It is required to obtain the proper sweep for the plate that runs up the slope of a roof which cuts into the side of a dome. If the dome is a semi-sphere, then the section of the dome formed by the plane of the roof passing through it would be a part of a circle. Produce A B, the plane of the roof (Fig. 1), until it joins the plan at A1; bisect A1 B to give the centre O1, and then draw a line at right angles to the ground line from A to cut the plan at C. The distance AC would be half the width of the section's base. To draw the section, set off a line at right angles to, and on both sides of, AB (Fig. 3). Make AC on both sides of AB equal to AC (Fig. 2), also make AB (Fig. 3) equal to AB (Fig. 1). Then mark off from A, AO1 on the section, equal to A O1 (Fig. 1). Use Ol as centre, and with radius to B draw the arc shown, Fig. 3, and this would be the part to be cut from the plate, so that it would fit the dome.

Roof Cutting into Side of Dome.