SECTION III. General Laws relating to the Development of Functions
depending on a single Variable.
1. Ratio of the increment of a continuous function to that of its variable 162
2. Derivative of a polynomial and multiple function...
3. Use of intermediate and converse functions....
4. Derivative of a functional product.....
5. Power of a function, derivative.....
1. Construction and definitions-complementary arcs, sine, &c.....
2. Sum of the squares of the sine and cosine, the sine an increasing, the
8. Sine and cosine developed in terms of arc........
9. Sine and cosine of the sum and difference of two arcs....
10. Corollaries-sin 2x, cos 2.x; 1+cos 2x, 1-cos 2x ; 1 + sin 2x, 1
2x; (1 + sin 2x)* ±(1— sin 2x); sin p+ sin q, sin p
cos p+ cos q, cos q-cos p;(sin p+sinq);(sin p
(90°+x), &c.....