You're really struggling with that analogy. Read it again, that's exactly what I said. Of course it's not what they did or what they were setting out to do. You criticized them for doing a proof using trig by comparing it to the people who proved the theorem without using trig.
Based on your earlier post, it seems you're just catching on to that fact and trying to change your tune. At any rate, I have no faith you will correctly interpret their proof.