... or is it a proof, just in case.

>Starting with
>the familiar 3-4-5 right triangle,

... or any other Pythagorean triangle with integer sides, right? (But what if the sides are not integer?)

>let each side serve as
>the base of an isosceles triangle, with height twice the
>base length.

This is probably not necessary. Why do you care about the height?

>Divide the bases into their 3,4,and 5 units,
>and also divide the heights of the isosceles triangles into
>3, 4, and 5 equal sections, respectively. Create
>smaller isosceles triangles within the larger by running
>lines from the base divisions and parallel to the sides of
>the large isosceles triangles as far as possible, within the
>triangles. There are 9 small triangles
>within the 3 unit base length isosceles triangle, 16 in the
>4 unit base one, and 25 in the 5 unit base triangle. These
>all correspond to the squares of the sides of the right
>triangle. And, of course, the two smaller values add up to
>the larger.

Right, but this is true because of the Pythagorean theorem. As far as I can see, nothing in your construction explains why this is so.