Table of Contents

1. An Advice to Students

2. Exponential and Logarithmic Series

3. Complex Quantities, De Moivre' Theorem

4. Expansion of sin ?0 and cos? 0 and Series for sin0 and cos0 in Powers of 0

5. Expansions of Sines and Cosines of Multiple Angles and of Power of Sines and Cosines

6. Exponential Series for Complex Quantities, Circular Functions for Complex angles, Hyperbolic Functions

7. Lograrithms of Complex Quantities

8. Gregory's Series: Calculation of the Values of ?

9. Summation of Series, Expansions in Series

10. Expates XVII

I 11. Resolution into Factors. Infinite Products for sin 0 and cos0 Errors of Observation

13. Miscellaneous Propositions

14. Inverse Circular Functions