let's say that I have a sphere in $N$-dimensions
$$x_1^2+x_2^2+...+x_N^2=R$$
If I want to know the projection on the $x_1-x_2$ plane in this case I can figure out myself that is a circle, but how can I get Mathematica to do the projection and plot it for me?
Of course I need to apply this to a more complicated case where the N-dimensional surface is not as simple and can only be defined implicitly by $f(x_1,...,x_N)=0$.
I hope I have not forgot too much math from school that I am asking mathematica to do this for me.