harmonic conjugates

plural noun

, Mathematics.

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

Word History and Origins

Origin of harmonic conjugates¹

First recorded in 1880–85

Example Sentences

The first part of the right-hand theorem in � 64 may be stated thus: any two conjugate lines through a point P without a conic are harmonic conjugates with regard to the two tangents that may be drawn from P to the conic.

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg

Then B and D are said to be “harmonic conjugates” with respect to A and C. 8.

From Project Gutenberg

If the line joining two conjugate poles cuts the conic, then the poles are harmonic conjugates with regard to the points of intersection; hence one lies within the other without the conic, and all points conjugate to a point within a conic lie without it.

From Project Gutenberg