@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:-WS61VZXF-C .

psr:-GKWK9C3G-P
  skos:prefLabel "géométrie euclidienne"@fr, "Euclidean geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-WS61VZXF-C .

psr:-WS61VZXF-C
  skos:exactMatch <https://en.wikipedia.org/wiki/Ceva%27s_theorem>, <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Ceva> ;
  skos:prefLabel "théorème de Ceva"@fr, "Ceva's theorem"@en ;
  skos:related psr:-Z6DZ5M0C-0, psr:-RX61SX55-G ;
  skos:broader psr:-XWZ8DNFJ-0, psr:-GKWK9C3G-P ;
  skos:inScheme psr: ;
  dc:created "2023-08-11"^^xsd:date ;
  dc:modified "2023-08-11"^^xsd:date ;
  skos:definition """En mathématiques, le théorème de Ceva est un théorème de géométrie affine plane qui donne une condition nécessaire et suffisante pour que trois droites passant par les trois sommets d'un triangle soient parallèles ou concourantes. Il s'interprète naturellement en géométrie euclidienne et se généralise en géométrie projective. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Ceva">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Ceva</a>)"""@fr, """In Euclidean geometry, <b>Ceva's theorem</b> is a theorem about triangles. Given a triangle <span class="texhtml">△<i>ABC</i></span>, let the lines <span class="texhtml mvar" style="font-style:italic;">AO, BO, CO</span> be drawn from the vertices to a common point <span class="texhtml mvar" style="font-style:italic;">O</span> (not on one of the sides of <span class="texhtml">△<i>ABC</i></span>), to meet opposite sides at <span class="texhtml mvar" style="font-style:italic;">D, E, F</span> respectively. (The segments <span class="texhtml mvar" style="font-style:italic;"><span style="text-decoration:overline;">AD</span>, <span style="text-decoration:overline;">BE</span>, <span style="text-decoration:overline;">CF</span></span> are known as cevians.) Then, using signed lengths of segments,
<br/>
<br/><dl><dd><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 {\\rac {\\\\overline {AF}}{\\\\overline {FB}}}\\\\cdot {\\rac {\\\\overline {BD}}{\\\\overline {DC}}}\\\\cdot {\\rac {\\\\overline {CE}}{\\\\overline {EA}}}=1.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>A</mi>
<br/>                <mi>F</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>F</mi>
<br/>                <mi>B</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>⋅<!-- ⋅ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>B</mi>
<br/>                <mi>D</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>D</mi>
<br/>                <mi>C</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>⋅<!-- ⋅ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>C</mi>
<br/>                <mi>E</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>E</mi>
<br/>                <mi>A</mi>
<br/>              </mrow>
<br/>              <mo accent="false">¯<!-- ¯ --></mo>
<br/>            </mover>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mn>1.</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {\\\\overline {AF}}{\\\\overline {FB}}}\\\\cdot {\\rac {\\\\overline {BD}}{\\\\overline {DC}}}\\\\cdot {\\rac {\\\\overline {CE}}{\\\\overline {EA}}}=1.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96e441c8416c9b1612115f0bcf576872cee58a2b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.838ex; width:22.103ex; height:7.176ex;" alt="{\\\\displaystyle {\\rac {\\\\overline {AF}}{\\\\overline {FB}}}\\\\cdot {\\rac {\\\\overline {BD}}{\\\\overline {DC}}}\\\\cdot {\\rac {\\\\overline {CE}}{\\\\overline {EA}}}=1.}"></span></dd></dl>
<br/>In other words, the length <span class="texhtml mvar" style="font-style:italic;"><span style="text-decoration:overline;">XY</span></span> is taken to be positive or negative according to whether <span class="texhtml mvar" style="font-style:italic;">X</span> is to the left or right of <span class="texhtml mvar" style="font-style:italic;">Y</span> in some fixed orientation of the line. For example, <span class="texhtml mvar" style="font-style:italic;"><span style="text-decoration:overline;">AF</span> / <span style="text-decoration:overline;">FB</span></span> is defined as having positive value when <span class="texhtml mvar" style="font-style:italic;">F</span> is between <span class="texhtml mvar" style="font-style:italic;">A</span> and <span class="texhtml mvar" style="font-style:italic;">B</span> and negative otherwise.
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Ceva%27s_theorem">https://en.wikipedia.org/wiki/Ceva%27s_theorem</a>)"""@en ;
  a skos:Concept .

psr: a skos:ConceptScheme .
psr:-Z6DZ5M0C-0
  skos:prefLabel "line"@en, "droite"@fr ;
  a skos:Concept ;
  skos:related psr:-WS61VZXF-C .

psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-WS61VZXF-C .