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Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

The 20 Cayley lines generated by a hexagon inscribed in a conic section pass four at a time though 15 points known as Salmon points (Wells 1991). There is a dual relationship ...

Two points on a surface which are opposite to each other but not farthest from each other (e.g., the midpoints of opposite edges of a cube) are said to be transitive points. ...

Given a quadrilateral ABCD, the three diagonal points P, Q, and R defined as the pairwise intersections of the lines determined by the sides AB intersection CD, AC ...

Given ∠AXB+∠AYB=pi radians in the above figure, then X and Y are said to be antigonal points with respect to A and B.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

The Bickart points are the foci F_1 and F_2 of the Steiner circumellipse. They have trilinear coordinates alpha_1:beta_1:gamma_1 and alpha_2:beta_2:gamma_2, where alpha_i = ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

There are two different definitions of the mid-arc points. The mid-arc points M_(AB), M_(AC), and M_(BC) of a triangle DeltaABC as defined by Johnson (1929) are the points on ...

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.