(1+y'2)dx
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Little is known of van Heuraet's life, all that is known that he was at Saumur, a town on the river Loire in western France, in 1658.
Van Schooten had established a vigorous research school in Leiden which included van Heuraet, and this school was one of the main reasons for the rapid development of Cartesian geometry in the mid 17th century.
Van Schooten edited and published a Latin translation of Descartes's La Géométrie in 1649. A second two-volume translation of the same work (1659-1661) contained appendices by de Witt, Hudde and van Heuraet.
In van Heuraet's only publication he effectively computes the integral
and applies his methods to the parabola. His methods of rectification of curves became part of a more general theory by Fermat which was produced independently and at about the same time.
Article by: J J O'Connor and E F Robertson
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JOC/EFR December 1996
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