The area of the convex surface of the right cylinder is measured by the product of the circumference of its base by its height.—This is also true of the right cylinder of any base.
Measure of the volume of a prism inscribed in the cylinder.—The volume of a right cylinder is measured by the product of the area of its base by its height.—This is also true of any cylinder, right or oblique, of any base whatever.
Of the sphere.
Every of the sphere, made by a plane, is a circle.—Great circles and small circles.
In every spherical triangle any one side is less than the sum of the other two. The shortest path from one point to another, on the surface of the sphere, is the arc of a great circle which joins the two given points.
The sum of the sides of a spherical triangle, or of any spherical polygon, is less than the circumference of a great circle.
Poles of an arc of a great or small circle.—They serve to trace arcs of circles on the sphere.
Every plane perpendicular to the extremity of a radius is tangent to the sphere.
Measure of the angle of two arcs of great circles.
Properties of the polar or supplementary triangle.