The calculus - some dates: ‘ Prehistory ’ 1635 Cavalieri (student of Galileo), ‘ Geometry of indivisibles ’ Descartes, ‘ Geometry ’ Galileo, ‘ Discourse concerning two new sciences ’. The search for a method 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 The discovery Newton ’ s first notebook containing sketch of his method Newton ’ s major (unpublished) manuscript, ‘ Method of Fluxions ’ Leibniz ’ discovery of his method Newton ’ s two letters to Leibniz with (cryptic) accounts of his discoveries Leibniz ’ first publication (short paper) Newton ’ s ‘ Principia ’ - calculus hidden in geometric language. The follow-up ’ s The brothers Johann and Jakob Bernoulli learn Leibniz ’ method, and, with him, publish works applying it to problems First textbook: L ’ Hospital ’ s ‘ Analyse des infiniment petits ’ (help from Johann Bernoulli) Main period of the ‘ priority dispute ’ Berkeley ’ s attack in ‘ The Analyst ’ Maria Agnesi ‘Analytical Instituions’ first major unified textbook

Portrait of Newton, 1680s

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

Leibniz

Johann Bernoulli

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

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

Bishop George Berkeley

Some of Berkeley’s questions

Frontispiece of Agnesi’s ‘Analytical Institutions’

A page from Agnesi’s book