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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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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

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

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

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

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 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

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