Pythagoras' Theorem
In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

James A. Garfield (1831-1881). Twentieth American President. Oil on Canvas by Ole Peter Hansen Balling. National Portrait Gallery, Washington.

Garfield was shot by a disappointed office seeker four months after becoming president and died from his wounds several weeks later.

Jim Garfield dabbled in mathematics.
In 1876 he published this simple and elegant proof.

To Prove: a2 + b2 = c2
Construction: Produce AC to D by a.
Draw DE of length b perpendicular to AD. Join CE and BE.



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