The Geometrical Lectures of Isaac Barrow (Phoenix Edition)

The culmination of all the seventeenth-century geometrical investigations that led to the development of the calculus, these lectures by Newton's teacher offer a systematic and detailed treatment of tangents, arcs, areas, and related subjects. Isaac Barrow (1630-1677) was the first to occupy the Lucasian chair at Cambridge — which he later resigned to Newton, whose superior abilities he readily acknowledged. This volume, published as Lectiones Geometricae, contains the important work on tangents that formed the starting point of Newton's work on the calculus.
A skillful geometer, Barrow gave little attention to analytical procedure or problem solving. He stated the main aims of these lectures as the investigation of tangents without the bother of calculation and the quick determination of the dimensions of many magnitudes by means of their tangents. In addition to their introduction of innovative methods, Barrow's lectures also integrate the concepts of time and motion with those of space suggested by Torricelli, Galileo, and Roberval. This edition of the classic work was translated, with notes and proofs, by J. M. Child.