The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes overstatus of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its...