In this chapter we show that the characterization of certain mathematical entities as fictions, far from being an invention of Leibniz’s to deflect criticisms of his use of infinitesimals, was in fact part of a well-established tradition in the mathematics of his time. After documenting this tradition, we show how Leibniz’s use of the terms ‘fiction’ and its cognate ‘feign’ are consonant with this tradition. We then discuss the status of these fictions in his work with respect to possibility, and in particular the issue of entities such as imaginary roots of equations being “accidentally impossible” (impossibile per accidens).