  This is a translation of a final paper. It contains proofs of some well-known
Positivstellens\"atze. The approach in this paper differs in two respects from
presentations in literature. We use the Stone-Weierstrass Theorem directly to
prove an inductive property, which makes the Kadison-Dubois Theorem superfluous
in our paper, and we also consider homogeneous and projective
Positivstellens\"atze. This leads us to a homogeneous version of Schm\"udgen's
theorem and a projective version of Putinar's theorem.
