In pure algebra Descartes expounded and illustrated the general methods of solving equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.'
The equations to the asymptotes are = t y/b and x = =y respectively.
Some of the most important results of his discoveries were communicated to the Royal Society in two memoirs upon "Systems of Linear Indeterminate Equations and Congruences" and upon the "Orders and Genera of Ternary Quadratic Forms" (Phil.
A long list of Boole's memoirs and detached papers, both on logical and mathematical topics, will be found in the Catalogue of Scientific Memoirs published by the Royal Society, and in the supplementary volume on Differential Equations, edited by Isaac Todhunter.
The well-known Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of Finite Differences, designed to serve as a sequel to the former work.
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