Elements of geometry and trigonometry . Secondly, If the angle C isacute, and B greater than A, thesame construction will again ap-ply, and DEF will be the trianglerequired. But if the angle C is acute, andthe side B less than A, then thearc described from the centre E,with the radius EF=B, will cutthe side DF in two points F andG, lying on the same side of D :hence there will be two trianglesDEF, DEG, either of which willsatisfy the conditions of the pro-blem. 33 j-. Scholium, If the arc described with E as a centre, shouldbe tangent to the line DG, the triangle would be right angled,and ther
Elements of geometry and trigonometry . Secondly, If the angle C isacute, and B greater than A, thesame construction will again ap-ply, and DEF will be the trianglerequired. But if the angle C is acute, andthe side B less than A, then thearc described from the centre E,with the radius EF=B, will cutthe side DF in two points F andG, lying on the same side of D :hence there will be two trianglesDEF, DEG, either of which willsatisfy the conditions of the pro-blem. 33 j-. Scholium, If the arc described with E as a centre, shouldbe tangent to the line DG, the triangle would be right angled,and there would be but one soluiion. The problem would beimpossible in all cases, if the side B were less than the perpen-dicular let fall from E on the line DF. BOOK III. PROBLEM XII. Tlie adjacent sides of a parallelogram, xcith ihe angle which theycontain, being given, to describe the parallelogram. Let A and B oe the given sides, and C the given angle. Draw the hne DE = A; at thepoint 1), make the angle EDF =C ; take DF = B ; describe twoarcs, the one from F as a cen-tre, with a radiuâ FG = DE, theother from E as a centre, witha radius EG=:DF; to the pointG, where these arcs intersecteach other, draw FG, EG ;DEGF will be the parallelogram required. For, the opposite sides are equal, by construction ; hence thefigure is a parallelogram (Book 1. Prop. XXIX.) : and it isformed with the given sides and the given angle. Cor. If the given angle is a right angle, the fi
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