## A Treatise on the Calculus of Functions |

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algebraical forms algebraical solutions analogy Analytical Society appear arbitrary constant arbitrary function arithmetical assume Babbage Calculus of Functions common Algebra Consequently considered continuous functions convertible functions cosine deduced denote derivative determine Differential Calculus differential equation discontinuous function eliminate equa equation of differences exponential inverse expression fiax finite func functional equation functional inverses functional symbol given function gives Hence inconvertible inverses independent infinite number instance integral inverse functions limit logarithm means modulus notation nth function nth roots obtained particular solution periodic function preceding equation preceding method question reduced relation result roots satisfies the equation second order sidered simultaneous substitution solu solve the equation substitution successive functions suppose symmetrical function theorem tion transcendental true whence whole number write zero zero-function