## Euclid's proof of Pythagoras' Theorem

This proof is essentially Euclid's own
proof of Proposition I.47.

Like many proofs, it partitions the
square on the hypotenuse by dropping a perpendicular
from the right angle through it. Then it performs
a sequence of shears and rotations
to show corresponding areas are equal.
It does not, however,
transform the areas directly concerned, but rather looks at triangles
obtained by halving them.

*Click on a figure to start an animation, to pause it
in the middle of an animation,
or to reset it to its initial configuration
if it is finished.*

The Jim Morey's
first Java proof of Pythagoras' Theorem
(which won Grand Prize in the first Java contest)
follows a variant of this argument.

### Exercise

In Euclid's diagram, three of the lines drawn seem to meet in
a single point around the middle of the triangle.
Do they? Prove your assertion.
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