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John Wallis, who was born in 1616, was one of the ablest and most original
mathematiclans of his day. He was a voluminous and erudite writer in a number
of fields and is said to have been one of the first to devise a system for teaching
deaf mutes. He was a student of Oughtred, and in 1649 he was appointed
Savilian professor of geometry at Oxford, a position he held for fifty-four years
until his death in 1703. He introduced series systematically in analysis, and his |
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Wallis was one of the first to discuss conics as curves of second degree rather than as sections of a cone. In 1655 appeared his Arithmetica infinitorun (dedicated to Oughtred)-a book that, in spite of some logical blemishes, remained a standard treatise for many years. His De algebra tractatus, historicus & practicus, written in 1673 but published in English in 1685 and in Latin in 1693, is considered a sthe first serious attempt at a history of mathematics in England. It is in this ork that we find the first recorded effort to give a graphic interpretation of the complex roots of a real quadratic equation. Wallis edited parts of the works of a number of the great Greek mathematicians and wrote on a wide variety of physical subjects. He was one of the founders of the Royal Society, and for years he assisted the government as a cryptoltgist. Whereas Wallis' chief contributions to the development of the calculus lay in the theory of integration, Isaac Barrow's most important contributions were perhaps those connedted with the theory of differentiation. Isaac Barrow was born in London in 1630. A story is told that in his eatly 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 who achieved recognition in mathematics, physics, astronomy, and theology. Entertaining stories are told of his physical strength, bravery, ready wit, and scrupulous conscientiousness. After serving for wou years as professor of geometry at Gresham College, London, he became, in 1644, the first to occupy the Lucasian chair at Cambridbe. In 1669, he resigned from his position at Camgridge to accept a call as chaplain to Charles II. The vacated lucasian chair was then, at Barrow's suggestion given to his young colleague Isaac Newton, whose remardable abilities he was one of the first to recognize and acknowledge. He died in Cambridge in 1677.
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Barrow's most important mathematical work is his Lectiones opticae et
geometricae, which appeared in the year he resigned his chair at Cambridge.
The preface of the treatise ackowledges indebtedness to Newton for some of
the material of 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 difrrerentiation, utilizing the so-called differential triangle that we find in our present-day textbooks. In spite of tenuous evidence pointing elsevhere,
Barrow is generally credited
as the first to realize in full generality that differentiation and integration
are inverse operations. |
This importat discovery in the so-called fundamental theorem of the calculus and appears to be stated and proved in Barrow's Lectiones.
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