Apollonius's Theorem relates the length of a median of a triangle to the lengths of the triangle's three sides, stating that the sum of the squares of two sides equals twice the square of the median to the third side plus twice the square of half that third side. Attributed to Apollonius of Perga, it is a classical result of Euclidean geometry that is a special case of the more general Stewart's Theorem.
Facts
StatementIn any triangle, the sum of the squares of two sides equals twice the square of half the third side plus twice the square of the median drawn to that third side. 1 Proof YearAttributed to Apollonius's lost treatise Plane Loci, circa 200 BCE; the earliest surviving proof is in Pappus's Collection, circa 340 CE. Classification
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Sources
1. Apollonius's Theorem (Wikipedia)
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It may have been in Apollonius of Perga's lost treatise Plane Loci (c. 200 BC), and was included in Robert Simson's 1749 reconstruction of that work.
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