The Surveyor in Foure Bookes

If a right line (straight line) falls on a right line, making the angles on either side equal, each of those angles are called right angles: And the line erected is called a perpendicular line unto the other.

Euclid, Book 1, Def. 10.

As in general there are three sorts of angles in respect of their lines, as aforesaid, so in particular, of right-lined angles there are three sorts in respect of their quantities: namely, an orthogonal or right angle; an obtuse or blunt angle; and an acute or sharp angle. According to this definition, the line A-B falling on the line C-D and making the angles on either side equal—namely, the angle A-B-C on the one side equal to the angle A-B-D on the other side—those two angles are called right angles. And the line A-B erected on C-D without inclination to either side is called a perpendicular or plumb line. And here note further, that usually an angle is described by three letters, of which the second or middle letter always represents the angle intended.

A geometric diagram showing a vertical line segment AB meeting a horizontal line segment CD at point B. Line AB is perpendicular to CD, creating two right angles labeled at points C, B, and D.

An angle which is greater than a right angle is an obtuse angle.

Euclid, Book 1, Def. 11.

Every angle in general (not being a right angle), whether greater or lesser, is called an oblique angle; but particularly, if greater than a right angle, it is called an obtuse angle; if lesser, an acute angle. As the angle B-D-C (being greater than the right angle A-D-C) is an obtuse angle; for it contains it, and also the angle A-D-B.

A geometric diagram illustrating different angles. A horizontal line segment CE has a vertical line AD meeting it at point D. A third line segment BD originates from point D and slants to the right, creating an obtuse angle BDC and an acute angle ADB.

An acute angle is that which is less than a right angle.

Euclid, Book 1, Def. 12.

This definition is manifest by the former diagram, wherein the angle A-D-B is an acute angle, being less than the right angle A-D-E; for the same right angle contains it, and also the angle B-D-E, which is likewise an acute angle.