F(x,y) ≥ 0

while it is obvious from the definition.

I am not wedded to the Pythagorean theorem or to its proofs. Sometimes I err in my selections, perhaps, even often so, but what I am on lookout for is elegance not a refutation of Elisha Loomis' opinions. So, no, this is not going to be proof #89.

Yes, sir. I realize that. I did not mean to sound like you were lock-in-step with Loomis.

>2. I have no patience with your link. He used calculus to
>argue that
>
>F(x,y) ≥ 0
>
>while it is obvious from the definition.

I need help on this. Did you mean that the statement was unnecessary, or that it depends on the PT and creates a circular argument?

>
>I am not wedded to the Pythagorean theorem or to its proofs.
>Sometimes I err in my selections, perhaps, even often so,
>but what I am on lookout for is elegance not a refutation of
>Elisha Loomis' opinions. So, no, this is not going to be
>proof #89.

Sorry, I jumped the gun on this a little and was wrong to suggest that you post this to your page as proof #89. I apologize if I offended you. Ironically, I am still "wedded" to my own Calculus proof and hope somehow to argue its validity. I suppose I am stubborn in that regard. It was my intention to look at this link as an improvement somewhat in my own thinking.

I am still having a hard time with the reasoning behind why my own calculus proof is circular. I suppose I am blind to some big assumptions I made on that, or else I am ignorant of the circularity somewhere. Rest assured, I am trying.

Also, I did post that proof on mathforum... And the discussion there got me to thinking that I should not assume that slope of a line can be gained apart from the PT. Am I headed in the right direction?

Again you have been very kind to respond to my barrage of posts recently. Thanks for your correspondence and commentary.

No, it is exactly as I wrote. He defined F(x, y) which is by defintion is not negative and then wasted a page proving that it is so by using calculus. There is not circularity but a waste.

>Also, I did post that proof on mathforum... And the
>discussion there got me to thinking that I should not assume
>that slope of a line can be gained apart from the PT.

Just continue the discussion there.