ABSTRACT
And what are…fluxions? The velocities of evanescent increments? And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities? (George Berkeley)
1 The fundamental principles of the calculus
There is a cluster of mathematical problems which at first sight seem quite disparate but which come together in a remarkable way. They have a history going back at least as far as Eudoxus and Archimedes, with their method of exhaustion, and continuing to the present day. This history is a vital component strand within the broader history of the infinite. I turn to it now, because some of the most significant breakthroughs that go to make it up were made in the seventeenth century.
