresión]]></kwd>
<kwd lng="es"><![CDATA[estructura]]></kwd>
<kwd lng="es"><![CDATA[estilos expresivos]]></kwd>
<kwd lng="en"><![CDATA[demonstration]]></kwd>
<kwd lng="en"><![CDATA[Euclid]]></kwd>
<kwd lng="en"><![CDATA[expression]]></kwd>
<kwd lng="en"><![CDATA[structure]]></kwd>
<kwd lng="en"><![CDATA[expressive style]]></kwd>
</kwd-group>
</article-meta>
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