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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45. Trace the curve whose equation is (c + ) y= (-1) aSee the Diagram, just referred to, inverted.
46. The equation of a curve being y3 a3- +ax2, it is
required to trace it. See the second Diagram of page (364)
reversed.
47. If the equation of a curve be y3+-a3+ aa2=o, it
is required to trace it. See the Diagram, just referred to,
inverted.
48. A curve being defined by the equation
y4 + (a2 + 2) y2 2 a2 2
it is required to trace it. See the first Diagram of page (365)
with its axes interchanged.
49. Trace the curve defined by the equation
4aZxy- (X2 + y2) (v + y)2.
See the Diagram, just referred to, with its axes changed through
half a right angle.
50. Trace the curve whose equation is
(2~ - A) y2 = _ (_m - I) (a2)
See the first Diagram of page (366).
51. Trace the circle whose equation is (y- a)2 = a2 - x2
finding the position of its centre and the magnitude of its
radius.
52. Describe the equilateral hyperbola as defined by the
equation (y- a)2 = X2 -a2.
53. Trace the rectangular hyperbola as defined by the
equation x (a - y) = y.
54. It is required to trace the circle as defined by the
equation x2 + y2 = aix + by.
55. Trace the common parabola by means of the equations
/y + V/ = V/a.
56. Trace the common parabola whose equation is
(y- )=3y.
57, Trace the ellipse as defined by the equation
y-2 2 xy + 3i,2 + 2 y - 4 3 =0o