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����the implicit function theorem is. along with its close cousin the inverse func- tion theorem�� one of the most important�� and one of the oldest�� paradigms in modcrn mathemarics. one can see the germ of the idea for the implicir func tion theorem in the writings of isaac newton ��1642-1727���� and gottfried leib-niz's ��1646-1716�� work cxplicitty contains an instance of implicit differentiation. ����whilc joseph louis lagrange ��1736-1813�� found a theorcm that is essentially a version of the inverse function theorem�� ic was augustin-louis cauchy ��1789-1857�� who approached the implicit function theorem with mathematical rigor and it is he who is gencrally acknowledgcd as the discovcrer of the theorem. in chap-ter 2�� we will give details of the contributions of newton�� lagrange�� and cauchy to the development of the implicit function theorem.