ELEMENTS, Book 1.

...makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing upon the other is called a perpendicular to that on which it stands. Definition 10 concludes here. A perpendicular line is defined by the equality of the angles it creates on both sides.

11. An obtuse angle is an angle greater than a right angle. original: "Ambleia gōnia." An angle wider than 90 degrees.
5 12. An acute angle is an angle less than a right angle. original: "Oxeia gōnia." An angle narrower than 90 degrees.
13. A boundary is that which is an extremity of anything. original: "Horos." This term can mean a limit, a definition, or a border.
14. A figure is that which is enclosed by one or more boundaries.
15. A circle is a plane figure enclosed by a single line 10 [which is called the circumference], such that all straight lines falling upon it from a single point among those lying within the figure [to the circumference of the circle] are equal to one another. Euclid defines the circle by the equidistance of its points from a central source.
16. This point is called the center of the circle.
15 17. A diameter of the circle is any straight line drawn through the center and ended in both directions by the circumference of the circle: such a line also divides the circle in half. The property of bisecting the circle is essential to Euclid's later proofs.
18. A semicircle is the figure enclosed by the diameter and the [circumference] cut off by 20 it...

11. Hero, Definition 21. Ammonius, On the Categories, page 58. Psellus, page 36. Martianus Capella, Book 6, section 710. Boethius, page 374, line 18. 12. Hero, Definition 20. Ammonius, in the place cited. Psellus, in the place cited. Martianus Capella, in the place cited. Boethius, page 374, line 19. 13. Philoponus, On Aristotle's On the Soul, folio a 2. Martianus Capella, Book 6, section 710. Boethius, page 374, line 22. 14. Hero, Definition 25. Scholia on Hermogenes, Volume 7, part 2, page 903. Compare Philoponus on Aristotle's On the Soul, section 7. Martianus Capella, Book 6, section 710. Boethius, page 374, line 21. 15. Hero, Definition 29. Taurus in Philoponus, Against Proclus, Book 6, section 21. Sextus Empiricus, page 719, line 16. Philoponus, On the Prior Analytics, Book 2, folio 28 verso; also compare folio 4 verso, 9 verso, 29 recto, 53 recto. Psellus, page 38. Martianus Capella, Book 6, section 710. Boethius, page 375, line 3. 16. Psellus, page 38. Martianus Capella, Book 6, section 711. Boethius, page 375, line 6. 17. Hero, Definition 30. Psellus, page 38. Martianus Capella, Book 6, section 711. Boethius, page 375, line 7. 18. Hero, Definition 31. Martianus Capella, Book 6, section 711. Boethius, page 375, line 12.