 The concept of infinitesimal was beset by controversy from its beginnings. The idea makes an early appearance in the mathematics of the Greek atomist philosopher Democritus c. 450 BCE, only to be banished c. 350 BCE by Eudoxus in what was to become official “Euclidean” mathematics. We have noted their reappearance as indivisibles in the sixteenth and seventeenth centuries: in this form they were systematically employed by Kepler, Galileo’s student Cavalieri, the Bernoulli clan, and a number of other mathematicians. In the guise of the beguilingly named “linelets” and “timelets”, infinitesimals played an essential role in Barrow’s “method for finding tangents by calculation” (1670 [1916: 119]), which appears in his Lectiones Geometricae of 1670. As “evanescent quantities” infinitesimals were instrumental (although later abandoned) in Newton’s development of the calculus, and, as “inassignable quantities”, in Leibniz’s. The Marquis de L’Hôpital, who in 1696 published the first treatise on the differential calculus (entitled Analyse des Infiniments Petits pour l’Intelligence des Lignes Courbes), invokes the concept in postulating that “a curved line may be regarded as being made up of infinitely small straight line segments” (1696: 3 [Postulate II]), and that “one can take as equal two quantities differing by an infinitely small quantity” (1696: 2 [Postulate 1]).