<?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>1665-1324</journal-id>
<journal-title><![CDATA[Signos filosóficos]]></journal-title>
<abbrev-journal-title><![CDATA[Sig. Fil]]></abbrev-journal-title>
<issn>1665-1324</issn>
<publisher>
<publisher-name><![CDATA[Universidad Autónoma Metropolitana, División de Ciencias Sociales y Humanidades]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-13242022000200088</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[El &#8216;método de superposición&#8217; en Euclides]]></article-title>
<article-title xml:lang="en"><![CDATA[The &#8216;method of superposition&#8217; in Euclid]]></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 Instituto de Filosofía ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Uruguay</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>24</volume>
<numero>48</numero>
<fpage>88</fpage>
<lpage>113</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-13242022000200088&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-13242022000200088&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-13242022000200088&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Se describe el &#8216;método de superposición&#8217; a través del uso singular del diagrama, pero corresponde estudiar este último en el contexto de la cooperación visual-lingüística, es decir, en el marco de la heterogeneidad expresiva inferencialmente relevante, característica de la demostración euclidiana. El propósito de este artículo es entonces examinar aquel método en detalle, en particular, su trama argumentativa, haciendo justicia a esa modalidad heterogénea o mixta. Dicho examen identifica dos rasgos sobresalientes: a) un uso inferencial original del diagrama (sistemáticamente contrabalanceado por la contribución lingüística), y b) una conciencia precisa de los límites deductivos de tal asociación.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The &#8216;method of superposition&#8217; is described through the singular use of the diagram, but it is appropriate to study the latter in the context of visual-linguistic cooperation, that is, in the framework of inferentially relevant expressive heterogeneity, characteristic of Euclidean proof. The purpose of this paper is then to examine the &#8216;method of superposition&#8217; in detail, in particular, its argumentative strategy, doing justice to such heterogeneous modality. This examination identifies two salient features: a) an original inferential use of the diagram (systematically counterbalanced by the linguistic contribution), and b) a precise awareness of the deductive limits of such an association.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[proof]]></kwd>
<kwd lng="en"><![CDATA[demonstrative patterns]]></kwd>
<kwd lng="en"><![CDATA[inferential heterogeneity]]></kwd>
<kwd lng="en"><![CDATA[geometry]]></kwd>
<kwd lng="en"><![CDATA[diagrams]]></kwd>
<kwd lng="es"><![CDATA[demostración]]></kwd>
<kwd lng="es"><![CDATA[patrones demostrativos]]></kwd>
<kwd lng="es"><![CDATA[heterogeneidad inferencial]]></kwd>
<kwd lng="es"><![CDATA[geometría]]></kwd>
<kwd lng="es"><![CDATA[diagramas]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chateaubriand]]></surname>
<given-names><![CDATA[Oswaldo]]></given-names>
</name>
</person-group>
<source><![CDATA[Logical Forms. Part II: Logic, Language, and Knowledge]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Campinas ]]></publisher-loc>
<publisher-name><![CDATA[Centro de Lógica, Epistemologia e História da Ciência]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<source><![CDATA[Elementos (Libros I-IV)]]></source>
<year>1991</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Gredos]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giaquinto]]></surname>
<given-names><![CDATA[Marcus]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Visualizing in mathematics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Mancosu]]></surname>
<given-names><![CDATA[Paolo]]></given-names>
</name>
</person-group>
<source><![CDATA[The Philosophy of Mathematical Practice]]></source>
<year>2008</year>
<page-range>22-42</page-range><publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gray]]></surname>
<given-names><![CDATA[Jeremy]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A note on lines and planes in Euclid&#8217;s geometry]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Risi]]></surname>
<given-names><![CDATA[Vincenzo de]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematizing Space. The Objects of Geometry from Antiquity to the Early Modern Age]]></source>
<year>2015</year>
<page-range>65-74</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Birkhäuser]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hartshorne]]></surname>
<given-names><![CDATA[Robin]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometry: Euclid and Beyond]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heath]]></surname>
