# Definition:Inclination

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## Definition

### Straight Line to Plane

In the words of Euclid:

*The***inclination of a straight line to a plane**is, assuming a perpendicular drawn from the extremity of the straight line which is elevated above the plane to the plane, and a straight line joined from the point thus arising to the extremity of the straight line which is in the plane, the angle contained by the straight line so drawn and the straight line standing up.

(*The Elements*: Book $\text{XI}$: Definition $5$)

### Plane to Plane

In the words of Euclid:

*The***inclination of a plane to a plane**is the acute angle contained by the straight lines drawn at right angles to the common section at the same point, one in each of the planes.

(*The Elements*: Book $\text{XI}$: Definition $6$)

## Also defined as

The word **inclination** is also used for the angular coordinate of a point expressed in polar coordinates.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**inclination**:**1.**