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- Q1101140 subject Q8824657.
- Q1101140 abstract "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.What is remarkable is that 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; it can also be defined in terms of the cross-ratio as (A, B; C, D) = −1.".
- Q1101140 thumbnail Pappusharmonic.svg?width=300.
- Q1101140 wikiPageExternalLink books?id=r3ILAAAAYAAJ.
- Q1101140 wikiPageExternalLink text-idx?c=math;cc=math;view=toc;subview=short;idno=Lach015.
- Q1101140 wikiPageExternalLink projective-geometry.
- Q1101140 wikiPageWikiLink Q1191139.
- Q1101140 wikiPageWikiLink Q12916.
- Q1101140 wikiPageWikiLink Q129916.
- Q1101140 wikiPageWikiLink Q1645406.
- Q1101140 wikiPageWikiLink Q16991395.
- Q1101140 wikiPageWikiLink Q1751490.
- Q1101140 wikiPageWikiLink Q177409.
- Q1101140 wikiPageWikiLink Q33760.
- Q1101140 wikiPageWikiLink Q3412598.
- Q1101140 wikiPageWikiLink Q49115.
- Q1101140 wikiPageWikiLink Q715358.
- Q1101140 wikiPageWikiLink Q7249469.
- Q1101140 wikiPageWikiLink Q77502.
- Q1101140 wikiPageWikiLink Q7758358.
- Q1101140 wikiPageWikiLink Q841893.
- Q1101140 wikiPageWikiLink Q8824657.
- Q1101140 wikiPageWikiLink Q899539.
- Q1101140 wikiPageWikiLink Q9267097.
- Q1101140 comment "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.".
- Q1101140 label "Projective harmonic conjugate".
- Q1101140 depiction Pappusharmonic.svg.