16. A Surface is that which has length and breadth without thickness.

17. A Plane is a surface such that if any two of its points be joined by a straight line, such line will be wholly in the surface. Every surface which is not a plane surface, or composed of plane surfaces, is a curved surface.

18. A Single Curved Surface is one in which only certain points may be joined by straight lines which shall lie wholly in its surface. The rounded surface of a cylinder or cone is a single curved surface.

Fig. 8. - An Equilateral Triangle

Fig. 9. - An Isosceles Triangle.

Fig. 10. - A Scalene Triangle.

Fig. 11. - Right-Angled Triangles.

19. A Double Curved Surface is one in which no two points can be joined by a straight line lying wholly in its surface. The surface of a sphere, for example, is a double curved surface.

20. A Plane Figure is a portion of a plane terminated on all sides by lines either straight or curved.

21. A Rectilinear Figure is a surface bounded by straight lines. (See Figs. 8, 16, 21, etc.)

22. Polygon is the general name applied to all rectilinear figures, but is commonly applied to those having more than four sides. A regular polygon is one in which the sides are equal.

23. A Triangle is a flat surface bounded by three straight lines. (Figs. 8, 9, 10, 11, 13, etc.)

24. An Equilateral Triangle is one in which the three sides are equal. (Fig. 8.)

25. An Isosceles Triangle is one in which two of the sides are equal. (Fig. 9.)

26. A Scalene Triangle is one in which the three sides are of different lengths. (Fig. 10.)

27. A Right-Angled Triangle is one in which one of the angles is a right angle. (Fig. 11.)

28. An Acute-Angled Triangle is one which has its three angles acute. (Fig. 12.)

29. An Obtuse-Angled Triangle is one which has an obtuse angle. (Fig 13.)

Fig. 12. - An Acute-Angled Triangle.

Fig. 13. - An Obtuse-Angled, Triangle.

Fig. 14. - Names of the Sides of a Right-Angled Triangle.

Fig. 15. - Names of the Parts of a Triangle.

30. A Hypothenuse is the longest side in a right-angled triangle, or the side opposite the right angle. A C, Fig. 14.

31. The Apex of a triangle is its upper extremity, as 15, Fig. 15. It is also called vertex.

32. The Base of a triangle is the line at the bottom. B C and A C, Figs. 14 and 15.

33. The Sides of a triangle are the including lines. A C, A B and B C, Figs. 14 and 15.

34. The Vertex is the point in any figure opposite to and furthest from the base. The vertex of an angle is the point in which the sides of the angle meet. B, Fig. 15.

35. The Altitude of a triangle is the length of a perpendicular let fall from its vertex to its base, as B D, Fig. 15,

36. A Quadrilateral figure is a surface bounded by four straight lines. There are three kinds of Quadrilaterals: The Trapezium, the Trapezoid and the Parallelogram.

37. The Trapezium has no two of its sides parallel.

(Fig. 16.)

38. The Trapezoid baa Only two of its sides parallel.

(Fig. 17.)

39. The Parallelogram has its opposite sides parallel. There are four varieties of parallelograms: The Rhomboid, the Rhombus, the Rectangle and the Square.

Fig. 16. - A Trapezium.

Fig. 17. - A trapezoid.

Fig. 22. - A Pentagon.

Fig. 2S. - A Hexagon.

Fig. 24. - A Heptagon.

Fig. 18. - A Rhomboid.

Fig. 19. - A Rhombus or Lozenge.

Fig. 25. - An Octagon.

Fig. 26. - A Decagon.

Fig. 27. - A Dodecagon.

Fig. 20. - An Equiangular Parallelogram Called a Rectangle.

Fig. 21. - An Equiangular and Equilateral Parallel ogram Called a Square.

Fig. 28. - Diagonals.

Fig. 29. - A Circle.

40. The Rhomboid has only the opposite sides equal, the length and width being different and its angles are not right angles. (Fig. 18.)

41. The Rhombus, Lozenge or diamond is a rhomboid all of whose sides are equal. (Fig. 19.)

42. The Rectangle is a parallelogram all of whose angles are right angles. (Fig. 20.)

43. The Square is an equilateral rectangle. (Fig. 21.)

44. A Pentagon is a plane figure of live sides. (Fig. 22.)

45. A Hexagon is a plane figure of six side.-(Fig. 23.)

46. A Heptagon is a plane figure of seven sides. (Fig. 24.)

47. An Octagon is a plane figure of eight sides. (Fig. 25.)

48. A Decagon is a plane figure of ten sides. (Fig. 26.)

49. A Dodecagon is a plane figure of twelve sides. (Fig. 27.)

50. The Perimeter is the line or lines hounding any figure, as A B C D E. Fig. 22.

51. A Diagonal is a straight line joining two opposite angles of a figure, as A B and C D, Fig. 28.