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

If C and D are harmonic conjugates with regard to A and B, then one of them lies in, the other without AB; it is impossible to move from A to B without passing either through C or through D; the one blocks the finite way, the other the way through infinity.

From Project Gutenberg

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 Project Gutenberg

It has the property that on the side p opposite P meet the tangents at A and B, and also those at C and D. From the harmonic properties of four-points and four-sides it follows further that the points L, M, where it cuts the lines AB and CD, are harmonic conjugates with regard to AB and CD respectively.

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

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