A complete treatise on practical land-surveying, in seven parts; . B E Draw the diagonal D B, and parallel to it draw C E, meetingA B produced in E. Join the points DE; so shall the triangleA D E be equal to the trapezium A B C D. Note.—This and the following Problem may be applied in finding theareas of trapeziums and irregular polygons by first reducingthemto triangles. Part I.) LAND-SURVEYING. 21 PROBLEM XVII. To reduce an irregular Polygon ABCDE, of Jive sides, to aTriangle of equal Area. C. Extend the side A E, both ways tit pleasure; and draw thediagonals C E, C A. Parallel to these diag
A complete treatise on practical land-surveying, in seven parts; . B E Draw the diagonal D B, and parallel to it draw C E, meetingA B produced in E. Join the points DE; so shall the triangleA D E be equal to the trapezium A B C D. Note.—This and the following Problem may be applied in finding theareas of trapeziums and irregular polygons by first reducingthemto triangles. Part I.) LAND-SURVEYING. 21 PROBLEM XVII. To reduce an irregular Polygon ABCDE, of Jive sides, to aTriangle of equal Area. C. Extend the side A E, both ways tit pleasure; and draw thediagonals C E, C A. Parallel to these diagonals draw the linesD F, and B G; join the points C F, G G; and G C F will bethe triangle required. Note.—Any irregular polygon of more than five sides, may be brought to atriangle of equal area, by reducing it successively to a figure with one side less*until you bring it to a figure of three sides. Thus the trapezium A B C F, orG C D E is equal to the polygon A B C D E, as well as the triangle G C F. PROBLEM XVIII. To raise a Perpendicular from any point D, in a given Line A B,by a Scale of equal f 5/ 30L m 3 c 3 D B 22 LAND-SURVEYING. (Part I. Make D m •=. 3; and from the points D and m, with the dis-tances 4 and .5, describe arcs intersecting each other in n. FromD, through the points n, draw the line D C, and it will he theperpendicular required. Note.—This Problem may be performed by any other numbers in thesame proportion ; but 3, 4, and 5, are the least whole number
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