An immediate predecessor to Newton, Isaac Barrow’s chief contributions to the development of calculus were perhaps those connected with the theory of differentiation.

Isaac Barrow was born in London in 1630. A story is told that in his early school days he was so troublesome that his father was heard to pray that should God decide to take one of his children he could best spare Isaac. Barrow completed his education at Cambridge and won renown as one of the best Greek scholars of his day. He was a man of high academic caliber, achieving recognition in mathematics, physics, astronomy, and theology. Entertaining stories are told of his physical strength, bravery, ready wit, and scrupulous conscientiousness. He was the first to occupy the Lucasian chair at Cambridge, from which he magnanimously resigned in favor of his great pupil, Isaac Newton, whose remarkable abilities he (Barrow) was one of the first to recognize and acknowledge. He died in Cambridge in 1677.

Barrow’s most important work is his Lectiones opticae et geometricae, which appeared in the year he resigned his chair at Cambridge. The preface of the treatise acknowledges indebtedness to Newton for some of the material in the book, probably the parts dealing with optics. It is in this book that we find a very near approach to the modern process of differentiation, utilizing the so-called differential triangle that we find in our present day textbooks.