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”.