A characteristic hallmark of medieval astronomy is the replacement of Ptolemy’s linear precession with so-called models of trepidation, which were deemed necessary to account for divergences between parameters and data transmitted by Ptolemy and those found by later astronomers. Trepidation is commonly thought to have dominated European astronomy from the twelfth century to the Copernican Revolution, meeting its demise only in the last quarter of the sixteenth century thanks to the observational work of Tycho Brahe. The present article seeks to (...) challenge this picture by surveying the extent to which Latin astronomers of the late Middle Ages expressed criticisms of trepidation models or rejected their validity in favour of linear precession. It argues that a readiness to abandon trepidation was more widespread prior to Brahe than hitherto realized and that it frequently came as the result of empirical considerations. This critical attitude towards trepidation reached an early culmination point with the work of Agostino Ricci, who demonstrated the theory’s redundancy with a penetrating analysis of the role of observational error in Ptolemy’s Almagest. (shrink)