Pythagorean theorem

Pythagoras discovered the most famous ：『 a2 + b2 = c2 』

In the right triangle, the squared of the hypotenuse is

equal to the sum of the squared of both sides.

Pythagorean theorem proof of the oldest

Proof 11.ΔBAF All equal DAC(SAS)2. Area of ACGF ＝ 2× Area of ΔBAF ＝ 2× Area of ΔDAC3. Area of AMLD ＝ 2× Area of ΔDAC4. ∴ Area of ACGF ＝ Area of AMLD5. Same Reason Area of BCHK ＝ Area of BMLE6. ∴ Area of ACGF ＋ Area of BCHK ＝ Area of ABED

Scilicet ： AC2 ＋ BC2 ＝ AB2

D E

A B

CF

H

L

G

K

M

< >幾何原本 中畢氏定理的證明

Proof 2Below left are two large squares of equal area

Also lost four identical right-angled triangle

Scilicet ：弦 2 ＝勾 2 ＋股 2

Problem

How to use the three squares to

prove the Pythagorean Theorem?