Sentence of the Pythagoras

 
Right-angled triangle with side squares and  rectangles

 
a ² +b ² =c ²

 
The set of the Pythagoras it means that in a right-angled triangle the surface of the large square over the hypotenuse is equal to the sum of the surfaces of the squares over the two sides.

 
Or:

 
A, b, c are the sides of a triangle with the largest side c. the square over c are equal-area to the sum of the squares over A and b exactly if the triangle is right-angled and is this right angle with c.

 
As formula:

 
a2 + b2 = c2

 
Side set of the Euklid

Side set: The two red ranges have the same area, likewise the two green increase.

Side set: The two red ranges have the same area, likewise the two green.

 
The point considered of the height divide the hypotenuse into two parts. The relationship of these two parts is described by the side set. It means that in right-angled triangles the rectangles are equal-area in each case in the square over the hypotenuse under the side squares these.

 
a ² =pc and b ² =qc

 
or:

 
If a, b, c are the sides of a right-angled triangle with the hypotenuse c. divide one this triangle at the height of h and if p the hypotenuse section over a, q the appropriate section over b is, then applies:

 
The square over a is equal-area to the rectangle with the sides p and c, and the square over b is equal-area to the rectangle with the sides q and c.

 
As formulas:

 
a^2=p . c

b^2=q . c

 
C elevator set of the Euklid

right-angled triangle with pq and h ²

 
h ² =pq

 
The elevator set means that in a right-angled triangle the square over the height is equal-area the rectangle from the hypotenuse sections.

 
Or:

 
A right-angled triangle with the height of h, which divide the hypotenuse into the sections p and q, is given. Then it is : 

 
h^2=p. q