NOTE: the network is implemented as:

      public struct neurone
      {  public int x,y;   // coord. for drawing
         public double output;
         public double[] inWeights;
         public double error;
      }
      
      public neurone[][] rete = new neurone[3][];
      
and backoprop (very basic) is:

      public double Backpropagation(double[] target)
      {  double output,sum,Dij,errore;
         int i,j,lev;

         errore = 0;       // global error
      
         for(j=0;j<rete[2].Length;j++)            // error of output neurons
         {  output = rete[2][j].output;
            rete[2][j].error = output * (1 - output) * (target[j] - output);
            errore = errore + (output - target[j])*(output - target[j]);
         }

         for(j=0;j<rete[1].Length;j++)             // error of hidden neurons
         {  sum = 0;

            for(i=0;i<rete[2].Length;i++)
               sum += rete[2][i].error * rete[2][i].inWeights[j];
               
            rete[1][j].error = sum * rete[1][j].output * (1 - rete[1][j].output);
         }   
         
         for(lev=2;lev>0;lev--)
         {  for(j=0;j<rete[lev].Length;j++)
            {  for(i=0;i<rete[lev-1].Length;i++)         // weights update
               {   Dij = LearningRate * rete[lev][j].error * rete[lev-1][i].output; // + eta * D[i,j.lev] momento
                   rete[lev][j].inWeights[i] += Dij;
               }
               
               Dij = - LearningRate * rete[lev][j].error;  // bias update
               rete[lev][j].inWeights[i] += Dij;
            }
         }
         return(errore);
      }