This chapter addresses four major aspects of the new probabilism of the seventeenth century: the 'prehistory' of seventeenth-century probabilistic notions; how and why the meaning of probability changed; origins and applications of mathematical probabilism; and meaning of probability. The first section deals with pre-seventeenth-century notions of chance, credibility, warranted belief, statistical frequencies, and probability. The second shows how Hugo Grotius, William Chillingworth, Marin Mersenne, and others responded to the Pyrrhonist challenge and, indirectly, to the controversy between Catholics and Protestants with a 'mitigated scepticism' that set new standards for rational belief and action. The third describes how the earliest formulations of mathematical probability came to be associated with the new reasonableness in the work of Blaise Pascal, Pierre Fermat, and Christiaan Huygens, and how this association influenced the applications of the fledgling mathematical theory. The final section examines the meaning of probability in Jakob Bernoulli's Ars conjectandi, and explains the link between probabilism and determinism.