 This slope is equal to \(\frac{(x+\epsilon)^2-x^2}{\epsilon}\). In order for this fraction to make sense, \(\epsilon\) must be non-zero. However, we can calculate that this value is \(\frac{2x\epsilon+\epsilon^2}{\epsilon}\), or \(2x+\epsilon\). At this point, we no longer need \(\epsilon\) to be non-zero, so the slope can be said to be just \(2x\). This sort of slippage between non-zero and zero for these infinitesimals is what made Berkeley refer to them as “the ghosts of departed quantities”. However, engineers, scientists and mathematicians who actually made use of the calculus rested content in the knowledge that the calculus delivered the goods.