We have CALCULATION. Papa=1548, Pat1 = 1920, p1p,= 1080, P=1959, P-Þ2Þ2=411, P−þ2Þ1=669, P−p1Þ1=879; log a = log 2 + log ▲ - log, = 1.7179877, 1 log b = log 2 + log ▲ — log, = 1·6388065, log = log 2 + log A-log,= 1.5616405; EXAMPLES. 1. A gentleman a garden had, Four score yards long, and three score broad; A walk of equal width half round He made, which took up half the ground; Ye skillful in geometry, Tell us how wide the walk must be. Ans. 20 yards. 2. If the length and breadth of the garden be 2mn and m2-n2, the breadth of the walk is n (m-n). Investigate these formulæ, and determine the particular values of m and n which satisfy question 1. Ans. m= 4√5, n = 2√5. 3. If ABCD be the garden, and AC a diagonal, shew that the breadth of the walk is equal to the radius of the circle inscribed in the triangle ABC. 4. The diameter of a semicircle is 39, and the length of a perpendicular ordinate 18; find the two parts into which the diameter is divided. Ans. 12, 27. 5. The sum of the perpendicular and hypothenuse of a right-angled triangle is 338, and the base is 52; find the other two sides. Ans. 165, 173. 6. The three sides of a triangle are 13, 15, 18; find the two parts into which the greater side is divided by the perpendicular from the opposite angle. Ans. 74, 105. 7. If d be the diameter of the earth, at what height I n will a person be able to see th part of the surface? 8. The sides of a triangle are in arithmetical progression, their sum is 84, and the area of the triangle is 126; find the sides. Ans. 15, 28, 41. 9. The sides of a triangle are in arithmetical progression, the common difference is 11, and the area is 156; find the sides. Ans. 15, 26, 37. IO. The sides of a triangle are in arithmetical progression, the square of the middle side exceeds the product of the other two sides by 529, and the area is 1116; find the sides. Ans. 39, 62, 85. II. If the sides of a right-angled triangle are in arithmetical progression, shew that they are proportional to the numbers 3, 4, 5. 12. Find the sides of a rectangle inscribed in a triangle whose sides are 13, 37, 40, having one side parallel to the greatest side of the triangle, and the ratio of the sides Ans. 30, 3. as 10 to 1. |