13. An angle which is greater than a right angle, is called. an obtufe angle. Plate 1. fig. 5. 14. A figure is that which is inclosed by one or more boundaries. 15. A triangle is bounded by three fstraight lines. 16. Quadrilateral figures are bounded by four straight lines. 17. Polygons are bounded by more than four ftraight lines. 18. An equilateral triangle is that which has all its fides equal. Plate 1. fig. 6. 19. An ifofceles triangle is that which has two of its fides. equal. Plate 1. fig. 7. 20. A fcalene triangle is that whofe fides are all unequal. Plate 1. fig. 8. 21. A right-angled triangle is that which has one right angle. Plate 1. fig. 9. 22. The longest fide of a right-angled triangle is called the hypothenuse. 23. An acute angled triangle is that whofe angles are all aPlate 1. fig. 10. cute. 24. An obtufe angled triangle is that which has one obtufe angle. See plate 1. fig. 11. 25. A quare is a figure whofe fides are equal, and all its angles right angles. See plate 1. fig. 12. 26. An oblong is that whofe parallel fides only are equal, and all its angles right angles. Plate 1. fig. 13. 27. A rhombus is that which has all its fides equal, but its angles not right angles. Plate 1. fig. 12. 28. A rhomboid is that whofe oppofite fides only are equal, but its angles not right angles. Plate 1. fig. 13. 29. A trapezium is a four-fided figure, which has none of its fides parallel. Plate 1. fig. 14. 30. A trapezoid is a quadrilateral figure, with two of its fides parallel. Plate 1. fig. 15. 31. A diagonal is a straight line, which joins any two oppoAte angles of a quadrilateral figure. Plate 1. fig. 16. 32. A circle is a figure bounded by one curve line, which is called the circumference. Plate 1. fig. 17. 33. The centre of a circle is a point A, within the figure, equidistant from every point in the circumference. 34. The radius of a circle is the distance between the centre and circumference. 35. The diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. A is the centre. AB the radius. CD the diameter. Note, The diameter is equal to twice the radius. 36. An arch is any part of the circumference. 37. The chord of an arch is a ftraight line, drawn between the extremities of an arch. 38. The fegment of a circle is that space contained between the chord and arch of the fame circle. 39. A regular polygon is that whofe fides are all equal. 40. An irregular polygon is a figure whofe fides are not all equal. 41. Polygons receive names according to the number of their fides and angles. Thus, A trigon has 3 fides. A tetragon 4 A pentagon 5 A hexagon 6 A heptagon 7 An eneagon 9 A decagon 10, &c. 42. A mixed angle is that which is formed by one curved line meeting another ftraight line. 43. A curve-lined angle is that which is formed by the meeting of two curved lines. GEOMETRICAL PROBLEMS. 1. To make an Equilateral Triangle upon a given line AB. FROM the centre A, at the distance AB, describe an arch; and from the centre B, with the fame radius, describe another arch, cutting the former in C; join CA and CB. Plate 1. fig. 18. PROBLEM II. To bifect any given line AB into two equal parts. Upon B for a centre, with a radius more than the half of AB, defcribe an arch; and on A for a centre, with the fame radius, defcribe another arch, cutting the former in the points C,D: Join CD, and CD will bifect AB in the point E. Plate 2. fig. 19. PROBLEM III. To erect a perpendicular from a given point A, in a given line AB. UPON any point, C for a centre, with the radius CA, de. fcribe a circle, cutting the given line alfo in D; draw the diameter DCE, and join EA; then fhall EA be the perpendicular. Plate 2. fig. 20. PRO PROBLEM IV. To erect a perpendicular from a given point A, in a given line AB, another way. FROM the given point A, with any radius AC, describe an arch, cutting the given line in C; from C, with the fame radius, cut the former arch in D and E; and upon these points as centres, describe arches cutting in R; join RA, and it will be the perpendicular required. Plate 2. fig. 21. PROBLEM V. From a given point C, to drop a perpendicular upon a given line AB. On C, the given point, as centre, with any convenient diftance, fweep an arch, cutting the given line in the points D,E; and from these points, with any radius more than half their distance, defcribe arches cutting each other either above or below the line; join the point of intersection and C, and it will be the perpendicular. Plate 2. fig. 22. PROBLEM VI. To bifect a given angle ABC. From B the angular point as centre, describe an arch cutting the containing fides in D,F; on D,F for centres, defcribe arches of equal radii, cutting each other in E; join BE, which will bifect the angle ABC. Plate 2. fig. 23. PRO PROBLEM VII. To trifect a right angle ABC. FROM the angular point B, with any radius defcribe the arch AC; from C as centre, with the fame radius, cut the arch AC in D; and from the centre A, with the fame radius cut the arch AC in E; then join DB, EB, and they will trifect the angle. Plate 2. fig. 24. PROBLEM VIII. To draw a line parallel to a given line AB. FROM any two points, D and E, defcribe arches of equal radii; draw CF to touch thefe arches, and CF will be parallel to AB. PROBLEM IX. To divide a line AB into any number of equal parts. LET it be required to divide AB into feven equal parts, from A draw AD at any angle; and from B draw BC parallel to AD. On each of these parallel lines lay off as many equal parts as AB is to be divided into: Join the oppofite points of division by ftraight lines, paffing through AB, and they will divide AB as required. Plate 2. fig. 26. PROBLEM X. To find a fourth proportional to three given lines. MAKE any angle ABC: Set off the firft term from B to D, the fecond from D to A, the third from B to E; join DE, and through |