@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-XWZ8DNFJ-0
  skos:prefLabel "géométrie affine"@fr, "affine geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-NFS3J16J-V .

psr:-GKWK9C3G-P
  skos:prefLabel "géométrie euclidienne"@fr, "Euclidean geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-NFS3J16J-V .

psr:-NFS3J16J-V
  skos:broader psr:-GKWK9C3G-P, psr:-XPFQM0ZH-H, psr:-XWZ8DNFJ-0 ;
  skos:definition """In projective geometry, the <b>harmonic conjugate point</b> of a point on the real projective line with respect to two other points is defined by the following construction:
         <dl><dd>Given three collinear points <span class="texhtml mvar" style="font-style:italic;">A, B, C</span>, let <span class="texhtml mvar" style="font-style:italic;">L</span> be a point not lying on their join and let any line through <span class="texhtml mvar" style="font-style:italic;">C</span> meet <span class="texhtml mvar" style="font-style:italic;">LA, LB</span> at <span class="texhtml mvar" style="font-style:italic;">M, N</span> respectively. If <span class="texhtml mvar" style="font-style:italic;">AN</span> and <span class="texhtml mvar" style="font-style:italic;">BM</span> meet at <span class="texhtml mvar" style="font-style:italic;">K</span>, and <span class="texhtml mvar" style="font-style:italic;">LK</span> meets <span class="texhtml mvar" style="font-style:italic;">AB</span> at <span class="texhtml mvar" style="font-style:italic;">D</span>, then <span class="texhtml mvar" style="font-style:italic;">D</span> is called the <b>harmonic conjugate</b> of <span class="texhtml mvar" style="font-style:italic;">C</span> with respect to <span class="texhtml mvar" style="font-style:italic;">A</span> and <span class="texhtml mvar" style="font-style:italic;">B</span>.</dd></dl>
         <br/>The point <span class="texhtml mvar" style="font-style:italic;">D</span> does not depend on what point <span class="texhtml mvar" style="font-style:italic;">L</span> is taken initially, nor upon what line through <span class="texhtml mvar" style="font-style:italic;">C</span> is used to find <span class="texhtml mvar" style="font-style:italic;">M</span> and <span class="texhtml mvar" style="font-style:italic;">N</span>. This fact follows from Desargues theorem.
         <br/>In real projective geometry, harmonic conjugacy can also be defined in terms of the cross-ratio as <span class="texhtml">(<i>A</i>, <i>B</i>; <i>C</i>, <i>D</i>) = −1</span>.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Projective_harmonic_conjugate">https://en.wikipedia.org/wiki/Projective_harmonic_conjugate</a>)"""@en, """En géométrie affine, quatre points alignés sont en division harmonique quand ils vérifient l'égalité des rapports de mesure algébrique indiquée ci-contre. Elle apparait naturellement dans plusieurs figures géométriques, par exemple le quadrilatère complet. C'est plus fondamentalement une notion de géométrie projective, puisqu'il s'agit d'exprimer qu'un birapport vaut –1. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Division_harmonique">https://fr.wikipedia.org/wiki/Division_harmonique</a>)"""@fr ;
  a skos:Concept ;
  skos:prefLabel "division harmonique"@fr, "projective harmonic conjugate"@en ;
  skos:altLabel "harmonic conjugate point"@en, "conjugaison harmonique"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Division_harmonique>, <https://en.wikipedia.org/wiki/Projective_harmonic_conjugate> ;
  dc:created "2023-07-17"^^xsd:date ;
  skos:inScheme psr: ;
  dc:modified "2023-07-26"^^xsd:date .

psr:-XPFQM0ZH-H
  skos:prefLabel "géométrie projective"@fr, "projective geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-NFS3J16J-V .

psr: a skos:ConceptScheme .