Plane Trigonometry and Mensuration

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1845 edition. Excerpt: ...--log. 47.5.. 1.676694 + log. 27... +1.431364 + log. 4.2... +0.623249 + log. 16.3.. +1.212188 2)4.943495 X a = (15 ft, 5 in.) x (7 ft. 9 in.) = 119 sq. ft. 69 sq. in. = s. 2d. Given b = 10 in.; b'--16 in.: a = 8-in.: required 8. Ans. 8 = 109.675 sq. inches. 3d. The lengths of the parallel sides of a trapezoidal field are 25.75 chains and 18.87 chains, respectively; and the perpendicular distance of the parallel sides is 10.54 chains: required the area of the field. Ans. 23 ac. 2 ro. 2.3584 poles. The value of y gives the length of the line of section (e F); and the value of x gives the distance (b K) of the line of section from the point b. If s Ac, x a: in this case EF intersects the lines B A, Bh, Bg, and Cd, below the base Ad. Examples. 1st. Given 6 = 20 in.; b'= 14 in.; a=12in., and therefore Ac = 204 sq. in.: it is required to cut from the trapezoid Ac a part containing 144 sq. in: Eequired the length of the line of section and its distance from the side Bc, to which it is parallel. Ans. y = 18.439 in.; x= 8.878 in. Calculation. r-l/""TM)+ " =V/T+"x 14j=V.44+196=3=18.439, a=2014(--14+ 18.439)=2 x 4.439 = 8.876. 2d. Given J = 76ft., i' = 36ft., a = 23 ft., s=560sq.ft.: required y and x. Ans. #=56.954ft.; x = 12.04855 ft. a. In the last problem, the part E c, whose area is s, is cut from the smaller end of the given trapezoid Ac. If the part which is to contain an area = s, is required to be cut from the greater end of A c, the formulae for determining the values of the line of section, Ef or y, and the altitude Hkon, require modification. Let it be supposed that Ef, which is parallel to Ad or Bc, cuts from the greater end of Ac a trapezoid ED whose area is s. The number of this log. is 5.6884.. 0.754990...