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.
Next definition: I.Def.11-12