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Extra resources for A Comprehensive Practical Geometry for Builders

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4. Draw the traces V - T and H - T. Draw a - b at right angles to X - Y. With centre a and radius to just touch V - T describe an arc to give c' on the X - Y line. Angle a - c' - b is the plane's inclination to the vertical plane. INTERSECTING OBLIQUE PLANES Figure 156 shows the traces of two planes V' - T' - H' and V" - T" - H" intersecting with one another. The plane with traces V' - T' - H' is inclined at 60° to the horizontal plane and the other, V" - T" - H" is inclined at 45° to the horizontal plane.

Draw a line from h to P cutting the centre line at y. This is the focal point of the parabola. Place any number of points on the curve and at any position, such as points P' and P". 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.

Figure 135 5. Figure 135 is similar to the preceding one, but this time a - b - c - d - e has been enlarged so that a - b now becomes a - b' in length. 40 Draw the moulding a - b - c. Project the various points across the width of the moulding downwards and beyond the base line. Project the various points through the thickness of the moulding across to a-c. Make a - e equal to the required thickness. Draw c - e and the lines from f and g parallel to c - e. With centre a and radii a - f', a - g' and a - e describe the arcs round to a-d.

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