In a generalized form, the cortical magnification theory of peripheral vision predicts that the thresholds of any visual stimuli are similar across the whole visual field if the cortical stimulus representations calculated by means of the cortical magnification factor are similar independently of eccentricity. Failures of the theory in spatial vision were analyzed, and the theory was tested with five visual acuity tasks and two hyperacuity tasks. Almost all increases in thresholds with eccentricity were explained by the theory in five of these tasks, which included the two-dot vernier hyperacuity test, the measurement of visual acuities with gratings, the Snellen E test, and two acuity tests that required either separation between dots or discrimination between two mirror-symmetric forms. The two-dot vernier thresholds could be explained as a special case of orientation discrimination, and orientation discrimination at different eccentricities was in agreement with the cortical magnification theory. The increase of thresholds in peripheral vision was larger than predicted by the theory in the Landolt visual acuity and bisection hyperacuity tests, possibly because of retinal undersampling.