<given-names><![CDATA[Thomas L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Euclid. The Thirteen Books of the Elements]]></source>
<year>1908</year>
<volume>1 and 2</volume>
<publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macbeth]]></surname>
<given-names><![CDATA[Danielle]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diagrammatic reasoning in Euclid&#8217;s elements]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Kerkhove]]></surname>
<given-names><![CDATA[Bart van]]></given-names>
</name>
<name>
<surname><![CDATA[Bendegem]]></surname>
<given-names><![CDATA[Jean Paul van]]></given-names>
</name>
<name>
<surname><![CDATA[Vuyst]]></surname>
<given-names><![CDATA[Jonas de]]></given-names>
</name>
</person-group>
<source><![CDATA[Philosophical Perspectives on Mathematical Practice]]></source>
<year>2010</year>
<volume>12: Texts in Philosophy</volume>
<page-range>235-67</page-range><publisher-loc><![CDATA[Londres ]]></publisher-loc>
<publisher-name><![CDATA[College Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mancosu]]></surname>
<given-names><![CDATA[Paolo]]></given-names>
</name>
</person-group>
<source><![CDATA[Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century]]></source>
<year>1996</year>
<publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Manders]]></surname>
<given-names><![CDATA[Kenneth]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The euclidian diagram (1995)]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Mancosu]]></surname>
<given-names><![CDATA[Paolo]]></given-names>
</name>
</person-group>
<source><![CDATA[The Philosophy of Mathematical Practice]]></source>
<year>2008</year>
<page-range>80-133</page-range><publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Manders]]></surname>
<given-names><![CDATA[Kenneth]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diagram-based geometric practice]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Mancosu]]></surname>
<given-names><![CDATA[Paolo]]></given-names>
</name>
</person-group>
<source><![CDATA[The Philosophy of Mathematical Practice]]></source>
<year>2008</year>
<page-range>65-79</page-range><publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Manders]]></surname>
<given-names><![CDATA[Kenneth]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diagram content and representational granularity]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Seligman]]></surname>
<given-names><![CDATA[Jerry]]></given-names>
</name>
<name>
<surname><![CDATA[Westerståhl]]></surname>
<given-names><![CDATA[Dag]]></given-names>
</name>
</person-group>
<source><![CDATA[Logic, Language, and Computation]]></source>
<year>1996</year>
<page-range>389-404</page-range><publisher-loc><![CDATA[Stanford ]]></publisher-loc>
<publisher-name><![CDATA[CSLI Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Netz]]></surname>
<given-names><![CDATA[Revlel]]></given-names>
</name>
</person-group>
<source><![CDATA[The Shaping of Deduction in Greek Mathematics]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<source><![CDATA[A Comentary on the First Book of Euclid&#8217;s Elements]]></source>
<year>1970</year>
<publisher-loc><![CDATA[Princeton ]]></publisher-loc>
<publisher-name><![CDATA[Princeton University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Risi]]></surname>
<given-names><![CDATA[Vincenzo de]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Euclid&#8217;s common notions and the theory of equivalence]]></article-title>
<source><![CDATA[Foundations of Science]]></source>
<year>2020</year>
<volume>26</volume>
<numero>2</numero>
<issue>2</issue>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Seoane]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Heterogeneidad inferencial]]></article-title>
<source><![CDATA[O que nos faz pensar]]></source>
<year>2021</year>
<volume>29</volume>
<numero>49</numero>
<issue>49</issue>
<page-range>78-99</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Seoane]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Demostraciones heterogéneas: repensando las preguntas]]></article-title>
<source><![CDATA[Representaciones]]></source>
<year>2016</year>
<volume>XII</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>87-108</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tannery]]></surname>
<given-names><![CDATA[Paul]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sur l&#8217;authenticité des axiomes d&#8217;Euclide]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Heiberg]]></surname>
<given-names><![CDATA[Johan Ludvig]]></given-names>
</name>
<name>
<surname><![CDATA[Zeuthen]]></surname>
<given-names><![CDATA[Hieronymus Georg]]></given-names>
</name>
</person-group>
<source><![CDATA[Mémories Scientifiques II]]></source>
<year>1912</year>
<page-range>48-63</page-range><publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Gauthier-Villars]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
