Notam cu [tex] x_{n} [/tex] termanii unei progresi aritmetice si avem: [tex] x_{n}= x_{1}+(n-1)r [/tex], deci [tex] a=x_{l}= x_{1}+(l-1)r;b= x_{m}= x_{1}+(m-1)r;c= x_{n}= x_{1}+(n-1)r [/tex].
Inlocuim in E si se obtine: E=[tex](m-n)[ x_{1}+(l-1)r]+(n-l)[ x_{1}+(m-1)r]+(l-m) [x_{1}+(l-m)r] [/tex]=[tex] x_{1}(m-n+n-l+l-m) +r(ml-nl-m+n+nm-n-lm+l+[/tex][tex]ln-l-mn+m=[/tex])=0
