Thanks!
Copy of your previous comments in other thread for context:
> Also while those are Han, the language is sophisticated to regular Chinese readers. I can't even make sense of the words (individually yes) as a native Chinese speaker.
> It's traditional chinese but it's a challenge. This is my best guess:
> Looks like they were using colour as variable/labels.
--
Most of my previous guess is wrong :( .
In the second diagrams, they use that the area of the triangles is 6, they are not ignoring the number.
In both pages they ignore the outer triangles. They are not painted in neither graph. If they were using "my" solution I'd expect that the outer triangles in the first diagram were painted with the same color as the inner triangles in the second diagram.
The first diagram makes no sense. It looks like a graphic to show a numerical equality, but the geometric properties give no insight of the numerical properties. Perhaps it was a usual writing style?
There is no 49 in the first graphic (nor in the second) so my previous explanation doesn't fit with the text.
--
My second unsupported attempt of translation is:
[Second diagram]
The area of each red triangle is 6 [because 4 * 3 / 2 = 6].
The side of the inner yellow square is 1 [because 4 - 3 = 1], so the area is 1 [ 1 * 1 = 1].
The area of the [rotated] square is the sum of the four red triangles and the small yellow square, it is 25 [because 6 + 6 + 6 + 6 + 1 = 25].
So the side of the [rotated] square is 5.
Then the sides of the triangle at the bottom are 3, 4, 5.
[First diagram]
If we subtract the area of a square with side 5 and a square of side 3 [painted in cyan], we get the area [painted in yellow] that is 16.
[Notice that 16 is the area of a square of side 4, that we never draw here.]
--
My current opinion:
The second diagram is a proof that in a right triangle with legs 3 and 4, the hypotenuse is 5. I think that this can be extended to any other Pythagorean triple, but one at a time. This doesn't look like a general proof for all of them. This looks more like the verification of an example than a general proof.
The first diagram is an auxiliary construction for the second diagram. It's not very enlightling.
The explanation of the side added in Fermat's library is no a transcript or an explanation of the proof in the main text. It's another proof of the Pythagorean Theorem with a somewhat similar graphic, but it's unrelated.