theorem Th26:
  a,b,c are_collinear & a,b,d are_collinear implies a,b // c,d
proof
  assume that
A1: a,b,c are_collinear and
A2: a,b,d are_collinear;
  now
    assume that
A3: a<>b and
A4: a<>c;
A5: a,b // a,c by A1;
    a,b // a,d by A2;
    then a,c // a,d by A3,A5,Def1;
    then a,c // c,d by Th7;
    hence thesis by A4,A5,Th8;
  end;
  hence thesis by A2,Th3;
end;
