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1637 René Descartes published Discours de la Methode containing three books or appendices on geometry. In pages 319 through 322, for example, Descartes investigated a problem involving point C on a curve. He stated, "pourceque CB & BA font deux quantites indeterminees & inconnues, ie les nomme l'vne y & l'autre x." Thus he located C by x and y coordinates. The Cartesian coordinate system, now studied in high school, is named for Descartes. An English translation of the work is available from Dover; ISBN 0-486-60068-8.
1858 In Plane Metallic Surfaces, Longman, Brown, and Co., Joseph Whitworth described an algorithm for creating a flat surface, an ingredient of the Cartesian coordinate system.
1970 In Foundations of Mechanical Accuracy, Moore Special Tool Co., Wayne R. Moore described an implementation of Whitworth's algorithm.
A study of Category Theory is the current activity in this work.