La Géométrie

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La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on Method), written by René Descartes. Descartes was in his own time, and has been since, recognized as a Great Thinker. In the Discourse, he presents his method for obtaining clarity on any subject. La Geometrie and two other appendices also by Descartes, the Optics and the Meteorology, were published with the Discourse to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, within the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience).

The work was responsible for introducing the Cartesian coordinate system, which is a mathematical graph in which x is the horizontal line and y is the vertical line, and in which the positive numbers on the x line are on the right and the negative numbers on the left, and the positive numbers on the y line are on the top and the negative numbers are on the bottom, and specifically discussed the representation of points of a plane, via real numbers; and the representation of curves, via equations. The work was also the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry, which means reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was pretty ground-breaking given that algebra and geometry were considered completely separate branches of mathematics with no connection to one another. It also contributed to the mathematical ideas of Leibniz and Newton and thus was important in the development of calculus.