Title of projective theorem

Set the height to divide the hypotenuse into two parts: m, n, (m >); N) the height is h

Then it is: h:(m+n)= 1:4.

m+n=4h

Also: h 2 = Mn, (vertical theorem)

[(m+n)/4]^2=nm

[m+n]^2= 16mn

m^2+n^2- 14mn=0

M=( 14n+8 3n)/2=(7+4 3) n.

M:n=(7+4 radical number 3): 1

That is, the ratio of the two parts is: 7+4.