 | Almanacs, English - 1842 - 108 pages
...of the curve formed by the intersection of the two surfaces. XV. OR PRIZE QUEST. (1703); by PASCAL. If the three pairs of opposite sides of a hexagon...conic section be produced to meet, the three points of section will be in a straight line ; required a demonstration without the aid of perspective, or any... | |
 | Charles Hutton - Mathematics - 1843 - 570 pages
...the arrangement of this chapter the foundation of Pascal's theorem, next in the series. PROP. XIV. The three pairs of opposite sides of a hexagon inscribed in a conic section, being produced to meet, the three points of intersection will all be situated in one straight line.... | |
 | John Hymers - Geometry, Analytic - 1845 - 248 pages
...B(?-TV SC, and CY be a perpendicular from the centre upon the tangent at P, then PY = SC. 99. If the opposite sides of a hexagon inscribed in a conic section...produced to meet, the three points of intersection will lie in a straight line. In fig. 114, draw any diagonal MM', and let the pairs of opposite sides... | |
 | John Hymers - Conic sections - 1845 - 252 pages
...the conic section at one of the angular points of the triangle, we fall upon Prob. 50. 100. If two pairs of opposite sides of a hexagon inscribed in a conic section be parallel to one another, the two remaining sides shall also be parallel to one another. Let MM' be... | |
 | Peter Guthrie Tait - Quaternions - 1867 - 366 pages
...one plane ; or, making the statement for any plane section of the cone, the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line. EXAMPLES TO CHAPTER VII. 1 . On the vector of a point P in the plane Sap... | |
 | Peter Guthrie Tait - 1867 - 364 pages
...one plane ; or, making the statement for any plane section of the cone, the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line. EXAMPLES TO CHAPTER VII. 1. On the vector of a point P in the plane Sap =... | |
 | George Hale Puckle - 1868 - 386 pages
...point (a/SyV which means the point whose trilincar co-ordinates are a, ft 7. 336. Pascal's Theorem, The three pairs of opposite sides of a hexagon inscribed in a conic intersect in points which all lie in one straight line. Let L = 0, M=0, N=0, R = 0, S=0, T = 0, be... | |
 | Peter Guthrie Tait - Quaternions - 1873 - 340 pages
...plane ; or, making the statement for any plane section of the cone, that the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a curve, may always lie in one straight line, the curve must be a conic section. EXAMPLES TO CHAPTER... | |
 | George Hale Puckle - Conic sections - 1887 - 404 pages
...G) ЦIг + By + F) AB H represents the axes, as proved in Art. 303, Ex. 1. 342. Pascal's Tiieorem. The three pairs of opposite sides of a hexagon inscribed in a conic intersect in points which all lie in one straight line. since the conic is circumscribed about the... | |
 | John Casey - Geometry, Analytic - 1893 - 601 pages
...identity aSi - b$2 = c/Ss - dS± gives aS\ — 0/83 = bSz, — dS^&c. Cor. — The intersections of the three pairs of opposite sides of a hexagon inscribed in a conic lie on a right line. If ABCDEF be the hexagon, and we take for /Si, $2, $3, $4 the pairs of lines (AD,... | |
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... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line. 
