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

158

121. Describe the least paraboloid about a given cylinder,
when their axes are coincident in direction.
122. Find that point in the surface of a given paraboloid
through which if two planes be drawn, one perpendicular to
the axis and the other perpendicular to the generating parabola and parallel to the axis, the sum of the areas of the sections shall be the greatest possible.
123. On a given triangle a pyramid is to be constructed
of a given volume; required its dimensions when the surface is
the least possible.
124. Find that point in the surface of a spherical triangle, from which if straight lines be drawn to the angular
points the pyramid thus formed shall be the greatest possible.
125. Given the greatest and least slant sides of an oblique
cone to find the diameter of the base, when the volume is the
greatest possible.
126. Required the area of the least isosceles triangle
that can circumscribe a given circle, and compare their perimeters.
127. Find the content of the least cone that can circumscribe a given sphere, and compare their surfaces.
128. It is required to inscribe the greatest parabola in
a given isosceles triangle, the axis of the parabola coinciding
in direction with the line bisecting the vertical angle of the
triangle.
129. Find the area of the least triangle which can circumscribe a given segment of a parabola.
130. Determine the content of the greatest paraboloid
that can. be inscribed in a right cone of given dimensions.
131. Find the content of the least cone that can circumscribe a paraboloid of given dimensions.
132. Determine the dimensions of the least paraboloid
that can circumscribe a given sphere.