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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100. Required the equation to the normal of the conic
section defined by y2 = mX + n a2; and thence deduce the values
of the subnormals on the axes of x and y for the parabola,
ellipse and hyperbola.
101. Find the equation to the normal of the curve
IV2 y2
defined by - + - =1; and determine the distances from
ay bx
the origin at which it intersects the co-ordinate axes.
102. Determine the equation to the normal of the curve
defined by 2y = a (ea-+ e -a); and the portions of it intercepted
between the curve and the axes of co-ordinates.
103. Prove that the equation to the normal of an hyperbola between the asymptotes is abxy, - x3x- a2b2 + x4 = 0;
and thence construct it.
104. Find the equation to the normal of the cissoid of
Dioces; and thence determine where the normal at the point
of its intersection with the generating circle meets the axes.
105. Required the equation to the normal of the curve
defined by y2 = ax - + x which shall make equal angles with
the axes of co-ordinates.
106. Determine the equation of the normal of a conic
section which shall pass through a given point a, 3; and find
the points of intersection with the axes.
107. The equation to the straight line drawn from the
point a, /3 of a curve perpendicular to the normal is
Y,-A= d (dx - )
required a proof.
108. The intersection of the normal with the perpendicular upon it from any point a, f3 of the curve may be
p2a+ x-p (3 —y)
determined from the equation,= 1+ required a proof.
109. If a straight line be drawn from the origin of the
co-ordinates to any point of a curve, another straight line