All propositions
Proposition I.47
The Pythagorean theorem
In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
Euclid’s windmill. The square on the hypotenuse equals the squares on the legs — proved not by similar triangles, but by shearing areas. It is the climax of Book I, and the most famous theorem in the world.
Step 1 of 5
The right triangle
Given
Let ABC be right-angled at C. We will show that the square on AB equals the square on BC together with the square on CA.