Illustration from Newton's *Principia* for his
proof that for a monotonic

function *f* defined
on an interval [*A,E*] the difference between the
upper

and lower sums with *n* equal subdivisions
is equal in absolute value to

(*f*(*E*)-*f*(*A*))(*E*-*A*)/*n*
(and therefore goes to 0 as *n* goes to infinity). Here *n*=4.

## SUNY at Stony Brook -- Calculus II -- Spring 1998

*
Anthony Phillips*

Math Dept SUNY Stony Brook

tony@math.sunysb.edu

May 5 1998