**"Infinitesimal Calculus" Article - Table of Contents**

**HISTORICAL INTRODUCTION**

Part 1. Introduction. Archimedes.

Part 2. Kepler. Cavalieri. Pascal. Wallis.

Part 3. Descartes.

Part 4. Fermat. Barrow. Roberval.

Part 5. Newton and Leibnitz.

Part 6. Objections to Infinitesimal Calculus: Catelan, Nieuwentijt, Rolle.

Part 7. How to Expound the Principles of Calculus. Lagrange.

Part 8. List of Works on Infinitesimal Calculus.

**PART I. DIFFERENTIAL CALCULUS**

Part 9. [Introduction.]

Part 10. Successive Differentiation.

Part 11. Taylor's Theorem and Development of Functions.

Part 12. Maxima and Minima.

Part 13. Symbolic Methods.

Part 14. Change of Independent Variable.

**PART II. INTEGRAL CALCULUS**

Part 15. [Introduction.]

Part 16. Definite Integrals.

Part 17. Differentiation under the Sign of Integration.

Part 18. Integration under the Sign of Integration.

Part 19. Area of Plane Curves.

Part 20. Rectification of Curves.

Part 21. Cubature of Curves.

Part 22. Quadrature of Surfaces.

Part 23. Elliptic Integrals.

**BIBLIOGRAPHY**

Part 24. Bibliography of Recent Works on Infinitesimal Calculus.

**The above article was written by:** Benjamin Williamson, F.R.S., Professor of Mathematics, Trinity College, Dublin.