1 EXAMPLE 4. Suppose a water-course to be the line between the lands of A and B, as under specified; which they agree to straiten by a line from the point C to D. Query, which must pay the other, and for how much land? DIVISION OF LAND. PROBLEM I. To cut off from a triangle any part thereof, by a line issuing from an angular point to the opposite side of the trianglë. RULE. As the area of the triangle, Is to the side the division is to fall on ; So is the part to be cut off, To its proportion of that side, EXAMPLE. Admit the triangle ABC, to contain 650 square perches, and 290 of them is required to be cut off towards A, by a line issuing from the point C, on to the line AB, which is 40 perches long. PROBLEM II. To cut off from a Triangle, any Part thereof, by a Line running parallel to one of it's Sides. RULE. As the area of the triangle, Is to the square of one side the division line is to be on; So is the area of the part to be taken off, To the square of its proportion of that side: The square-root of which will be the length required. EXAMPLE. Suppose the triangle ABC to contain 500 square perches, and it is required to cut off 1.20 towards A, by a line parallel to BC; the line AB being 40 perches long, and AC 36. D C G 40 × 40 = 1600, square of AB. 2 B As 500 1600 :: 120 ✓ 384 = 19.6 nearly, the distance from A to G. PROBLEM III. To cut off from a Triangle, any Part thereof, by a Line issuing from a given Point in one of it's Sides. EXAMPLE. In the annexed triangle, containing 800 square perches AB is 50 perches long, and AC 40, and it is required to cut off towards A, 500 square perches, by a line issuing from the point. F 36 perches from A. By Problem 1, cut off 500 square perches, by a line |