Algebra
Project Gutenberg EPUB3 edition
Poincaré, Henri and Halsted, George Bruce
The theory of algebraic equations will still long hold the attention of geometers; numerous and very different are the sides whence it may be attacked.
We need not think algebra is ended because it gives us rules to form all possible combinations; it remains to find the interesting combinations, those which satisfy such and such a condition. Thus will be formed a sort of indeterminate analysis where the unknowns will no longer be whole numbers, but polynomials. This time it is algebra which will model itself upon arithmetic, following the analogy of the whole number to the integral polynomial with any coefficients or to the integral polynomial with integral coefficients.