Complex sentence: Note that, since ratios are used, multiplying the three homogeneous coordinates by a common, non-zero factor does not change the point represented--unlike Cartesian coordinates, a single point can be represented by infinitely many homogeneous coordinates.
Split into simpler sentences: Note that, since ratios are used, multiplying the three homogeneous coordinates by a common, non-zero factor does not change the point represented. Thus unlike Cartesian coordinates, a single point can be represented by infinitely many homogeneous coordinates.