1. A point, is that which has position, but not magnitude. 2. A right line is the shortest that can be drawn between any two points, and the shortest distance from A to B. 3. Parallel lines are at the same distance from each other at every point; they can never meet: CD. 4. A wave line is used in the construction of maps, &c.: E F. 5. A curve line is one which changes its direction at every point: GH. 6. Two curve lines are parallel, when they are at the same distance from each other; they will not meet each other: O P. 7. Oblique lines are those which approach each other, and if prolonged will meet. Fig. 5. H Fig. 6. Fig. 7. Horizontal lines are parallel to the horizon, or to the water 8. An angle is the opening, or inclination of two lines which meet each other in a point, as the lines A C, A B, form an angle at the point A. The lines A C and A B are A Fig. 8. B the sides of the angle, and their intersection, A, the vertex, or angle A. 9. A perpendicular is when a straight line meets another straight line, and makes the angles, or both sides of it, equal to each other. The angle formed by the base and perpendicular is a right angle, and contains 90°, or one-fourth of a great circle of the earth. 360÷4=90.j The base of a figure is the side on which it stands. 10. An acute angle is less than a right angle; the point of intersection is called the angular point, which may be greater or less, according as they are more or less inclined or opened. 11. An obtuse angle is greater than a right Fig. 9. 90 Right Angle. Fig. 10. Acute Angle. Fig. 11. angle. 12. An equilateral triangle has three sides, all equal. 13. An isosceles triangle has only two of its sides equal. Obtuse Angle. Fig. 12. Fig. 13. 17. A circle is a plain figure, formed by the revolution of a right line about one of its extremities, which remains fixed. It is sometimes called the circumference. Fig. 17. 18. The radius of a circle is a straight line drawn from the centre to any part of the circumference. Fig. 18. diam rad seg chord The diameter of a circle is a right line passing through the centre, terminated both ways by the circumference. An arc of a circle is any part of its periphery, or circumference. A chord is a right line joining the extremities of an arc. cen quad A segment of a circle is any part of a circle bounded by an arc and its chord. A quadrant is a quarter of a circle. 19. A sector is any part of a circle bounded by an arc, and its two radii drawn to its extremities. A semicircle is one-half of a circle. Fig. 19. sec semi 20. The versed sine or height of an arc, is that part of the diameter contained between the middle of the chord and the arc, as D B=D E. 21. A zone is a part of a circle included between two parallel chords, and their intercepted arcs. Zone. SECTION 3.-PLANE FIGURES. A plane figure is a part of a plane, terminated on all sides by lines, either straight or curved. If the bounding lines are straight, the space they enclose is called a rectilineal figure, or polygon. 22. A polygon of three sides is called a triangle. Fig. 22. 23. A polygon of four sides is called a quadrilateral. Fig. 23. Fig. 24. 24. A polygon of five sides is called a pentagon. A polygon of six sides is called a hexagon. A polygon of twelve sides is called a dodecagon. The lines of a polygon, taken together, are called the perimeter of the polygon. The perimeter of a polygon is the sum of all its sides. An equilateral polygon is one which has all its sides equal. An equiangular polygon is one which has all its angles equal. All polygons are either regular or irregular polygons. QUADRILATERALS. 25. A square is a quadrilateral, whose sides are all equal, and its angles all right angles. All plain figures bounded by four right lines, are called quadrangles, or quadrilateral. 26. A rectangle has its angles right angles, and its opposite sides equal and parallel: called also an "oblong square." 27. A parallelogram has its opposite sides parallel, but its angles not right angles. Fig. 26. Fig. 27. Fig. 25. Fig. 28. angled. 28. A lozenge has its sides equal, but is not right |