1. A point is that which is without parts. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A right line, is that which lies evenly between its extremities.

5. A superficies, is that which has only A length and breadth.

6. The boundings of a superficies are lines.

7. A plane superficies, is that which lies evenly between its extreme right lines.

8. A rectilineal angle, is the inclination

of two right lines to each other, which touch, but do not form one straight line.

An angle is designated either by one letter at the vertex; or three, of which the middle one is at the vertex, the remaining two any place on the legs.

A

B

9. The legs of an angle, are the lines which make the angle.

10. The vertex of an angle is the point in which the legs mutually touch each other.

B

11. When a right line standing on a right line makes the adjacent angles equal, which are ABC and ABD, each of these angles is equal to a right angle, and the right line AB standing on the other, is called the perpendicular.

12. The angle ABC, which is greater than a right angle, is called obtuse.

13. The angle A B D, which is less than a right angle, is called acute.

14. A plane figure is a plane superficies, bounded on every side by one or more lines.

15. A circle is a plane figure, contained by one line, which is called the circumference; to which from a certain point within the figure, all right lines drawn are equal.

16. That point is called the centre of the circle.

17. A diameter of a circle is a right line drawn through the centre, and both of its extremities terminate in the circumference.

18. A radius is a right line drawn from the centre to the circumference.

19. A semicircle, is the figure which is contained by the diameter and the part of the circumference which the diameter cuts off.

20. A rectilineal figure, is a plane superficies contained by right lines.

21. A triangle is a plane superficies, which is contained by three right lines.

22. An equilateral triangle is that which has three sides equal.

23. Anisosceles triangle (or æquicrurum) is that which hath two equal sides.

ΔΔΔ

24. A scalene triangle, is that which hath three unequal sides.

25. A right angled triangle is that which has a right angle.

26. An obtuse angled

triangle is that which hath an obtuse angle.

27. An acute angled triangle is that which hath three acute angles.

28. Parallel right lines, are those which are in the same plane, and although produced, never meet.

29. A quadrilateral figure,

is a rectilineal figure which is contained by four right lines.

30. A parallelogram, is a quadrilateral figure, whose opposite sides are parallel.

31. A square is a quadrilateral, which is equilateral and equiangular.

32. Rectilineal figures which have more than four sides, are called polygons.

POSTULATES.

1. Let it be granted that a right line can be drawn from any point to another.

2. That a terminated right line can be produced to any distance.

3. That a circle can be described from any centre, with any radius.

COMMON NOTIONS, OR AXIOMS.

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

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

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