The following is as given in Sir Thomas L. Heath's translation, which can be found in the book The Thirteen Books of The Elements, Vol. 1.

Book I | Book II | Book IX |
---|---|---|

Definitions, Postulates, and Common Notions | Definitions | Proposition 20 |

Proposition 1, Proposition 3, | Proposition 14 | Proposition 36 |

Proposition 5, Proposition 6, | ||

Proposition 29, Proposition 47 |

- A
**point**is that which has no part. - A
**line**is breadthless length. - The extremities of a line are points.
- A
**straight line**is a line which lies evenly with the points on itself. - A
**surface**is that which has length and breadth only. - The extremities of a surface are lines.
- A
**plane surface**is a surface which lies evenly with the straight lines on itself. - 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. - And when the lines containing the angle are straight, the angle is called
**rectilineal**. - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is
**right**, and the straight line standing on the other is called a**perpendicular**to that on which it stands. - An
**obtuse angle**is an angle greater than a right angle. - An
**acute angle**is an angle less than a right angle. - A
**boundary**is that which is an extremity of anything. - A
**figure**is that which is contained by any boundary or boundaries. - 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; - And the point is called the
**centre**of the circle. - A
**diameter**of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle. - A
**semicircle**is the figure contained by the diameter and the circumference cut off by it. And the centre of the semicircle is the same as that of the circle. **Rectilineal figures**are those which are contained by straight lines,**trilateral**figures being those contained by three,**quadrilateral**those contained by four, and**multilateral**those contained by more than four straight lines.- Of trilateral figures, an
**equilateral triangle**is that which has its three sides equal, an**isosceles triangle**that which has two of its sides alone equal, and a**scalene triangle**that which has its three sides unequal. - Of quadrilateral figures, a
**square**is that which is both equilateral and right-angled; an**oblong**that which is right-angled but not equilateral; a**rhombus**that which is equilateral but not right-angled; and a**rhomboid**that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called**trapezia**. **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.

Let the following be postulated:

- To draw a straight line from any point to any point.
- To produce a finite straight line continuously in a straight line.
- To describe a circle with any centre and distance.
- That all right angles are equal to one another.
- That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.