Projective harmonic conjugate

Projective harmonic conjugate

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A, B. The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem.
http://dbpedia.org/resource/Projective_harmonic_conjugate

Projective harmonic conjugate

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A, B. The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem.
http://dbpedia.org/resource/Projective_harmonic_conjugate
has abstract
Die harmonische Teilung bezeic ...... Punktepaaren auf einer Gerade.
@de
Em geometria projetiva, o pont ...... armônico de C em relação A, B.
@pt
En geometría proyectiva, se di ...... yección de la figura original.
@es
En géométrie affine, quatre po ...... me quadratique qui la définit.
@fr
In projective geometry, the ha ...... ss-ratio as (A, B; C, D) = −1.
@en
Van vier verschillende punten ...... van de punten gelijk is aan .
@nl
Гармоническая четвёрка точек — ...... ической. В этом случае пишут .
@ru
Гармонійна четвірка точок — че ...... йною. В цьому випадку пишуть .
@uk
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
Link from a Wikipage to another Wikipage
wikiPageUsesTemplate
subject
comment
Die harmonische Teilung bezeic ...... e obige Gleichung sich auch so
@de
Em geometria projetiva, o pont ...... armônico de C em relação A, B.
@pt
En geometría proyectiva, se di ...... r como: Propiedad fundamental:
@es
En géométrie affine, quatre po ...... rimer qu'un birapport vaut –1.
@fr
In projective geometry, the ha ...... ollows from Desargues theorem.
@en
Van vier verschillende punten ...... van de punten gelijk is aan .
@nl
Гармоническая четвёрка точек — ...... ической. В этом случае пишут .
@ru
Гармонійна четвірка точок — че ...... йною. В цьому випадку пишуть .
@uk
label
Conjugado harmônico projetivo
@pt
Cuaterna armónica
@es
Division harmonique
@fr
Harmonische Teilung
@de
Harmonische ligging
@nl
Projective harmonic conjugate
@en
Гармоническая четвёрка
@ru
Гармонійна четвірка
@uk
sameAs
wasDerivedFrom
isPrimaryTopicOf