cover -- title page -- copyright page -- Preface -- The Ancients -- Zeno holds a mirror to the infinite -- The `infinitely small' -- Archimedes exhausts a parabolic segment -- Patterns -- The evolution of notation -- Furthermore -- East of Greece -- Ibn al-Haytham sums the fourth powers -- Ibn al-Haytham's parabolic volume -- Jyesthadeva expands 1/(1+x) -- Jyesthadeva expresses as a series -- Furthermore -- Curves -- Oresme invents a precursor to a coordinate system -- Fermat studies the maximums of curves -- Fermat extends his method to tangent lines -- Descartes proposes a geometric method -- Furthermore -- Indivisibles -- Cavalieri's quadrature of the parabola -- Roberval's quadrature of the cycloid -- Worry over indivisibles -- Furthermore -- Quadrature -- Gregory studies hyperbolas -- De Sarasa invokes logarithms -- Brouncker finds a quadrature of a hyperbola -- Mercator and Wallis finish the task -- Furthermore -- The Fundamental Theorem of Calculus -- Newton links quadrature to rate of change -- Newton reverses the link -- Leibniz discovers the transmutation theorem -- Leibniz attains Jyesthadeva's series for -- Furthermore -- Notation -- Leibniz describes differentials -- The fundamental theorem with new notation -- Leibniz integrates the cycloid -- Furthermore -- Chords -- Preliminary results known to the Greeks -- Jyesthadeva finds series for sine and cosine -- Newton derives a series for arcsine -- Furthermore -- Zero over zero -- D'Alembert and the convergence of series -- Lagrange defines the `derived function' -- Taylor approximates functions -- Bolzano and Cauchy define convergence -- Furthermore -- Rigor -- Cauchy defines continuity -- Bolzano invents a peculiar function -- Weierstrass investigates the convergence of functions -- Dirichlet's nowhere-continuous function -- A few final words about the infinite -- Furthermore.

References -- Index -- About the Author.