harmonic conjugates

American  

plural noun

Mathematics.

1. two points whose cross ratio with two specified points equals −1.

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Etymology

Origin of harmonic conjugates

First recorded in 1880–85

Example Sentences

It follows that, “if of four harmonic conjugates two coincide, then a third coincides with them, and the fourth may be any point in the line.”

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various

Then, since A, P, B, and the point at infinity on AB are four harmonic points, we have the theorem Conjugate diameters of the hyperbola are harmonic conjugates with respect to the asymptotes.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Corresponding rays of the involution are harmonic conjugates with respect to the double rays.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Since corresponding points in the involution have been shown to be harmonic conjugates with respect to the double points, the center is midway between the double points when they exist.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Also, conjugate diameters are harmonic conjugates with respect to the asymptotes.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman