Proposition: 2.05: Rectangle is Difference of Two Squares
(Proposition 5 from Book 2 of Euclid's “Elements”)
If a straight line is cut into equal and unequal (pieces) then the rectangle contained by the unequal pieces of the whole (straight line), plus the square on the (difference) between the (equal and unequal) pieces, is equal to the square on half (of the straight line).
Modern Formulation
With \(a:=AC=CB\) and \(b:=CD\), this propositions states that \[(a+b)(ab)=a^2b^2\]
which is one of the binomial formulae.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5
Sections: 6
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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"