Pappus's hexagon theorem, often just called 'Pappus's theorem', a theorem named for Pappus of Alexandria
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.
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In its earliest known form, Pappus's Theorem is Propositions 138, 139, 141, and 143 of Book VII of Pappus's Collection.
Practically nothing of his life is known except that the mathematician Pappus of Alexandria refers to him as Aristaeus the Elder which presumably means that Pappus was aware of another later mathematician also named Aristaeus.
(This theorem is also known as the Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria.)
Pappus, in his Collections, treats its history, and gives two methods by which it can be generated.