This chapter focuses on the Cartesian coordinate system and how it provides a link between geometry and algebra. In Geometria, René Descartes introduced a new idea for notation, a rule: beginning letters of the alphabet were to be reserved for fixed known quantities and letters from p onward were to represent variables or unknowns that could take on a succession of values. To this day, this division of the alphabet at p remains the loose standard rule. The chapter also considers the Pythagorean theorem as a way of finding the distance between any two points in space; how the algebraic operations of addition, subtraction, multiplication, division, and extraction of a square root could actually be performed; and who came up with the idea of the vinculum.
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