Lectures On the Geometry of Position

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" 254. In conclusion, a problem may here be inserted which is clearly not of the second order, but which is closely related to the one last discussed, namely, In a plane are given a triangle ABC and an involution point-range of the first order n, so situated that neither double point of if lies on a side of the triangle and u passes through no vertex of the triangle. It is required so to circum scribe a conic about the triangle that all pairs of corresponding points of u are conjugate with In a... plane are given a triangle and an involution sheaf of rays of the first order 5, so situated that neither double ray of S passes through a vertex of the triangle and the centre S lies upon no side of the triangle. It is required so to inscribe a conic in the triangle that all pairs of corresponding rays of 6 are conjugate with respect to the curve.
respect to the curve.
Let the points K and M (Fig. 82), in which u is cut by the lines AB and BC respectively, be coordinated in the involution FIG.


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