# Definition:Vertical

## Definition

### Vertical Line

A line is **vertical** if and only if it is parallel to the path taken by a body released from rest in a constant gravitational field.

Hence the adjective **vertically**, meaning **in a vertical line**.

### Vertical Plane

A plane is **vertical** if and only if it contains a vertical line.

## Terminology

The term **the vertical** is frequently seen, particularly in the context of specifying the spatial orientation of a given (straight) line: the angle it makes to **the vertical**.

It needs to be borne in mind that the terms **vertical** and **horizontal** are meaningful only in the context of an environment with a gravitational field, and therefore one where **up** and **down** have a meaning.

In the context of the presentation of mathematical graphics on, for example, a piece of paper arranged horizontally, **the vertical** is that direction **towards and away from** the reader. Thus such a direction *would* be *actually* vertical if that paper were held in a vertical plane oriented for normal reading.

Computer screens are, in normal usage and to a first approximation, vertical planes already, so on such a medium, the terms are literal.

It is of course noted that it is difficult at this level to define **vertical** and **horizontal** without the definitions at some point becoming circular. An appeal to an intuitive understanding is therefore necessary to a certain extent.