IV - Analytical Geometry

Abstract

This chapter discusses the coordinates and polar coordinates in analytical geometry. It presents an assumption where a straight line l is divided by a point O of l in two half lines of which one can be called as the positive half line, and the other as the negative half line. Each point P of l not coinciding with O is determined by the distance OP, and by the half line on which P is lying. To avoid confusion, before the number representing the distance OP a plus sign can be written if P lies on the positive half line and a minus sign if P lies on the negative half line of l. The distance OP is determined if one choose on the positive half line a point E with the agreement that OE = 1. The coordinate determining the position of P is then equal to the quotient OP/OE. In this way, each point P of l has a real coordinate, and with each real number there corresponds in a one-to-one way a point P of l.