An elementary treatise on geometry : simplified for beginners not versed in algebra . the perpendicular is to be erected. 1. Take any distance, BD, on one side of the point D,and make DA equal to it. 2. From the point B, with any radius greater thanBD, describe an arc of a circle, and from the point A,with the same radius, another arc, cutting the first. 3. Through the point of intersection, C, and the pointD, draw a straight line, CD, which will be perpendiculartp the line MN. Demox. The three sides of the triangle BCD, fire equal to theAree sides of the triangle ACD, each to each, viz. the s
An elementary treatise on geometry : simplified for beginners not versed in algebra . the perpendicular is to be erected. 1. Take any distance, BD, on one side of the point D,and make DA equal to it. 2. From the point B, with any radius greater thanBD, describe an arc of a circle, and from the point A,with the same radius, another arc, cutting the first. 3. Through the point of intersection, C, and the pointD, draw a straight line, CD, which will be perpendiculartp the line MN. Demox. The three sides of the triangle BCD, fire equal to theAree sides of the triangle ACD, each to each, viz. the side BC equal to AC « BD « DA « « CD CD;therefore the three angles in the triangle BCD are also equal tothe three angles of the triangle ADC, each to each (page 40);and the »ngle x opposite to the side BC in the triangle BCD, isequal to the angjp y opposite to the equal side AC in the triangleACD; and as the two adjacent angles, which the line CD makpswith the line MN, are equal to one another, the line CD is per-pendicular to MN. (Definitions of perpendicular lines, page 12.). 14S II. Solution. Let MN be the given straight line,and A the point in which the perpendicular is to bedrawn to it. 1. From a point, O, as a centre, with a radius, OA,greater than the distance O from the straight line MN,describe the circumference of a circle. 2. Through the point B and the centre O, of the cir-cle, draw the diameter BC. 3. Through C and A draw a straight line, which willbe perpendicular to the line MN. Demon. The angle BAC, at the circumference, measures halfa» many degrees as the arc BPC intercepted by its legs (page 111,1st). But the arc BPC is a semi-circumference; therefore the angleBAC, measures a quadrant; consequently the angle BAC is a rightangle (page 107, Remark 3), and the line AC is perpendicular toMN. Problem III. To bisect a given angleSolution. Let BAC be the givenangle. 1. From the vertex. A, of the angleBAC, with a radius, AE, taken atpleasure, describe an arc of a
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