Elements of geometry and trigonometry . angle 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,
Elements of geometry and trigonometry . angle 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 figure will bea rectangle ; if, in addition to this, the sides are equal, it willbe a PROBLEM XIIL To find (he centre of a gieen circle or arc. Take three points, A, B, C, anywhere in the circumference, or thearc ; draw AB, BC, or suj)pose t hemto be drawn ; bisect those two lines|jy the perpendiculars DE, FG :the point O, where these perpen-diculars meet, w ill be the centresf)ught (Prop. W. Sch.). Sclioliujn. The samci constnic-tion serves f^r making a circum-fcrcnrc pass through three given points A, B, C ; and also fordescribuig a circumli rence, in which, a given triangle ABGshall be inscribed.
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