According to J. L. Coolidge (A history of geometrical methods) the book you mention used π = 3 consistently. It also dealt with pythagorean triples - this is mentioned in may sources.

Referring to that diagram in proof #4, Coolidge remarks that the comment in the original is incomprehensible without the diagram, but, although it refers specifically to the 3-4-5 triangle, it is not a proof that they did not know a more general statement. My guess is that, with so much good will, he would mention another proof or a more general statement if one was available.