"Pappus's hexagon theorem" meaning in English

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        "A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the \"Pappus line\". These three points are the points of intersection of the \"opposite\" sides of the hexagon AbCaBc."
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        "(geometry) A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the \"Pappus line\". These three points are the points of intersection of the \"opposite\" sides of the hexagon AbCaBc."
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        "A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the \"Pappus line\". These three points are the points of intersection of the \"opposite\" sides of the hexagon AbCaBc."
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        "(geometry) A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the \"Pappus line\". These three points are the points of intersection of the \"opposite\" sides of the hexagon AbCaBc."
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