. The railroad and engineering journal . ntersectat E. By the preceding problem bisectthe angle J E g by the line /; E, whichwill also bisect the angle between thelines -•/ B and C D. Problkm 14 (fig. 46). Fo trisect \ aright angle. First Method.—\l D A E is a rightangle it may be divided into three equalparts by drawing an arc, D F G E, fromthe vertex .1 as a center with any radius,and then dividing this arc with a pair ofdividers into three c(|ual parts, and draw-ing lines -•; /■ and A G through the pointsof division. The angles D A F, FA G,and U .1 li will then all be equal. Second Method.
. The railroad and engineering journal . ntersectat E. By the preceding problem bisectthe angle J E g by the line /; E, whichwill also bisect the angle between thelines -•/ B and C D. Problkm 14 (fig. 46). Fo trisect \ aright angle. First Method.—\l D A E is a rightangle it may be divided into three equalparts by drawing an arc, D F G E, fromthe vertex .1 as a center with any radius,and then dividing this arc with a pair ofdividers into three c(|ual parts, and draw-ing lines -•; /■ and A G through the pointsof division. The angles D A F, FA G,and U .1 li will then all be equal. Second Method. — Draw the D FGEas before. Then with the same radius,and from /:; as a center, draw the arc i Iintersecting D F G £ /, and from J) as a center draw 2 the points of intersection /and G draw lines A /-and * To bisect means to divide into two equal parts,t To trisect means to divide into three equal parts. Vol. LXIV, No. 6.] ENGINEERING JOURNAL. 275 A G, and they will divide the angle DAE into three Fig. 46a. Problem 15 (fig. 461;). To divide any angle into any niimti(.rof equal parts. Let DAB, fig. 46 a, be an angle to be divided into, say, fiveequal parts. From the vertex A, as a center, and with any radius draw an arc a b e d e f. With a pair of dividers, by re-pealed trial, divide thfs arc into the required number of equalparts—in this case five—and through the points of division,be de, draw the lines A E, A F, A G and A II. These lineswill then enclose equal angles. TRIANGLES.* Problem 16 (fig. 50)eonstnicl a triangle. Let the length of these sides be Having the length of the three sides to 2f, 4* and 5+°. Lay down one of these sides, A B. fig. 50, preferably the longest. Then,with the compasses, take the length of one of the other sides,and from B, the extremity of A B, describe an arc 11, andwith the length of the third side and ^ as a center draw another Fig. 50.
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectrailroa, bookyear1887
