. The railroad and engineering journal . istances f i, 2 2, 3 3, from theline C D the curve. A semi-ellipse may, therefore, be laidoff by drawing ordinates below C Z> and multiplying one-halfthe minor axis, or 8 8, by the complements, and laying off thelengths of the ordinates below CD.\ * An ordinate^ is a line drawn perpendicular to either axis of the ellipseand terminating in the curve. Thus in Fig. i i, 2 3. 3 3, are From Molesworths Pocket-Book of Engineering Formula;. Vol. LXV, No. 5-] ENGINEERING JOURNAL. 231 Problem 75. An ellipse being !;iven to find the
. The railroad and engineering journal . istances f i, 2 2, 3 3, from theline C D the curve. A semi-ellipse may, therefore, be laidoff by drawing ordinates below C Z> and multiplying one-halfthe minor axis, or 8 8, by the complements, and laying off thelengths of the ordinates below CD.\ * An ordinate^ is a line drawn perpendicular to either axis of the ellipseand terminating in the curve. Thus in Fig. i i, 2 3. 3 3, are From Molesworths Pocket-Book of Engineering Formula;. Vol. LXV, No. 5-] ENGINEERING JOURNAL. 231 Problem 75. An ellipse being !;iven to find the axes and foci.*U A C B A fig- 253. is the ellipse, draw any two chords, asE A and G H, parallel to each other. Bisect each of these in /and/, and draw // through the points of division and to inter-sect the ellipse at K and /. This line divides the ellipseobliquely into two equal parts. Bisect L I\ at O, which willbe the center of the ellipse. From 0, with any radius, draw acircle cutting the ellipse \xi M N P Q. Join these four points. Fig- 253- by lines, which will form a rectangle within the ellipse. Bisectthe sides of this rectangle in Jf, S, T aad U, and .draw linesA B and CD through the points of division. These lines willbe the axes of the ellipse. The foci may be found by describing arcs from Cor/) ascenters, with 0 i5 as a radius, so as to intersect A B 3\ ^FandV. The points of intersection will then be the foci. Problem 76. To draw a line perpendicular to the curve of anellipse at a given point A, fig. 254. Find the axes and foci, as in the last figure. From the foci/f^and Kdraw lines through A, and extend them outside of theellipse. Bisect the angle B A C, and draw a bisecting line A D,which will be perpendicular to the curve of the ellipse at stones of which an elliptical arch are formed may be laidout by repealing this process. Problem 77. To draw a tangent to the curve of an ellipse at agiven point E, fig. 254. Draw lines VE WE from the foci through th
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectrailroa, bookyear1887
