Content of Cayley-Menger Determinant

Theorem
Let $d$ be an arbitrary number of dimensions and $\lambda_{ij} = \vert{v_i,v_j}\vert$, for all $0 \le i < j \le d$.

Then for every simplex $\Delta = ( v_0, v_1 ... v_d ) \subset \R^d$, we have:

Also see

 * Tartaglia's Formula