1. The calculus - some dates: ‘ Prehistory ’ 1635 Cavalieri (student of Galileo), ‘ Geometry of indivisibles ’. 1637 Descartes, ‘ Geometry ’. 1638 Galileo, ‘ Discourse concerning two new sciences ’. The search for a method. 1630-1660 Numerous works in Italy (Torricelli), France (Roberval, Pascal, Fermat), England (Wallis, Barrow) applying infinite methods to finding areas of curves ( ‘ quadrature ’ ), tangents, lengths ( ‘ rectification ’ ). Pascal first to use ‘ infinitesimal triangle ’ ; Fermat probably closest to understanding method; Wallis (Arithmetica infinitorum, 1656) most prepared to innovate. The discovery. 1666 Newton ’ s first notebook containing sketch of his method. 1670 Newton ’ s major (unpublished) manuscript, ‘ Method of Fluxions ’. 1675 Leibniz ’ discovery of his method. 1676 Newton ’ s two letters to Leibniz with (cryptic) accounts of his discoveries. 1684 Leibniz ’ first publication (short paper). 1687 Newton ’ s ‘ Principia ’ - calculus hidden in geometric language. The follow-up. 1690 ’ s The brothers Johann and Jakob Bernoulli learn Leibniz ’ method, and, with him, publish works applying it to problems. 1696 First textbook: L ’ Hospital ’ s ‘ Analyse des infiniment petits ’ (help from Johann Bernoulli). 1706-1712 Main period of the ‘ priority dispute ’. 1734 Berkeley ’ s attack in ‘ The Analyst ’. 1748 Maria Agnesi ‘Analytical Instituions’ first major unified textbook

2. Portrait of Newton, 1680s

5. William Blake ’ s vision of Newton (1795) - a single, narrow mathematical universe.

6. Leibniz

7. Johann Bernoulli

8. Picture from L’Hopital’s book illustrating his ‘rule’: curve AMD is the quotient of two curves which both tend to zero at B.

9. The curve described by a heavy chain is called a ‘ catenary ’ ; its shape was described using the calculus in the 1690 ’ s.

10. Bishop George Berkeley

11. Some of Berkeley’s questions

12. Frontispiece of Agnesi’s ‘Analytical Institutions’

13. A page from Agnesi’s book