Trees in tropical forests are very high, and if monkey were about to fall down, chances are good he/she couldn't survive 30 meter fall. Bu there is this amazing ability that monkeys have that enables them tree-swaying and moving through the trees in search for food.
Smaller monkeys like chimpanzees use flexing of their limbs to bring their body closer to the branch, so they do not miss it, while larger monkeys like orangutans have developed a special way to move through the trees, they move in an irregular way which includes upright walking, four-limbed suspension from branches and tree-swaying, they use highly sophisticated method of moving branches backwards and forwards, with increasing magnitude, until they are able to cross large gaps between trees.
I wonder what style had Tarzan used? Orangutan or chimpanzee? Since he's kind a big compared to chimpanzees I would say orangutan style.