Page:IntroductionToMathematicsWhitehead.pdf/56

We have seen that the essence of motion is that a body was at ${\displaystyle A}$ and is now at ${\displaystyle C}$. This transference from ${\displaystyle A}$ to ${\displaystyle C}$ requires two distinct elements to be settled before it is completely determined, namely its magnitude (i.e. the length ${\displaystyle AC}$) and its direction. Now anything, like this transference, which is completely given by the determination of a

magnitude and a direction is called a vector. For example, a velocity requires for its definition the assignment of a magnitude and of a direction. It must be of so many miles per hour in such and such a direction. The existence and the independence of these two elements in the determination of a velocity are well illustrated by the action of the captain of a ship, who communicates with different subordinates respecting them: he tells the chief engineer the number of knots at which he is to steam, and the helmsman