Taking any number n to be represented by a point on a line at distance nL from a **fixed point** 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.

If a point be in motion in any orbit and with any velocity, and if, at each instant, a line be drawn from a **fixed point** parallel and equal to the velocity of the moving point at that instant, the extremities of these lines will lie on a curve called the hodograph.

The C.P. of water lines passing through a **fixed point** lies on a straight line, the antipolar of the point; and thus the core of a triangle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the diagonals of which are the middle third of the median lines.

There can be no exact computation of time or placing of events without a **fixed point** or epoch from which the reckoning takes its start.

In the history of Babylonia, the **fixed point** from which time was reckoned was the era of Nabonassar, 747 B.C. Among the Greeks the reckoning was by Olympiads, the point of departure being the year in which Coroebus was victor in the Olympic Games, 776 B.C. The Roman chronology started from the foundation of the city, the year of which, however, was variously given by different authors.