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Substituting the co-ordinates of Q in the equation of the curve and neglecting the squares and higher powers of e and a as compared with their first powers he obtained e : a. But if a be an infinitesimal quantity a2 must be infinitely smaller and therefore may be neglected when compared with the quantities 2ay and pe. In 1662 he was made professor of geometry at Gresham College and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge.

His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's and Newton went on to develop calculus in a modern form. Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular for the discovery of the fundamental theorem of calculus.