The volume computing for the continuous geometry in n-dimensions

     The integral calculation for the volume of the continuous geometry $R$ in n-dimensions can be defined as follows

$\mathrm{Vol}(R)=\int_{s\in R}\mathrm{1\bullet d}s$

     For the above volume computing, we have the following theorem.

     [Theorem 1] If the boundary $\partial R$ of the continuous geometry $R$ in $n$ -dimensions is known, the volume of the geometry $R$ can be calculated as follows

$\mathrm{Vol}(R)=\cfrac{1}{n}\int_{z\in\partial R}\left|\mathrm{det}[z,c_{1},c_{2},...,c_{n-1}]\right|\mathrm{d}z_{1}\mathrm{d}z_{2}...\mathrm{d}z_{n-1}$

where $\mathrm{d}z$ is the ( $n-1$ )-dimensions tangent plane on the point $z$ in the boundary $\partial R$ and can be represented as follows

$\mathrm{d}z=c_{1}\mathrm{d}z_{1}+c_{2}\mathrm{d}z_{2}+\cdots+c_{n-1}\mathrm{d}z_{n-$ 1}

where $\mathrm{rank}[z,c_{1},c_{2},\cdots,c_{n-1}]=n$ ; $\mathrm{d}z_{i}(i=1,2,\cdots,n-1)$ are the parametric variables described the ( $n-1$ )-dimensions tangent plane.

   The above theorem is a fundamental theorem for the volume computing, and should be presented and proven early. Which literature presented firstly the theorem can be found?