. Elements of geometry : containing books I to III. Join l,l> and draw CF parallel to BD, mooting ED pro-duced in /•. and join BF. Then will quadrilateral ABFE» pentagon ABODE. For . BDF .!:, on Bame base BD and betweensum- parallels. If, then, from the pentagon we remove a BCD, and add BDF to the remainder, we obtain a quadrilateral ABFEeq livalent to the pentagon ABODE. Books I. & II.] AREA OF AX IRREGULAR POLYGON, ior The quadrilateral may then, by a similar process, be con-verted into an equivalent triangle, and thus a polygon of anynumber of sides may be gradually converted into an equ
. Elements of geometry : containing books I to III. Join l,l> and draw CF parallel to BD, mooting ED pro-duced in /•. and join BF. Then will quadrilateral ABFE» pentagon ABODE. For . BDF .!:, on Bame base BD and betweensum- parallels. If, then, from the pentagon we remove a BCD, and add BDF to the remainder, we obtain a quadrilateral ABFEeq livalent to the pentagon ABODE. Books I. & II.] AREA OF AX IRREGULAR POLYGON, ior The quadrilateral may then, by a similar process, be con-verted into an equivalent triangle, and thus a polygon of anynumber of sides may be gradually converted into an equiva-lent triangle. The area of this may then be found. III. The third method is chiefly employed in practice bySurveyors. a f Let ABCDEFG be an irregular polygon. Draw AE, the longest diagonal, ami drop perpendicularson AE from the other angular points of the polygon. The polygon is thus divided into figures which are eitherright-angled triangles, rectangles, or trapeziums ; and the areasof each of these figures may be readily calculated. 102 EUCLIDS ELEMENTS* (Books I. & ii. Note 7. On, Projections. The projection of a point B, on a straight line of unlimitedlength JE, is the point M at the foot of the perpendiculardropped from B on AE. The projection of a straight Km BC, on a straight line ofunlimited length AE, is MN,—the part of Ah interceptedbetween perpendiculars drawn from />and C. When two lines, as All and J /•,, form an angle, the pro-jection of AB on AE is AM.
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