The philosophy of mathematics · Auguste Comte
THE THEORY OF EQUATIONS.
These two departments, which constitute the immediate object of the calculus of direct functions, are subordinate to a third one, purely speculative, from which both of them borrow their most powerful resources, and which has been very exactly designated by the general name of _Theory of Equations_, although it as yet relates only to _Algebraic_ equations. The numerical resolution of equations, because of its generality, has special need of this rational foundation. This last and important branch of algebra is naturally divided into two orders of questions, viz., those which refer to the _composition_ of equations, and those which concern their _transformation_; these latter having for their object to modify the roots of an equation without knowing them, in accordance with any given law, providing that this law is uniform in relation to all the parts.[9]
Text from Project Gutenberg, public domain in the United States.