Machiavelli’s advice for the prince(s) is multifaceted but the undercurrent remains stable: to do what is expedient for the state even if it requires resorting to evil practices, cruelty, and deceit. Machiavelli has no compunctions about recommending that the new prince destroy the old prince and his entire family in order to eliminate the possibility of insurrection from the old regime. Even though Machiavelli urges violence when necessary, he also tempers his advice to include prudence on the part of the prince so that the injuries inflicted can raise no possibility of vengeance.
Hobbes's determination to avoid the "insignificant" (that is, meaningless) speech of the scholastics also overlaps with his admiration for the emerging physical sciences and for geometry. His admiration is not so much for the emerging method of experimental science, but rather for deductive science - science that deduces the workings of things from basic first principles and from true definitions of the basic elements. Hobbes therefore approves a mechanistic view of science and knowledge, one that models itself very much on the clarity and deductive power exhibited in proofs in geometry. It is fair to say that this a priori account of science has found little favor after Hobbes's time. It looks rather like a dead-end on the way to the modern idea of science based on patient observation, theory-building and experiment. Nonetheless, it certainly provided Hobbes with a method that he follows in setting out his ideas about human nature and politics. As presented in Leviathan , especially, Hobbes seems to build from first elements of human perception and reasoning, up to a picture of human motivation and action, to a deduction of the possible forms of political relations and their relative desirability. Once more, it can be disputed whether this method is significant in shaping those ideas, or merely provides Hobbes with a distinctive way of presenting them.