"We have ten elementary formulas; and, few as they are, they may give rise to an infinite number of analytical combinations. There is no reason for supposing that there can never be more. We have more than Descartes had, and even Newton and Leibnitz; and our successors will doubtless introduce additions, though there is so much difficulty attending their augmentation, that we cannot hope that it will proceed very far."
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Ref: Auguste Comte, "Enumeration of Functions, The Philosophy of Mathematics (1851) Book I. Analysis, Ch I. General View of Mathematical Analysis, p. 51, translated by W. M. Gillespie from the Cours de Philosophie Positive of Auguste Comte:1st couple(Sum, Difference); 2nd couple(Product, Quotient); 3rd couple(Power, Root), 4th couple(Exponential, Logarithmic), 5th couple(Direct Circular, Inverse Circular).
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