Wrong Solution

[Phil8659]

If one searches for producing a square in a right triangle, they will generally get a figure which, does produce a square, but the answer is wrong.

Ever since at least Plato, if you view Greek Mathematics boxed set,
https://archive.org/details/greek-mathe ... 01%20Unit/

You see that the Greek were looking for a way to use the right triangle to form a duplicate ratio. No one figured it out. I have, however, shown the solution in every production of the Delian Quest. The correct square in a right triangle produces a duplicate ratio, which is part of the Delian Solution. The odd thing is, the solution is actually quite simple. Insisting on doing things wrong does produce, sometimes, a blindness to the obvious.

So, the Delian Solution has been claimed impossible, because they could not figure out how to use a right triangle correctly to achieve a duplicate ratio. The Square is produced on the hypotenuse, not by making perpendiculars to the other two sides. The solutions are found in The Delian Quest for the year 1993, shortly after I started my study of Geometry.
So, I just did a rework of the figure, in the revisit I am doing.

The Delian Quest, and other works I have done are actually my homework files, problems I gave myself to work on, so, each time I do a revision, I try to clean the mess up a bit.

I actually found, I study the way Plato said to study. Ask questions and answer them.

Every right triangle, has one square you can place on the hypotenuse which produces a duplicate ratio and points to the answer. I show how simple it is to find that square, and I show more than one method to do it. The Greeks were right, as to what figure would show the way, they just went about it wrong.

[Phil8659]

One can put the problem this way.

Given a Right Triangle, use a square to divide it into duplicate ratio's. As A is to B, so too is C to D, and As C is to D, so too is E to F. A and B is from one triangle, C and D from he second, E and F the third.