@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:-GKWK9C3G-P
  skos:prefLabel "géométrie euclidienne"@fr, "Euclidean geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-ZRLNBDB6-Z .

psr:-ZRLNBDB6-Z
  dc:modified "2023-08-11"^^xsd:date ;
  skos:prefLabel "théorème de Ménélaüs"@fr, "Menelaus's theorem"@en ;
  skos:broader psr:-GKWK9C3G-P, psr:-ST8XF8P3-G ;
  skos:inScheme psr: ;
  skos:definition """En mathématiques, et plus précisément en géométrie, le théorème de Ménélaüs, dû à Ménélaüs d'Alexandrie, précise les relations existant entre des longueurs découpées dans un triangle par une sécante. Il en existe une version plane et une version pour le triangle sphérique. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_M%C3%A9n%C3%A9la%C3%BCs">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_M%C3%A9n%C3%A9la%C3%BCs</a>)"""@fr, """<b>Menelaus's theorem</b>, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle △<i>ABC</i>, and a transversal line that crosses <i>BC</i>, <i>AC</i>, and <i>AB</i> at points <i>D</i>, <i>E</i>, and <i>F</i> respectively, with <i>D</i>, <i>E</i>, and <i>F</i> distinct from <i>A</i>, <i>B</i>, and <i>C</i>. A weak version of the theorem states that
<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 {|AF|}{|FB|}}\\	imes {\\rac {|BD|}{|DC|}}\\	imes {\\rac {|CE|}{|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/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>A</mi>
<br/>              <mi>F</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>F</mi>
<br/>              <mi>B</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>×<!-- × --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>B</mi>
<br/>              <mi>D</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>D</mi>
<br/>              <mi>C</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>×<!-- × --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>C</mi>
<br/>              <mi>E</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>              <mi>E</mi>
<br/>              <mi>A</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo stretchy="false">|</mo>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mn>1</mn>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {|AF|}{|FB|}}\\	imes {\\rac {|BD|}{|DC|}}\\	imes {\\rac {|CE|}{|EA|}}=1,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3f638e7376b24be5fb1d01cd89ef9d3bbe935bf" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:27.715ex; height:6.509ex;" alt="{\\\\displaystyle {\\rac {|AF|}{|FB|}}\\	imes {\\rac {|BD|}{|DC|}}\\	imes {\\rac {|CE|}{|EA|}}=1,}"></span></dd></dl>
<br/>where "| |" denotes absolute value (i.e., all segment lengths are positive). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Menelaus%27s_theorem">https://en.wikipedia.org/wiki/Menelaus%27s_theorem</a>)"""@en ;
  skos:related psr:-RX61SX55-G ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Menelaus%27s_theorem>, <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_M%C3%A9n%C3%A9la%C3%BCs> ;
  dc:created "2023-08-11"^^xsd:date .

psr:-ST8XF8P3-G
  skos:prefLabel "geometric drawing"@en, "construction géométrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-ZRLNBDB6-Z .

psr: a skos:ConceptScheme .
psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-ZRLNBDB6-Z .