Mathematics Operation Axioms

[shahar]

On which Axioms can I can count on (Artimethical Axioms) to prove the Pathogorain Theorem by Chinese old scholar Chou Peui Saun Ching the side of the inner rectangle is (b-a)?

a, b are both each perpendicular.
c is hypotenuse side.

c is also the side of the outer rectangle.

 

[wolf]

Could you post a graphic?

 

[shahar]

 

[shahar]

order of sizes:
a < b < c

 

[wolf]

I redrew your drawing with the a, b, and c drawn in.
As for the Chou Peui Saun Ching proof I found this explanation: (See Example #9)

Pythagorean Theorem and its many proofs

www.cut-the-knot.org

That's about as much as I can help. Someone else will need to explain it further.

 

[Dr.Peterson]

It's not clear what you are asking for, when you ask about axioms. I doubt that the original author was thinking about axioms; but it is very likely that you mean something other than what you have said, since you often use the wrong words. Maybe you just want a statement of the proof based on this drawing.

Can you explain your goal using more words, so we can get an idea what you want?

 

[shahar]

O. K.
I mean to that question:
How I know that the same a letter that indicate in the expressetion (b-a) is equal to the expression a
?
Happy Daily routine...
[The holidays are over]
Back to daily routine

 

[wolf]

Basically the Pythagorean Theorem states that:
a^2 + b^2 = c^2 (where "c" is the hypotenuse)
We could rearrange that to a^2 = c^2 - b^2 and then:
a = square root (c^2 - b^2)
That is how you would solve for "a".

 

[Dr.Peterson]

O. K.
I mean to that question:
How I know that the same a letter that indicate in the expressetion (b-a) is equal to the expression a

This is almost incomprehensible. Of course a is a.

Presumably you are asking about the proof in post #5; doesn't the drawing in that post answer your question? The side of the square in the middle, plus side a of one right triangle, equals side b of a different (congruent) right triangle. So that length is b - a.