Two triangles are in perspective from a point if and only if they are in perspective from a line, meaning corresponding sides meet at three collinear points. Named for Girard Desargues, it is a foundational result of projective geometry.
Facts
StatementTwo triangles are in perspective axially, meaning their corresponding sides meet at three collinear points, if and only if they are in perspective centrally, meaning the lines joining their corresponding vertices all meet at one point. 2 Proof YearDesargues never published the theorem himself; it first appeared in a 1648 appendix by his friend and pupil Abraham Bosse. Classification
Statement FormCharacterization Theorem 1 Connections
Sources
1. Wikipedia: Desargues's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally.
2. Desargues' Theorem (Wikipedia)
Wikimedia FoundationLead section, opening theorem statement
Two triangles are in perspective axially if and only if they are in perspective centrally.
Lead section, sentence on the 1648 Bosse publication
Desargues never published this theorem, but it appeared in an appendix entitled Universal Method of M. Desargues for Using Perspective (Manière universelle de M. Desargues pour practiquer la perspective) to a practical book on the use of perspective published in 1648 by his friend and pupil Abraham Bosse
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