The Artizan . Let A E he the length of the beam, and E F the base; then divide A Ein four equal parts, thus : AB = BC = CD = DE= 12in. each; E F =24in.; then by the property of the parabola, AE : ad :: fes : GD2 that is 48 : 36 :: (24)2 : 432 lie square root of which is 2078 = G D. and A E : A C :: F E2 : H C2 that is, 48 : 24 :: 576 : 288 the square root of 288 = 16-97 = H C. and AE : AB :: F E2 : IB2 that is, 48 : 12 :: 576 : 144 the square root of 144 = 12 = IB. A line drawn through the points F, G, H, I, and A will be a parabola. Sow to draw a Tangent to a Point of a Parabola.(The point he
The Artizan . Let A E he the length of the beam, and E F the base; then divide A Ein four equal parts, thus : AB = BC = CD = DE= 12in. each; E F =24in.; then by the property of the parabola, AE : ad :: fes : GD2 that is 48 : 36 :: (24)2 : 432 lie square root of which is 2078 = G D. and A E : A C :: F E2 : H C2 that is, 48 : 24 :: 576 : 288 the square root of 288 = 16-97 = H C. and AE : AB :: F E2 : IB2 that is, 48 : 12 :: 576 : 144 the square root of 144 = 12 = IB. A line drawn through the points F, G, H, I, and A will be a parabola. Sow to draw a Tangent to a Point of a Parabola.(The point here is F.) From the vertex, A, of the parabola draw A K perpendicular to A E, andmake it equal to \ F E; then draw K F, and K F will he the tangentrequired. How to deaw a Cubic Let A F be the length of the beam, and F G the base; then divide A Fin five equal parts, thus :—A B = B C = &c. = 12in. each, F G = 24in.;then by the property of the cubic parabola, *3 * VAFthat is, V~W V~W = 3-915; a/48 andthat is,andthat is,andthat is, V a E :: F G : EH V 48 :: 24 : 22-27 = E H: 3-634 x 24 = 87-2 and 87-2-r- 3915 = 22-27. V~AT : V~AD :: F G : DI V 60 : V 36 :: 24 : 20-24 = D I. V~aT: ^a~c::FG : CK V~&F : V~W:: 24 : 17-67 = CK vXf : /ll:: F G : B L v 60 : vTsT :: 24 : 14-02 A line drawn through the points G, H, I, K, L, and A will be a cubicparabola. Sow to draw a Tangent to a Point of a Cubic Parabola. (Here the point is G.) From the vertex A of the cubic parabola draw A M perpendicular toA F, divide A M in three equal parts, A 0, 0 N, and N M, draw a linefrom N to G, and N G will be the tangent required. The deflection of beams is a question on which we are still in want offurther decisive experiments to give exact formulae for the different kindsof mater
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