By A.B. Emary

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This article suits any path with the observe "Manifold" within the name. it's a graduate point publication.

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3. Draw the major axis a - b and on this line place the focal points F' and F2. With radius a - c and centres F' and F2 in turn, describe intersecting arcs above and below the axis to obtain the position and length of the minor axis c - d. The ellipse can now be drawn using one of the methods described previously. 32 Figure 101 A comprehensive practical geometry for builders 11. THE PARABOLA To set out the curve of a parabola (figure 102), let 0' - 5' be half the span and 0' - 0 the rise. 5. 6.

3. 47 Drop vertical lines from c' and d' to meet horizontal lines brought out from the points on the plan so that the shape of the disc can be obtained. OBLIQUE PLANES Figure 152 is a pictorial view of an oblique plane a - b - c -d. To develop its shape: DEVELOPMENT OF IRREGULAR INCLINED SURFACES Figure 150 shows how an inclined triangle can be developed. 1. 2. 3. Draw the plan and elevation. With centre a and radius a - b in the elevation describe an arc to give b' on the X - Y line. Drop a vertical line from b' to give b" on a horizontal line brought out from b in the plan.

Join these two points to the point x on the curve where the tangent is required. Bisect angle F' - x - F2 to obtain the normal and draw the tangent at right angles to the normal. The ellipse WORKSHOP METHODS 31 hr-----~--~~~----_,g The next method (figure 98) is a very accurate way to draw an ellipse and can be used in the workshop as well as in the drawing office. It is referred to as the string and pin method. 1. 2. 3. 4. a~--------~~~------~b Draw the rectangle a - b - c - d and the two axes.