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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minor axis, when the ellipse always passes through a fixed
point.
216. Given one focus of an ellipse, a point through which
it passes and the magnitude of the major axis, to determine the
locus of the vertex.
217. Given the centre of an ellipse, a point through
which it passes, and the position of a tangent at that point,
to find the locus of the focus.
218. Ellipses having a given centre and eccentricity
touch a given line, it is required to find the loci of the extremities of their major axes.
219. Given the position of the centre of an hyperbola
and the magnitude of its major axis, to find the locus of the
focus when it always passes through a given point.
220. Given the position of the vertex of an hyperbola,
a point through which it passes and the position of a tangent
at that point, to determine the locus of the focus.
221. Given the vertex of an hyperbola, a point through
which it passes and the magnitude of the major axis, to determine the locus of the focus.
222. Find the locus of the centre of an ellipse which
touches two given straight lines at two given points.
223. If two sides of a triangle be divided into the same
number of equal parts and the points of division of one side
beginning from the base be joined with those of the other side
beginning from the vertex, find the curve in which the intersections of every pair of consecutive lines taken in this order are
situated.
224. If on two sides of an isosceles triangle equal parts
be assumed, it is required to find the curve in which the
points of intersection of every pair of lines joining the successive points of division are situated.
225. Determine the locus of the vertices of the osculating parabolas to a given curve; and prove that for the
cubical parabola, it is a curve of the same species.