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Fig. 52 -JB =2? L' 26 FIRST PRINCIPLES OF will be seen, is tantamount to bisecting a line from D to E, and drawing a line through its bisection and point A, the only requisite condition being that the two points D and E in the lines forming the angle must be equi-distant from the angular point A. Problem 5 (Fig. 48). To draw a line parallel to a gicen line at a given distance from it. Here it is evident that if from any two points C and D in the given line AB, arcs be drawn, of a radius equal to the given distance the two lines are to be apart, and a line EF be drawn tangent to those arcs, then the line EF will be parallel to the given line AB. This is the simplest possible solution of the problem, involving the least work, but requires care in drawing the parallel line exactly tangent to the arcs. Another solution, requiring much more work in the construction, is the following : At the points C and D, in line AB (Fig. 48), erect two perpendiculars to AB, and set off on each of them from C and D the distance the parallel lines are to be apart. Through the two points obtained draw a line, and it will be parallel to the given line AB. Problem 6 (Fig. 49). Through a point P, to draw a line parallel to a given line AB. With P as a centre and any convenient radius, describe an arc EC, cutting the given line AB in C, and from C as a centre, with the same radius, draw an arc through P, cutting AB in D. Set off the distance