Fermat, Leibniz, Euler, and the Gang: The True History of the Concepts of Limit and Shadow

摘要

The theories as developed by European mathematicians prior to 1870 differed from the modern ones in that none of them used the modern theory of limits. Fermat develops what is sometimes called a "precalculus" theory, where the optimal value is determined by some special condition such as equality of roots of some equation. The same can be said for his contemporaries like Descartes, Huygens, and Roberval.