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

The plane spanned by the normal vector N and the binormal vector B.

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

The centroid of the four points constituting an orthocentric system is the center of the common nine-point circle (Johnson 1929, p. 249). This fact automatically guarantees ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

A line and a plane are parallel if they do not intersect.

The fixed point with respect to which a pedal curve or pedal triangle is drawn.

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The function giving the volume of the spherical quadrectangular tetrahedron: V=(pi^2)/8f(pi/p,pi/q,pi/r), (1) where (2) and D=sqrt(cos^2xcos^2z-cos^2y). (3)

A section of a solid is the plane figure cut from the solid by passing a plane through it (Kern and Bland 1948, p. 18).