1: A point is that which has no parts.


2: A line is length without breadth.


3: The extremities of a line are points.


4: A straight or right line is that which lies evenly between its extremities.


5: A surface is that which has length and breadth only.


6: The extremities of a surface are lines.


7: A plane surface is that which lies evenly between its extremities.


8: A plane angle is the inclination of two lines to one another, in a plane, which meet together, but are not in the same direction.


9: A plane rectilinear angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.


10: 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.


11: An obtuse angle is an angle greater than a right angle.


12: An acute angle is less than a right angle.


13: A boundary is that which is an extremity of anything.


14: A figure is that which is contained by any boundary of boundaries.


15: A circle is a plane figure contained by one line such that all the straight lines falling from one point among those lying within the figure are equal to one another.


16: This point (from which the equal lines are drawn) is called the centre of the circle.


17: A diameter of a circle is a straight line drawn through the centre, terminated both ways in the circumference.


18: A semicircle is the figure contained by the diameter, and the part of the circle cut off by the diameter.


19: Rectilineal figures are those which are contained by straight lines: trilateral figures (triangles) being those contained by three; quadrilateral, those contained by four; and multilateral, those contained by more than four straight lines.


20: Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle, that which has two of its sides equal, and a scalene triangle, that which has its three sides unequal.


21: Further, of trilateral figures, a right-angled triangle is that which has a right angle, and obtuse-angled triangle is that which has an obtuse angle, and an acute-angled triangle is that which has its three angles acute.


22: Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong is that which is right-angled but not equilateral; a rhombus is that which is equilateral but not right-angled; and a rhomboid is that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilateral other than these be called trapezia.


23: 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.