When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is *right,* and the straight line standing on the other is called a *perpendicular* to that on which it stands.

In the figure, the two angles The word orthogonal is frequently used in mathematics as a synonym for perpendicular. |

This is the first mention in the *Elements* of magnitudes being equal. There are several different kinds of magnitudes in the *Elements* besides angles. Lines, plane figures, and solids are also kinds of magnitudes. Some of the assumptions about magnitudes are stated later as common notions C.N., which are often called axioms. One thing that magnitudes of the same kind can be is “equal,” as the angles in this definition can be. Nowhere does Euclid explicitly state what it means for angles to be equal—or for that matter, for lines, plane figures, or solids to be equal—although much can be determined by the way he uses equality.