Question

Euclids theorem...

Answer 1

pythagor theorem maybe?

Answer 2

what do
ca and cb
represent?

Answer 3

@electrokid

Answer 4

triangles ABC ~ DBA ~ DCA
and hence their corresponding sides are equal
\[
{C_a\over c}={c\over a}\qquad,\qquad{C_b\over h}={h\over C_a}\\
h^2=C_aC_b\\
\;\\
a^2=b^2+c^2=b^2+h^2+C_a^2\\
{a^2\over b^2}=\frac{b^2+C_aC_b+C_a^2}{b^2}\\
{a^2\over b^2}=\frac{h^2+C_b^2+C_aC_b+C_a^2}{h^2+C_b^2}\\
{a^2\over b^2}=\frac{C_a^2+2C_aC_b+C_b^2}{C_b(C_a+C_b)}\\
{a^2\over b^2}=\frac{(C_a+C_b)^2}{C_b(C_a+C_b)}\\
{a^2\over b^2}=\frac{(C_a+C_b)}{C_b}\\
\Large {a^2\over b^2}={C_a\over C_b}+1
\]