Proposition: 2.06: Square of Sum with One Halved Summand
(Proposition 6 from Book 2 of Euclid's “Elements”)
If a straight line is cut in half, and any straight line added to it straighton, then the rectangle contained by the whole (straight line) with the (straight line) having being added, and the (straight line) having being added, plus the square on half (of the original straight line), is equal to the square on the sum of half (of the original straight line) and the (straight line) having been added.
Modern Formulation
Algebraically, with \(a:=AB\) and \(b:=BD\), the proposition states that
\[\left(\frac a2\right)^2+(a+b)b=\left(\frac a2+b\right)^2.\]
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"