or l'Hospital's rule, n. a rule permitting the evaluation of the limit of an indeterminate quotient of functions as the quotient of the limits of their derivatives. For example, is an indeterminate of the form 0/0, but it can be evaluated as (Named after the French analyst and geometer, Guillaume François Antoine de l'Hôpital, Marquis de St Mesme (1661-1704), who was the author of the first textbook on differential calculus, but is believed to have bought the rights to this rule from its discoverer.)