In this paper we go through the historical, logical and mathematical paths which join infinitesimal calculus to the non-standard analysis of Abraham Robinson, and this to paraconsistent differential calculus - a calculus proposed by Newton da Costa, supported by paraconsistent logic and paraconsistent set theory. We present for this calculus, some unpublished concepts and properties, including a transfer theorem establishing the conditions under which a given formula is a theorem of classical calculus if, and only if, there is an "interpretation" of the same which is a theorem of paraconsistent calculus. We conclude the paper with some considerations about the teaching of Calculus with emphasis on use of infinitesimal approach.
Calculus infinitesimalis; Paraconsistent calculus; Non-standard analysis; History; Costa, Newton da
