. . "In geometry, the Braikenridge\u2013Maclaurin theorem, named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem."@en . . . . "Braikenridge\u2013Maclaurin theorem"@en . . . . . . . "En geometria, el teorema de Braikenridge\u2013Maclaurin, anomenat aix\u00ED pels matem\u00E0tics escocesos del segle xviii William Braikenridge i Colin Maclaurin, \u00E9s l'invers del teorema de Pascal. Diu que si els tres punts d'intersecci\u00F3 dels tres parells de rectes prolongaci\u00F3 dels costats oposats d'un hex\u00E0gon estan en una mateixa recta , aleshores els sis v\u00E8rtexs de l'hex\u00E0gon estan en un c\u00F2nica . El teorema es pot aplicar a la construcci\u00F3 de Braikenridge-Maclaurin que \u00E9s una construcci\u00F3 sint\u00E8tica d'una c\u00F2nica definida per cinc punts, variant el sis\u00E8 punt. El teorema de Pascal afirma que, donats sis punts d'una c\u00F2nica (els v\u00E8rtex d'un hex\u00E0gon), les tres l\u00EDnies definides per les seves cares oposades s'intersecaran en tres punts colineals."@ca . . "En geometria, el teorema de Braikenridge\u2013Maclaurin, anomenat aix\u00ED pels matem\u00E0tics escocesos del segle xviii William Braikenridge i Colin Maclaurin, \u00E9s l'invers del teorema de Pascal. Diu que si els tres punts d'intersecci\u00F3 dels tres parells de rectes prolongaci\u00F3 dels costats oposats d'un hex\u00E0gon estan en una mateixa recta , aleshores els sis v\u00E8rtexs de l'hex\u00E0gon estan en un c\u00F2nica ."@ca . "In geometry, the Braikenridge\u2013Maclaurin theorem, named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem. The Braikenridge\u2013Maclaurin theorem may be applied in the Braikenridge\u2013Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three collinear points. This can be reversed to construct the possible locations for a sixth point, given five existing ones."@en . . . . . . . . . . . . . . . . . "1994"^^ . . . . . . . . . . . "Teorema de Braikenridge-Maclaurin"@ca . . "986741503"^^ . . . "26275483"^^ .