By Wells J.R. (ed.)
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Sample text
These pairs intersect in the points P, Q and R respectively. Pascal's Theorem states that P, Q and R lie in a straight line. The hexagon can be taken as abfedca ; and then another straight line such as PQR results. A useful construction, used in Problem 54b on the next page, is that for a conic required to pass through a given point and to touch two tangents at given points. This construction will be approached by considering first the construction for extra points on (a) a conic defined by five points; and (b) a conic defined by a tangent point and three points.
A useful construction, used in Problem 54b on the next page, is that for a conic required to pass through a given point and to touch two tangents at given points. This construction will be approached by considering first the construction for extra points on (a) a conic defined by five points; and (b) a conic defined by a tangent point and three points. (a) Extra points on a conic defined by five points. Suppose the five points a c d e f (fig. I) to be given, but not b. We wish to obtain points such as b.
31 R PROBLEM 44 TO CONSTRUCT AN ELLIPSE B BY THE TRAMM EL METHOD. DR SHORT TRAMMEL . I kJ c I I R LONe i TRAMMEL fp B D A c PROBLEM TO CONSTRUCT AN APPROXIMATE §l TRAMMEL FOR LARGE ELLIPSES . ELLIPSE USING ARCS OF CIRCLES . 32 CONIC SECTIONS-THE ELLIPSE Chap. 3 Conjugate Diameters. jugate, because PQ is pari to tangents at Rand S, or because RS is pari to tangents at P and Q. It may be proved that PO + SCI = VCI + BO. Two diams. are conjugate if they are so situated that each is pari to the tangents at the extremities of the other ; in fig.