Euclid's Elements Book I — Definitions 1–23

Definitions (Foundation Layer)

First appearance links to the proposition where each term is first used.

1. Point — that which has no part. First: Prop I.1
2. Line — breadthless length. First: Prop I.1
3. Ends of a line are points. First: Prop I.1
4. Straight line — lies evenly with points on itself. First: Prop I.1
5. Surface — length and breadth only. First: Prop I.1
6. Edges of a surface are lines. First: Prop I.1
7. Plane surface — lies evenly with straight lines. First: Prop I.1
8. Plane angle — inclination of two meeting lines. First: Prop I.9
9. Rectilinear angle — lines are straight. First: Prop I.9
10. Right angle, perpendicular — when a straight line standing on another makes adjacent angles equal. First: Prop I.11
11. Obtuse angle — greater than a right angle. First: Prop I.12
12. Acute angle — less than a right angle. First: Prop I.12
13. Boundary — extremity of anything. First: Prop I.1
14. Figure — contained by boundary or boundaries. First: Prop I.1
15. Circle — plane figure, equal lines from center. First: Prop I.1
16. Center of the circle. First: Prop I.1
17. Diameter — straight line through center to circumference. First: Prop I.1
18. Semicircle — figure contained by diameter and circumference. First: Prop I.31
19. Rectilinear figures — trilateral, quadrilateral, multilateral. First: Prop I.1
20. Triangles — equilateral, isosceles, scalene. First: Prop I.1
21. Triangles — right-, obtuse-, acute-angled. First: Prop I.1
22. Quadrilaterals — square, oblong, rhombus, rhomboid, trapezia. First: Prop I.34
23. Parallel straight lines — do not meet in either direction. First: Prop I.27