file writing without overwriting

How can i insert text from multiple files in one file? The file where i would want to write to doesnt have an extension.
My problem is that I want to insert data in a file that already contains data. when i do something like this:

try
    // source file
    assignfile(sourcefile,'C:\Documents and     Settings\Administrator\Desktop\source');
    reset(sourcefile);
    // destination file
    Rewrite(destination,'c:\destination);
    append(destination);
    pointer := eof(destination);
    while not eof(source') do
    begin
      ReadLn( source', line);
      writeln(destination,line);
    end;
  finally
    CloseFile(source');
    CloseFile(destination);
  end;

when i run this multiple times, it overwrites data in the destination file. that sux.