 The literature in this area is enormous and we refer to Goldenbaum and Jesseph (2008) for a recent collection of essays on Leibnizian infinitesimals. The debates on the foundations of the calculus led to some lively contributions, such as Berkeley’s The Analyst (1734) and more mathematical work. But even after infinitesimals were eliminated from the calculus through the combined work of Cauchy, Bolzano, Dedekind, and Weierstrass in the 19th century, they were widely employed in geometry. Moreover, contemporary alternative theories of analysis (non-standard analysis, infinitesimal analysis etc.) have led to rigorous theories that, taken with a grain of salt, can be seen as vindicating some of the 17th century intuitions. We will come back to these developments below.