51Թ

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harmonic conjugates

plural noun

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


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51Թ History and Origins

Origin of harmonic conjugates1

First recorded in 1880–85
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Example Sentences

Examples have not been reviewed.

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.

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

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

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

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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.

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