What I find most interesting about reading these short passages on Pythagoras is how little of what he did and thought seems to have passed into the semi-canonical knowledge we possess, especially considering the one bit that is taught to every middle school kid, the Pythagorean theorem. The observation I would make regarding this is that the piece of Pythagoras that survived is from the branch of Pythagorean thinking called mathemata, which seems to me to be analogous to more logical thought of modern times and less about religion. I was not aware of anything else Pythagoras thought, especially the idea of cyclical reincarnation.
In fact, this selection of passages does not go into much detail about the ideas of mathematics, but instead features moral and spiritual concepts. There are tales of his encounters with soul transference, from a supposed discovery of a friend's soul in an animal to the story of Pythagoras' own reincarnations. It is interesting to observe that, by Diogenes Laertius word, Pythagoras' soul inhabited many humans instead of animals, and that these humans were rather prominent figures. If the story were in Pythagoras' own writings instead of another person's, I would be inclined to suspect him of inflating his own story and status by creating a doctrine of his own wisdom that could not be struck down.
Perhaps the most philosophical concepts I drew from these passages were the ideas of searching for wisdom, which seems to be connected to reincarnation somehow, and a prototype arrangement of ideas, appearing as a dichotomy and as a conception of how to search for knowledge. The akousmata school of thinking, the counterpart to mathemata, is more concerned with moral acts and metaphysics. It observes what things are beyond mathematic observation and what moral behaviors we should observe. So I suppose my ending thought on Pythagoras is that I am glad there is more to him than right triangles.