513 DI BOOK I. Definitions. 'The two angles formed are then equal to each other. Thus, if the line DB is perpendicular to AC, the angle DBA will be equal to DBC. 21. When two lines are perpendicular to each other, the angles which they form are called right angles. Thus, DBA and DBC are called right angles. 22. An acute angle is less than a right angle. Thus, DBC is an acute angle. 23. An obtuse angle is greater than a right angle. Thus, DBC is an obtuse angle. 24. The circumference of a circle is a curve line all the points of which are equally distant from a certain point within called the centre. Thus, if all the points of the curve AEB are equally distant from the centre C, this curve will be the circumference of a circle. 25. Any portion of the circumference, as AED, is called an arc. 26. The diameter of a circle is a straight line passing through the centre and terminating at the circumference. Thus, ACB is a diameter. 27. One half of the circumference, as ACB is called a semicircumference; and one quarter of the circumference, as AC, is called a quadrant Definitions. 28. The circumference of a circle is used for the measure. ment of angles. For this purpose it is divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds are marked thus ° '"; and 9° 18′ 16", are read, 9 degrees 18 minutes and 16 seconds. 29. Let us suppose the circumference of a circle to be divided into 360 degrees, beginning at the p... B. If through the point of division CE, then, the angle kod 40, we draw will be equal to 40 degrees. If CF were drawn through 180 90 80 the point of division marked 80, the angle BCF would be equal to 80 degrees. OF LINES. 30. Two straight lines are said to be parallel, when being produced either way, as far as we please, they will not meet each other. 31. Two curves are said to be parallel or concentric, when they are the same distance from each other at every point. 32. Oblique lines are those which approach each other, and meet if sufficiently produced. 33. Lines which are parallel to the horizon, or to the water level, are called horizontal lines. 34. Lines which are perpendicular to the horizon, or to the water level, are called vertical lines. Definitions. OF PLANE FIGURES. 35. A Plane Figure is a portion of a plane terminated on all sides by lines, either straight or curved. 36. If the lines which bound a figure are straight, the space which they inclose is called a rectilineal figure, or polygon. The lines themselves, taken together, are called the perimeter of the polygon. Hence, the perimeter of a polygon is the sum of all its sides. 37. A polygon of three sides is called a triangle. 38. A polygon of four sides is called a quadrilateral. 39. A polygon of five sides is called a pentagon. 40. A polygon of six sides is called a hexagon. 41. A polygon of seven sides is called a heptagon. 42. A polygon of eight sides is called an octagon. Definitions. 43. A polygon of nine sides is called a nonagon. First. An equilateral triangle, which has its three sides all equal. Second. An isosceles triangle, which has two of its sides equal. Third. A scalene triangle, which has its three sides all unequal. Fourth. A right angled triangle, which has one right angle. In the right angled triangle ABC, the side AC, opposite the right angle, is called the hypothenuse. 47. The base of a triangle is the side on which it stands. Thus, AB is the base of the triangle ACB. The altitude of a triangle is a line drawn from the angle opposite the base and per-A D pendicular to the base. Thus, CD is the altitude of the tri angle ACB. Definitions. 48. There are three kinds of quadrilaterals. 1. The trapezium, which has none of its sides parallel. 2. The trapezoid, which has only two of its sides parallel. 3. The parallelogram, which has its opposite sides parallel. 49. There are four kinds of parallelograms: 1. The rhomboid, which has no right angle. 2. The rhombus, or lozenge, which is an equilateral rhomboid. 3. The rectangle, which is an equiangular parallelogram. 4. The square, which is both equilateral and equiangular. |