A complete treatise on practical land-surveying, in seven parts; . of land, consisting of more than four sides, mayhe surveyed by reducing it into triangles and trapeziums. Thus, a field of fire sides mav he reduced into a triangle anda trapezium : of six. into two trapeziums ; of seven, into two trapeziums and a triangle : of eight, into three trapeziums. &c 57 Part III.) LAND-SURVEYING. The propriety of dividing fields in this manner, dependsentirely on the relation which the angles have to one another:it is, therefore, sometimes more accurate to divide them intotriangles. TO COMPUTE THE CON
A complete treatise on practical land-surveying, in seven parts; . of land, consisting of more than four sides, mayhe surveyed by reducing it into triangles and trapeziums. Thus, a field of fire sides mav he reduced into a triangle anda trapezium : of six. into two trapeziums ; of seven, into two trapeziums and a triangle : of eight, into three trapeziums. &c 57 Part III.) LAND-SURVEYING. The propriety of dividing fields in this manner, dependsentirely on the relation which the angles have to one another:it is, therefore, sometimes more accurate to divide them intotriangles. TO COMPUTE THE CONTENT. Rule.—By the rules given in the last two problems, find thedouble area of each triangle and trapezium contained in thefigure, Collect all the double areas into one sum, which divide by 2,and the quotient will be the whole area. EXAMPLES. 1. Lay down a field, and find its area from the followingnotes. CE 1666 Diag. 1326 496 A. 1000 D 376 573KoffC ~KW «* 1433 Diag. 1000 B 273 643 Begin at A. Range W. Per. on the left. Diag. Per. on the right. 1> \. 58 land-surveying. (Part III. CONSTRUCTION. From the notes, the figure obviously consists of five sides,and is divided into a triangle and a trapezium. Draw the baseA C, which make = 1433 links; at 643 links, let fall the per-pendicular a B, upon which lay off 273 links; join A B and C B,and the triangle is completed. Then, with A as a centre, and496 links in your compasses as a radius, describe an arc; andwith C as a centre, and 1326 as a radius, describe another arc,intersecting the former in b.—Through b draw the diagonalC E = 1666 links; upon which, at 573 links, erect the per-pendicular c D = 376 links. Join C D, D E, and E A, andthe figure will be completed. Note.—If the learner fully comprehend-the above construction, he will notfind it difficult to lay down the figures belonging to -the following examples ;as the same process will succeed in all similar cases. Triangle ABC. 1433 base. 273 per. 429910031 2866 391
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