‎"ROBINSON, ABRAHAM.‎
‎Non-Standard Analysis. - [THEORY OF INFINITESIMALS]‎

‎Amsterdam, North-Holland, 1966. 8vo. Publishers full cloth with dust jacket. Both in fine condition. Previous owners signature to front free end paper.Otherwise completely clean throughout. A fine copy.‎

Reference : 35775

‎First edition of this foundational work in mathematics. In this book Robinson gave the first rigorous formulation of Analysis using infinitesimals. Both Leibniz and Newton had used the notion of infinitesimals when they developed the Differentail and Integral Calculus in the 17th century. As Leibniz argued the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or large compared to the real numbers. However, neither he nor his disciples and succesors were able to give a rational development leading up to a system of this sort. As a result, the theory of infinitesimals gradually fell into disrepute and was replaced by eventually by the classical theory of limits. Robinson was the first to show that Leibniz's ideas in fact can be fully vindicated and that they lead to a fruitful approach to classical Analysis. He coined his model ""Non-Standard Anlysis"".‎