# who invented projective space $\mathbb{P}^n$?

Who invented projective space $\mathbb{P}^n$ as an extension of the usual affine space $\mathbb{A}^n$?

Who was the first person to consider projective closure of plane affine algebraic curves (curves in $\mathbb{A}^2$)? Was it the same person?

• Start here? en.wikipedia.org/wiki/Projective_geometry – Michael Joyce Apr 3 '13 at 14:46
• I do not know. Anyway, it seems that homogeneous coordinates were introduced by Moebius en.wikipedia.org/wiki/Homogeneous_coordinates – Francesco Polizzi Apr 3 '13 at 14:48
• Francesko, thank you. Very helpful. Interestingly, the article says that "Möbius' original formulation of homogeneous coordinates specified the position of a point as the center of mass (or barycenter) of a system of three point masses placed at the vertices of a fixed triangle". -- I.e., his goal was different rather than the completion of $\mathbb{A}^n$! – Maxim Leyenson Apr 3 '13 at 15:15
• Michael, the current version of the Wikipedia page on Projective geometry does not answer these questions, I checked before posting... – Maxim Leyenson Apr 3 '13 at 17:37
• The idea of the projective plane is at least implicit in the work of the ancient Greek Pappus. It's not clear to me that one can say when projective space was developed. Anyway, it's still an interesting question, but I think it might be helpful to indicate exactly which aspect of projective space you are interested in. (I realize your second question does that, but I didn't know how to interpret your first question. Are you specifically interested in when people understood the generalization to $n$-dimensional space, or the first incarnations when $n = 2, 3$?) – Michael Joyce Apr 3 '13 at 19:08