Definitions
Reference list for the basic terms used throughout Euclid’s Elements (Book I).
Showing 24 definitions.
Postulates →- 1
Point
A point is that which has no part.
- 2
Line
A line is breadthless length.
- 3
Extremities of a line
The ends of a line are points.
- 4
Straight line
A straight line is a line which lies evenly with the points on itself.
- 5
Surface
A surface is that which has length and breadth only.
- 6
Extremities of a surface
The edges of a surface are lines.
- 7
Plane surface
A plane surface is a surface which lies evenly with the straight lines on itself.
- 8
Plane angle
A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
- 9
Rectilinear angle
And when the lines containing the angle are straight, the angle is called rectilinear.
- 10
Right angle
When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is a right angle.
- 11
Obtuse angle
An obtuse angle is an angle greater than a right angle.
- 12
Acute angle
An acute angle is an angle less than a right angle.
- 13
Boundary
A boundary is that which is an extremity of anything.
- 14
Figure
A figure is that which is contained by any boundary or boundaries.
- 15
Circle
A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.
- 16
Center of the circle
And the point is called the center of the circle.
- 17
Diameter
A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle; and such a line also bisects the circle.
- 18
Semicircle
A semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle.
- 19
Rectilinear figures
Rectilinear figures are those which are contained by straight lines.
- 20
Trilateral / quadrilateral / multilateral
Trilateral figures are those contained by three straight lines, quadrilateral by four, and multilateral by more than four straight lines.
- 21
Equilateral / isosceles / scalene triangle
Of trilateral figures, an equilateral triangle has three equal sides, an isosceles triangle has two equal sides, and a scalene triangle has three unequal sides.
- 22
Right / obtuse / acute triangle
Further, of trilateral figures, a right-angled triangle has a right angle, an obtuse-angled triangle has an obtuse angle, and an acute-angled triangle has three acute angles.
- 23
Square / oblong / rhombus / rhomboid / trapezium
Of quadrilateral figures, a square is equilateral and right-angled; an oblong is right-angled but not equilateral; a rhombus is equilateral but not right-angled; a rhomboid has opposite sides equal and parallel but is neither equilateral nor right-angled; and a trapezium is a quadrilateral having no pair of sides parallel.
- 24
Parallel straight lines
Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.