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

They will therefore cut the principal axis in two points, which are conjugate in the involution considered in � 84; hence they are harmonic conjugates with regard to the foci.

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

In an hyperbolic involution any two conjugate points are harmonic conjugates with regard to the two foci.

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

Hence— Any two conjugate diameters of an hyperbola are harmonic conjugates with regard to the asymptotes.

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

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

If A and C are harmonic conjugates with respect to B and D, then B and D are harmonic conjugates with respect to A and C.

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