An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

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20. If the inscribed cone be equilateral, the surface of
the spherical segment is twice as great as the convex surface
of the cone.
21. If a right-angled cone circumscribe a hemisphere,
the surface of the hemisphere: the convex surface of the
cone:: 1: /2.
22. The surface of a right-angled cone circumscribed
about a hemisphere is twice as great as that of the inscribed
cone, whether the convex or whole surfaces be taken.
23. The surface of a sphere: the convex surface of an
equilateral inscribed cone:: 8: 3.
24. The whole surface of an equilateral cone inscribed
in a sphere: the surface of the sphere:: 32: 42.
25. The surface of a sphere: the whole surface of the
circumscribed equilateral cone:: 22: 32.
26. A sphere is equal to a cone whose height is the
radius and base equal to four great circles of the sphere.
27. A hemisphere is twice as great as its inscribed cone.
28. A right cone, sphere and cylinder of the same base
and altitude are as the numbers 1, 2, 3.
29. Sectors of spheres are to one another in the compound ratios of their radii and convex surfaces.
30. Find the content and surface of the middle zone of a
sphere.
31. If the altitude of a cylinder be equal to the diameter
of its base, the whole surface is equal to six times the area of
the base, required a proof.
32. If the bases of a cylinder and of a cone have the
same radius as a sphere, and each of their altitudes equal to
the diameter of the sphere, the solidity of the cone is equal
to the excess of the cylinder above the sphere.