If the length of the hypotenuses of the triangles is $c$ and the length of the sides is $a$ and $b$ ($b$ is the longer side), the area of the outer square is $c^2$ which is equal to the sum of the areas of the four triangles and the smaller white square:  and so $$ 4×\frac{1}{2}ab+(b−a)^2 \\ =2ab+(b^2−2ab+a^2)=a^2+b^2=c^2 $$ These two pages are from the Zhoubi suanjing (Arithmetical Classic of the Gnomon and the Circular Paths of Heaven), one of the oldest Chinese books on astronomy and mathematics dated to approximately 100 BCE. In particular, these images are from a Ming dynasty copy printed in 1603. The Pythagorean theorem was known long before Pythagoras, but supposedly he was the first to prove it around 500 BCE. These diagrams were added to the original text at some point in an attempt to illustrate a dissection proof of the "Pythagorean Theorem," known by the Chinese as the Gougu theorem. This is just Pythagoras original proof. You start by inscribing a square inside a bigger square creating 4 identical triangles. Each triangle has side lengths a and b and hypotenuse c.  If we group the triangles in pairs so that they share the same hypotenuse, we end up with two rectangles and 2 white squares with areas $a^2$ and $b^2$.  Since the only thing we did was rearranging the geometric figures, the white area of this new arrangement has to be equal to the area of the first figure ($c^2$) and so $$ a^2+b^2=c^2 $$ It is not obvious if the chinese already knew about this proof or derived it independently. Would you care to give references to the “original proof” by Pythagoras? I’m not sure I can see these diagrams as “the same proof” as you give since there is no diagrammatic evidence to suggest that such a “rearrangement” is performed. In addition, for this to be a proof, an explanation as to why the central (tilted) quadrilateral has to be a square should be given. I can understand it might be inferred that it is a rhombus (equal sides and a parallelogram) but square? I don't see any indication of that — unless it is in the text.