...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...

...of 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...produced to meet, the three points of intersection mill range in the same straight line. — (Pascal's Hexagram.) And again (art. 5), " if three or more...

...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 which...

...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...

...equation for that of QR ; hence PR, QR, coincide, and P, Q, R are in a straight line ; or, (A). If the opposite sides of a hexagon inscribed in a conic section...produced to meet, the three points of intersection range in a straight line. Again, let ABCDEF be a hexagon circumscribing a conic section. If the alternate...

...which shows that K, II, 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 lie produced to meet, the three points of intersection will range in the same straight line. — (Pascal's...

...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...

...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 =...

...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...

...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...