Elements of geometry and trigonometry . Produce AB towards D ; at the point B, make the angleDBE = C ; draw BO perpendicular to BE, and GO perpen-dicular to AB, through the middle; point G ; and from the pointO, where these perpondicwhirs meet, as a centre, with a dis-tance OB, describe a circle : the required segment will beAMB. For, since BF is a perpendicular at the extremity of theradius OB, it is a tangent, and the angle ABF is measured byhalf the arc AKB (Prop. XXI.). Also, the angle AMB, beingan inscribed aufjle, is jneasiired bv half the arc AKH : hencewe have AMB ABF-EIU)-0: hence all
Elements of geometry and trigonometry . Produce AB towards D ; at the point B, make the angleDBE = C ; draw BO perpendicular to BE, and GO perpen-dicular to AB, through the middle; point G ; and from the pointO, where these perpondicwhirs meet, as a centre, with a dis-tance OB, describe a circle : the required segment will beAMB. For, since BF is a perpendicular at the extremity of theradius OB, it is a tangent, and the angle ABF is measured byhalf the arc AKB (Prop. XXI.). Also, the angle AMB, beingan inscribed aufjle, is jneasiired bv half the arc AKH : hencewe have AMB ABF-EIU)-0: hence all fho angles in-scribed in th<; segment AMB are equal to llie given angle C. F* t) 66 GEOMETRY. Scholium. If the given angle were a right angle, the requiredsegment would be a semicircle, described on AB as a diameter. PROBLEM XVÏL To find the numerical ratio of two given straig^it lines, these linesbeing supposed to have a common measure^ Let AB and CD be the given lines» 4 g From the greater AB cut off a part equal to the lessCD,
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
