Then he asks that he divide each of the four squares in half
Then he asks the boy that he divide each of the four squares in half, by drawing a line from corner to corner, and that he does this in such a manner that the dividing lines together, form a square.
Once it was don, he asked the boy in essence: Is the resulting inner square, not twice as large in area as the original square?
The boy agrees that the inner square is twice as large, because the inner square contains 4 triangles, while the original square contains only 2 triangles.
Socrates asked then, "Can you say then with absolute certainty that the inner square is twice as big in area, than the original square?"
Of course it is, the boy answers. "The original square contains 2 triangles, the new square contains 4. It is twice as big in area. It's as simple as that."
