@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: a skos:ConceptScheme .
psr:-TW94Z6HZ-B
  skos:prefLabel "centre du triangle"@fr, "triangle center"@en ;
  a skos:Concept ;
  skos:narrower psr:-D1LDBSDF-L .

psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-D1LDBSDF-L .

psr:-D1LDBSDF-L
  skos:altLabel "point de Jacobi"@fr, "Jacobi point"@en, "théorème de Fermat-Toricelli généralisé"@fr, "théorème isogonal"@fr ;
  skos:inScheme psr: ;
  a skos:Concept ;
  skos:broader psr:-TW94Z6HZ-B ;
  skos:prefLabel "théorème de Jacobi"@fr, "Jacobi's theorem"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Jacobi_(g%C3%A9om%C3%A9trie)>, <https://en.wikipedia.org/wiki/Jacobi%27s_theorem_(geometry)> ;
  skos:definition """En géométrie, le <b>théorème de Jacobi</b>, ou <b>théorème de Fermat-Toricelli généralisé</b> ou <b>théorème isogonal</b> désigne un résultat de géométrie du triangle. Un <b>point de Jacobi</b> est un point du plan euclidien déterminé par un triangle <i>ABC</i> et un triplet d'angles <i>α</i>, <i>β</i> et <i>γ</i>. Cette information est suffisante pour déterminer trois points <i>X</i>, <i>Y</i> et <i>Z</i> tels que <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="{\\	extstyle {\\\\widehat {ZAB}}={\\\\widehat {YAC}}=\\\\alpha }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>Z</mi>
<br/>                <mi>A</mi>
<br/>                <mi>B</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>Y</mi>
<br/>                <mi>A</mi>
<br/>                <mi>C</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mi>α<!-- α --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle {\\\\widehat {ZAB}}={\\\\widehat {YAC}}=\\\\alpha }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1de4184a22d10962a9f16de0f51fb3c917e28a0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:18.155ex; height:3.176ex;" alt="{\\	extstyle {\\\\widehat {ZAB}}={\\\\widehat {YAC}}=\\\\alpha }"></span>, <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="{\\	extstyle {\\\\widehat {XBC}}={\\\\widehat {ZBA}}=\\eta }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>X</mi>
<br/>                <mi>B</mi>
<br/>                <mi>C</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>Z</mi>
<br/>                <mi>B</mi>
<br/>                <mi>A</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mi>β<!-- β --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle {\\\\widehat {XBC}}={\\\\widehat {ZBA}}=\\eta }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67dc4ac421c2c619da8f75ffb4cead86f92dfa30" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:18.227ex; height:3.509ex;" alt="{\\	extstyle {\\\\widehat {XBC}}={\\\\widehat {ZBA}}=\\eta }"></span> et <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="{\\	extstyle {\\\\widehat {YCA}}={\\\\widehat {XCB}}=\\\\gamma }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>Y</mi>
<br/>                <mi>C</mi>
<br/>                <mi>A</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mover>
<br/>              <mrow>
<br/>                <mi>X</mi>
<br/>                <mi>C</mi>
<br/>                <mi>B</mi>
<br/>              </mrow>
<br/>              <mo>^<!-- ^ --></mo>
<br/>            </mover>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mi>γ<!-- γ --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle {\\\\widehat {YCA}}={\\\\widehat {XCB}}=\\\\gamma }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b73f8c37ee7f356e3fe54833b818b6b632a421" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:18.252ex; height:3.676ex;" alt="{\\	extstyle {\\\\widehat {YCA}}={\\\\widehat {XCB}}=\\\\gamma }"></span>. Puis, par un théorème de Karl Friedrich Andreas Jacobi, les droites (<i>AX</i>), (<i>BY</i>) et (<i>CZ</i>) sont concourantes, en un point <i>N</i> qu'on appelle point de Jacobi. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Jacobi_(g%C3%A9om%C3%A9trie)">https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Jacobi_(g%C3%A9om%C3%A9trie)</a>)"""@fr, """In plane geometry, a <b>Jacobi point</b> is a point in the Euclidean plane determined by a triangle <span class="texhtml">△<i>ABC</i></span> and a triple of angles <span class="texhtml mvar" style="font-style:italic;">α, β, γ</span>. This information is sufficient to determine three points <span class="texhtml mvar" style="font-style:italic;">X, Y, Z</span> such that 
         <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\egin{aligned}\\\\angle ZAB&=\\\\angle YAC&=\\\\alpha ,\\\\\\\\\\\\angle XBC&=\\\\angle ZBA&=\\eta ,\\\\\\\\\\\\angle YCA&=\\\\angle XCB&=\\\\gamma .\\\\end{aligned}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
         <mtr>
         <mtd>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>Z</mi>
         <mi>A</mi>
         <mi>B</mi>
         </mtd>
         <mtd>
         <mi></mi>
         <mo>=</mo>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>Y</mi>
         <mi>A</mi>
         <mi>C</mi>
         </mtd>
         <mtd>
         <mo>=</mo>
         <mi>α<!-- α --></mi>
         <mo>,</mo>
         </mtd>
         </mtr>
         <mtr>
         <mtd>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>X</mi>
         <mi>B</mi>
         <mi>C</mi>
         </mtd>
         <mtd>
         <mi></mi>
         <mo>=</mo>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>Z</mi>
         <mi>B</mi>
         <mi>A</mi>
         </mtd>
         <mtd>
         <mo>=</mo>
         <mi>β<!-- β --></mi>
         <mo>,</mo>
         </mtd>
         </mtr>
         <mtr>
         <mtd>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>Y</mi>
         <mi>C</mi>
         <mi>A</mi>
         </mtd>
         <mtd>
         <mi></mi>
         <mo>=</mo>
         <mi mathvariant="normal">∠<!-- ∠ --></mi>
         <mi>X</mi>
         <mi>C</mi>
         <mi>B</mi>
         </mtd>
         <mtd>
         <mo>=</mo>
         <mi>γ<!-- γ --></mi>
         <mo>.</mo>
         </mtd>
         </mtr>
         </mtable>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{aligned}\\\\angle ZAB&=\\\\angle YAC&=\\\\alpha ,\\\\\\\\\\\\angle XBC&=\\\\angle ZBA&=\\eta ,\\\\\\\\\\\\angle YCA&=\\\\angle XCB&=\\\\gamma .\\\\end{aligned}}}</annotation>
         </semantics>
         </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73fba8283d600b1037a308e738127274e38a842d" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:27.46ex; height:8.843ex;" alt="{\\\\displaystyle {\\egin{aligned}\\\\angle ZAB&=\\\\angle YAC&=\\\\alpha ,\\\\\\\\\\\\angle XBC&=\\\\angle ZBA&=\\eta ,\\\\\\\\\\\\angle YCA&=\\\\angle XCB&=\\\\gamma .\\\\end{aligned}}}"></div>
         Then, by a theorem of Karl Friedrich Andreas Jacobi, the lines <span class="texhtml mvar" style="font-style:italic;">AX, BY, CZ</span> are concurrent, at a point <span class="texhtml mvar" style="font-style:italic;">N</span> called the Jacobi point.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Jacobi%27s_theorem_(geometry)">https://en.wikipedia.org/wiki/Jacobi%27s_theorem_(geometry)</a>)"""@en ;
  skos:related psr:-RX61SX55-G ;
  dc:created "2023-08-11"^^xsd:date ;
  dc:modified "2023-08-11"^^xsd:date .