 | Almanacs, English - 1842 - 108 pages
...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 inscribed in a conic section be produced to meet, the three points of section will be in a straight line ; required a demonstration... | |
 | 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... | |
 | 1856 - 360 pages
...which shows that K, H, G are in the same straight line. We have therefore the following theorem : If the three pairs of opposite sides of a hexagon inscribed in a conic section be produced to meet, the three points of intersection mill range in the same straight line.... | |
 | James Joseph Sylvester, James Whitbread Lee Glaisher - Mathematics - 1862 - 410 pages
...совА — 2m coeB—2n cos(7= 0. July, 1861. PASCAL'S THEOREM. By HW CHALLIS. rrilK intersections of opposite sides of a hexagon inscribed in a conic lie on one straight line. Let P, Q (fig. 16) be intersections of two pairs of opposite aides. Suppose F to... | |
 | 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 = 1 a... | |
 | Peter Guthrie Tait - History - 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 = 1... | |
 | 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... | |
 | Charles Smith - Conic sections - 1883 - 452 pages
...with one anotlier can be projected into concentric circles. Ex. 3. The three points of intersection of opposite sides of a hexagon inscribed in a conic lie on a straight line. [Pascal's Theorem.] Project the conic into a circle, and the line joining the points... | |
 | 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... | |
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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. 
