Talk:Minkowski's first inequality for convex bodies

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This is not what I was taught to be Minkowski's First Theorem on Convex Sets. From W. Scmidt's Diophantine Approximations and Diophantine Equations I was taught:

Let B$\subseteq$R^n be a convex set which is symmetric about the origin of volume V(B)>(2^n)*det$\Lambda$ where $\Lambda$ is a lattice. Then B contains a non-zero lattice point.

I was wondering if this is equivalent to what I learned, or whether yours is a generalization. I would be interested to know, for I am considering doing an article on his Second Theorem. Thank you. Dkettles