PROBLEM III.

A figure being generated by the revolution of a plain figure, having two perpendicular legs, and the other side being irregular, or straight, or a curve line of any kind; the figure being made to revolve about one of its perpendicular legs. To find the figure of the section cut any where across the base, and right angles to the plane of the base, having that section which passes through the axis given.

1. Let A FE G D be the circle of the base, and let the section required be cut across F G; also let A B C be a section of the solid passing through the axis.

2. From the centre O, draw the concentric circles H h Ii, Kk, Ll, to cut A B in the points H, I, K, L: and FG, in the points h, i, k, l.

3. Erect perpendiculars to the lines A B and F G, both ways from these points, to cut A C in H, I, K, L.

4. Make the distances hh, ii, kk, 1 l, equal to their corresponding distances H H, II, K K, L L; a curve being drawn through these points, it will be the section required.

If the given section is a triangle, the section is an upright hyperbola.

If the given section is a semicircle, the required section will also be a semicircle; these appear plain by the figures, and in this case there is no tracing required.

VOL. I.

H

THE