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harmonic conjugates

American  

plural noun

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


Etymology

Origin of harmonic conjugates

First recorded in 1880–85

Example Sentences

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

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

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

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

It is not difficult to see that the double-points in the involution are harmonic conjugates with respect to corresponding points in the involution.

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

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 Derrick Norman Lehmer

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 Derrick Norman Lehmer

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