**Definitions**

1. A point is that which has no part.

2. A line is breadthless length.

3. The extremities of a line are points.

4. A straight line is a line which lies evenly with the
points on itself.

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

6. The extremities of a surface are lines

7. A plane surface is a surface which lies evenly with
the straight lines on itself.

8. 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. And when the lines containing the angle are straight,
the angle is called rectilineal.

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 an angle 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 or
boundaries.

15. 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. And the point is called the centre of the circle.

17. 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.

18. 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.

19. 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.

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 alone 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, an obtuse-angled triangle that which
has an obtuse angle, and an acute angled triangle that which has its three
angles acute.

22. 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.

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.

**Postulates.**

Let the following be
postulated:

1. To draw a straight line
from any point to any point.

2. To produce a finite
straight line continuously in a straight
line.

3. To describe a circle with
any centre and distance.

4. That all right angles are
equal to one another.

5. 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.

**Common Notions**

1. Things which are equal to
the same thing are also equal to one
another.

2. If equals be added to
equals, the wholes are equal.

3. If equals be subtracted from
equals, the remainders are equal.

4. Things which coincide with
one another are equal to one another.

5. The whole is greater than
the part.

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