. The New York coach-maker's magazine. n space is represented by its twoprojections (a b, a/ b), and the sides of the right an-gles of the vertical trapeze that passes that line, and byits horizontal projection a b, are represented by the ver-tical lines a a0, bJba, which are respectively carried froma to A and from b to B. LXXXV. If the horizontal plane P (fig. 56) be ele-vated until it touches the line A B at its lower end A, thenew horizontal projection of the line will be found trans-ferred to A c parallel to a b, and the ground line in acparallel to X Y. Then the line A B is equal to the
. The New York coach-maker's magazine. n space is represented by its twoprojections (a b, a/ b), and the sides of the right an-gles of the vertical trapeze that passes that line, and byits horizontal projection a b, are represented by the ver-tical lines a a0, bJba, which are respectively carried froma to A and from b to B. LXXXV. If the horizontal plane P (fig. 56) be ele-vated until it touches the line A B at its lower end A, thenew horizontal projection of the line will be found trans-ferred to A c parallel to a b, and the ground line in acparallel to X Y. Then the line A B is equal to the hy-pothenuse of a rectangular triangle A c B, the sides of theright angle being the horizontal projection A c and theelevation Be or b c of the other extremity of the lineabove the horizontal plane. To construct this triangle on the horizontal plane, itwill be observed that the projectien a b being equal toA c, one of the sides of the right angle, it suffices to draw Q Jig. 57 ^^ a 31 t^^^^*^ . . !p \ Y r tt. J- ^H* 2 \/b-. a perpendicular b u iu uiat line by one ot the extremitiesb, and to carry over on to that perpendicular the otherside of the right angle B c or ^efrom b to D. The linea Dtlrat joins the points a and Dis the hypothenuse ofthe triangle a b D, equal to the triangle Ac B. Thesame construction is made on the geometrical planes offigure 57. * The two planes of projection being rectangular, theoperations that have been effected on one (figs. 56 and 57)could have been carried out upon the other, and wouldhave yielded the same result. In general, whatever maybe the plane of projection considered, the length of a linein space (a b, ab) (fig. 58), when oblique to two projection, is equal to the hypothenuse Ab of a rectan- 36 THE NEW YORK COACH-MAKERS MAGAZINE, August. gular triangle A a b, of which the sides of the right angleare: 1°. The projection a b from the line on to one ofthe two planes of projection; 2°. The difference ac1of the distances of its ext
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Keywords: ., bookcentury1800, bookdecade1850, bookidnewyorkcoach, bookyear1858
