A Comprehensive Practical Geometry for Builders by A.B. Emary

By A.B. Emary

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Draw the normals x' - P' and x" - P" and repeat this process for as many points on the curve as required. 1. 2. 3. 4. Pointed arch in stone The pointed parabolic stone arch, illustrated in figure 104 shows how the geometry of the last two drawings can be used in a practical application. 5. Draw a - b, the directrix, and c - d, the axis, and on c d place point e (the vertex) and the focal point. The vertex e is mid-way between the focal point and the directrix. Plot any number of points on c - d from e and number these 1, 2, 3 etc.

With centre y (the focal point) and with radii y - P' and y - P" draw arcs to cut the centre line at x' and x". Draw the normals x' - P' and x" - P" and repeat this process for as many points on the curve as required. 1. 2. 3. 4. Pointed arch in stone The pointed parabolic stone arch, illustrated in figure 104 shows how the geometry of the last two drawings can be used in a practical application. 5. Draw a - b, the directrix, and c - d, the axis, and on c d place point e (the vertex) and the focal point.

Place the trammel over the axes so that the major axis mark is on the minor axis and the minor axis mark is on the major axis. Mark the position of the end (c) of the trammel and repeat for several different positions as shown in the figure. Joining up the marks will produce an ellipse. FINDING THE LENGTH OF THE MINOR AXIS Figure 101 is a simple problem where the length of the major axis and the positions of the focal points are given, and you are required to draw the ellipse. 1. 2. 3. Draw the major axis a - b and on this line place the focal points F' and F2.

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