Full Idea
The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero.
Gist of Idea
Infinitesimals were sometimes zero, and sometimes close to zero
Source
Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2)
Book Reference
Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.121
A Reaction
Colyvan gives an example, of differentiating a polynomial.