10. An ANGLE is the inclination of two lines which meet

at a point.

The point of meeting, B, is called the vertex, and the lines A B, B C, the sides of the angle.

B

A

An angle is sometimes designated by the letter at its vertex, as the angle B; but when a number of angles have the same vertex, each angle is designated by three letters, the middle letter showing the vertex, and the other two, with the middle letter, the sides; as the angle A B C.

11. If a straight line meets another straight line, so as to make the angles equal to each other, each of these angles is called a right angle; and the two lines are said to be perpendicular to each other. Thus, ACD and D C B are right angles, and AB and CD are perpendicular to each other.

12. An ACUTE ANGLE is less than a right angle; as BDE.

13. An OBTUSE ANGLE is greater than a right angle; as ADE.

D

-B

E

A

B

D

15. A PLANE FIGURE is a plane surface bounded by lines either straight or curved.

16. When the boundary lines are straight, the figure is called a polygon.

17. Of Polygons, the simplest has three sides, and is called a triangle; one of four sides is called a quadrilateral; one of five, a pentagon; one of six, a hexagon; one of seven, a heptagon; one of eight, an octagon; one of ten, a decagon;

18. An EQUILATERAL TRIANGLE is one whose sides are all equal; as A B C.

19. An IsosCELES TRIANGLE is one which has two of its sides equal; as D E F.

20. A SCALENE TRIANGLE is one which has its three sides unequal; as GHI.

21. A RIGHT-ANGLED TRIANGLE is one which has a right angle; as J K L.

The side opposite the right angle is called the hypothenuse, and the other two sides the legs, or the base and perpendicular.

22. An OBTUSE-ANGLED TRIANGLE is one which has an obtuse angle; as M NO.

23. An ACUTE-ANGLED TRIANGLE is one which has all its

angles acute; as A B C.

Acute and obtuse-angled triangles are called obliqueangled triangles.

The sum of all the angles of a triangle is equal to two right angles therefore a triangle can have but one right angle, or but one obtuse angle; and the sum of the two acute angles of a right-angled triangle is equal to a right

24. A PARALLELOGRAM is a quadrilateral whose opposite sides are parallel; as A B CD, or EFG H, or I J K L, or MNO P.

25. A RECTANGLE is a parallelogram whose angles are right angles; as A B C D.

26. A SQUARE is a rectangle whose sides. are equal; as E F G H.

27. A RHOMBOID is a parallelogram whose angles are not right angles; as I J K L.

28. A RHOMBUS is a rhomboid whose

sides are equal; as M N O P.

29. A TRAPEZOID is a quadrilateral which has only two of its sides parallel; as Q R S T.

30. A TRAPEZIUM is a quadrilateral which has none of its sides parallel; as UV WX.

31. A DIAGONAL is a line joining the vertices of two opposite angles; as UW.

32. The side upon which a triangle or quadrilateral is supposed to stand is called the base; and the perpendicular

triangle or quadrilateral Thus, IJ is the base and LY the altitude of I J K L.

33. A CIRCLE is a plane bounded by a curved line, called the circumference, every point of which is equally distant from a point within, called the B centre; as A B D E. The circumference of every circle is supposed to be divided into 360 equal parts, called degrees (°), each degree into 60 equal

A

E

parts, called minutes ('), and each minute into 60 equal parts, called seconds (").

34. The RADIUS of a circle is a line drawn from the centre to the circumference; as C B.

All radii of the same circle are equal.

35. The DIAMETER of a circle is a line drawn through the centre and terminating at both ends in the circumference; as AD. It divides the circle into two equal parts, called semicircles.

36. An ARC of a circle is any part of the circumference; as A FE.

37. A CHORD is the straight line joining the ends of an arc; as A E.

38. A SEGMENT of a circle is the part of the circle cut off by a chord; as the space included by the arc A FE and the chord A E.

39. A SECTOR of a circle is the part of the circle included by two radii; as the space A B C.

NOTE.

-The sum of all the angles of a triangle is equal to 180°. Hence the sum of the two acute angles of a right-angled triangle is equal to 90°.

CHAPTER III.

INSTRUMENTS USED IN DRAWING. L

PROBLEMS.

GEOMETRICAL

12. The only instruments for drawing required in commón Surveying are the dividers and the rule.

The dividers are too well known to require a description. They should always be made with a screw passing through the joint, so that they can be tightened at pleasure.

The rule includes the two instruments commonly described in text-books under the titles of the plane scale and the protractor. It is about six inches in length.

The section of the rule presented above contains the plane scale, or the diagonal scale of equal parts. The sides of the square (half-inch) at the right have each been divided into ten equal parts; from the first point of division at the top, a line has been drawn to the second point at the bottom; from the second at the top, to the third at the bottom, and so on. From right to left have been drawn parallel lines through the points of division of the square. The lines passing from any point of division at the top to the bottom are one tenth of one of the small divisions farther to the right, as they cross any line, than where they crossed the preceding line. So that, if the half-inch which is divided be considered unity, each of the small divisions will be .1, and each of the oblique division lines will be .01 farther to the right on any horizontal line than on the one