'No-force' condition and BPS combinations of p-branes in 11 and 10 dimensions

The condition of vanishing of the static force on a q-brane probe in the gravitational background produced by another p-brane is used to give a simple derivation of the pair-wise intersection rules which govern the construction of BPS combinations of branes. These rules, while implied also by supersymmetry considerations, thus have a purely bosonic origin. Imposing the no-force requirement makes it possible to add branes 'one by one' to construct composite BPS configurations (with zero binding energy) of 2-branes and 5-branes in D = 11 and of various p-branes in D = 10. The advantage of this elementary approach is its universality, i.e. the cases of different dimensions and different types of branes (e.g., NS-NS, R-R and 'mixed' combinations of NS-NS and R-R branes in D = 10) are all treated in the same way.