Karl Pearson's seminal article on the criterion is reviewed, formalized in modern notation and its method is extended beyond the normal distributions using the Mahalanobis distance as a vehicle. The extension yields a simple method, firmly rooted in history, for computing exact p-values and acceptance regions for hypotheses under a large class of probability distributions and of arbitrary dimension. As a by-product it is for example shown that the so-called method of acceptance intervals by percentiles is a univariate special case of Pearson's method. The article's content is discussed in context of other sources, in particular Pearson's The Grammar of Science, yielding a holistic approach to verification/falisfication of hypotheses through empirical observation.