In one realization of brane-worlds, the visible universe, i.e., the brane, is located on the boundary of a single (4+1)-dimensional region, namely, the bulk. This bulk in its simplest implementation is a five dimensional Anti-de Sitter space (AdS_5). Cosmology then can be defined on the brane by many different approaches and the modified FRW evolutions are derived. It is, however, interesting to re-examine the FRW equations by embedding the brane+bulk system into Euclidean M(2,4) spacetime. Here, I first look at Einstein's equations on the brane and next in the bulk to establish connections between the radius of this six dimensional Euclidean spacetime and the cosmological constant in the bulk. Shapes of the singularities can be achieved for each of the cosmologies on the brane. Finally, I argue that by looking at the behavior of the brane in six dimensions one finds many shortcuts in calculations and visualizing the concepts related to brane-worlds.