http://www72.homepage.villanova.edu/alan.gluchoff/PASHoM/

Thursday, March 21, 2024 - 6:30pm to 8:00pm

Daniel Otero, PhD

Associate Professor, Mathematics

ABSTRACT: There are a handful of methods used to determine the integral of the secant function. We examine in this session what may be the earliest attempt to handle this challenging integral in the Lectiones Geometricae (1670) of Isaac Barrow (1630—1677). Barrow operated in the days when analysis of curves and their properties were pre-eminent in geometry, a generation before Newton successfully employed these ideas to describe a theory of gravitation and Leibniz clarified the relation between derivative and integral, and about 100 years before Euler recast the calculus as a collection of powerful and versatile techniques for their study. The diagram above comes from the Appendix to Lectio XII of the Lectiones Geometricae. In seventeenth-century geometric language, Barrow provides a derivation of what we would interpret today as the integral of the secant function. This talk will invite the audience into a reading of Barrow’s text (and a wrangling of the nest of curves in the figure above!) to clarify this interpretation.