5. Arc of a parabola, measured from vertex,

6. Perimeter of ellipse, semi axes a and b, = π (a + b) approximately.

12. Area of parallelogram, sides a, b including ▲ A,

= ab sin 4.

14. Area of trapezium, altitude p, parallel sides a, b,

17. Area of annulus, exterior and interior radii, R, ï, = π (R2 — p2).

18. Area of circular sector, LA,

21. Area of parabola cut off by a double ordinate 2y,

22. Area of ellipse semi axes a, b,

= παό.

23. Simpson's Rule for determining the approximate area of any curvilinear figure.

Let the base be divided into any number of parts each D, and from the points of section draw perpendiculars to meet the curve.

=

Let

F denote the first, I the last perpendicular.
E = sum of all the even perpendiculars.
0 = sum of all the odd perpendiculars.

26. Surface of prism, perimeter of base P,

Vol. of rectangular parallelopiped, sides a, b, c,

34. Vol. of spherical segment, height h,

I. Function of one or more variable quantities.—An algebraical expression whose value depends upon that of one or more of the variable quantities which it involves.

II. Limiting value of a function. That quantity from which the function may be made to differ as little as we please by making the difference between the variable and some particular value of it as small as we please.

General Notation.

a, b, c denote constant quantities generally.

variable quantities generally.
functions of one or more variables.
function of x.