@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:-ST8XF8P3-G
  skos:prefLabel "geometric drawing"@en, "construction géométrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-KD2VRVC0-M .

psr: a skos:ConceptScheme .
psr:-H51D6H37-3
  skos:prefLabel "cercle"@fr, "circle"@en ;
  a skos:Concept ;
  skos:related psr:-KD2VRVC0-M .

psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-KD2VRVC0-M .

psr:-KD2VRVC0-M
  skos:altLabel "cercle médian"@fr, "cercle de Feuerbach"@fr, "nine-point circle"@en, "cercle des neuf points"@fr, "Feuerbach's circle"@en, "Terquem's circle"@en, "mid circle"@en, "six-points circle"@en, "cercle de Terquem"@fr, "twelve-points circle"@en ;
  skos:related psr:-H51D6H37-3, psr:-RX61SX55-G ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Nine-point_circle>, <https://fr.wikipedia.org/wiki/Cercle_d%27Euler> ;
  skos:inScheme psr: ;
  skos:prefLabel "cercle d'Euler"@fr, "Euler's circle"@en ;
  dc:created "2023-07-13"^^xsd:date ;
  a skos:Concept ;
  skos:broader psr:-ST8XF8P3-G ;
  skos:definition """In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are :
<br/>- The midpoint of each side of the triangle
<br/>- The foot of each altitude
<br/>- The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Nine-point_circle">https://en.wikipedia.org/wiki/Nine-point_circle</a>)"""@en, """En géométrie, le <b>cercle d'Euler</b> d'un triangle (aussi appelé <b>cercle des neuf points</b>, <b>cercle de Feuerbach</b>, <b>cercle de Terquem</b>, <b>cercle médian</b>) est l'unique cercle passant par les neuf points remarquables suivants&nbsp;:
<br/><ul><li>Les trois milieux <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle I_{i}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>I</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle I_{i}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d896cad5ad71ce7719175ca29d4d109333d4c320" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.823ex; height:2.509ex;" alt="I_{i}"></span> des trois côtés du triangle&nbsp;;</li>
<br/><li>Le pied <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle H_{i}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>H</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle H_{i}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bd0312f590cc5a400008938f3cc304d42ad3986" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.509ex;" alt="H_i"></span> de chacune des trois hauteurs du triangle&nbsp;;</li>
<br/><li>Le milieu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle J_{i}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>J</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle J_{i}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07a98dbd556141d7f0a16eed84fe0ae6467dcd23" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.09ex; height:2.509ex;" alt="J_{i}"></span> de chacun des trois segments reliant l'orthocentre <span class="texhtml mvar" style="font-style:italic;">H</span> à un sommet du triangle.</li> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Cercle_d%27Euler">https://fr.wikipedia.org/wiki/Cercle_d%27Euler</a>)"""@fr ;
  dc:modified "2023-08-11"^^xsd:date .