Given two lines each carrying three points, the three intersection points formed by connecting the points across the two lines in crossing pairs are always collinear. Attributed to Pappus of Alexandria, it is one of the earliest results in projective geometry.
Facts
Partially Attested
Proof YearApproximate. MacTutor dates Pappus's Collection, which records this result in Book VII, to around 340 AD, though some historians place its completion by 325 AD; no more precise year is available. StatementIf A, B, C lie on one line and a, b, c lie on another line, then the three intersection points formed by crossing the lines Ab with aB, Ac with aC, and Bc with bC are always collinear, on the Pappus line. 1 Connections
In Branch
Proved By
Source Pappus, Biography (MacTutor History of Mathematics)
Sources
1. Pappus's Hexagon Theorem (Wikipedia)
Wikimedia FoundationOrigins sectionQuote, Origins section
What we call Pappus's Theorem is found in chapters 202, 206, 207, 209, and 211, also numbered as Propositions 134, 138, 139, 141, and 143, of Book VII of Pappus's Collection.
2. Pappus, Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsPage text
Pappus's major work in geometry is Synagoge or the Mathematical Collection which is a collection of mathematical writings in eight books thought to have been written in around 340 ( although some historians believe that Pappus had completed the work by 325 AD ) .
Proved By: Pappus of Alexandria, Biography
one of his theorems is cited as the basis of modern projective geometry
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