By L. Auslander, R. Tolimieri
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Extra info for Abelian Harmonic Analysis Theta Functions and Function Algebras on a Nilmanifold
In almost all contexts in 18th - and 19th -century writings, however, the adjective does not in fact qualify the noun equation. It refers instead to what the writer has in mind as a strategy for solution. The former refers to the search for a formula, the latter to iterative numerical methods. Thus Lagrange’s great works [Lagrange (1767)], [Lagrange (1798)], with titles involving la résolution des équations numériques have the adjective numerical qualifying the plural noun equations, and yet their subject is numerical methods for finding accurate approximations to the roots of polynomial equations.
If one casts a general glance over algebra, one sees first that, setting aside ordinary operations (numbered among which one can include elimination), this science is divided naturally into three principal parts. 1st. The general theory of equations, that is to say, the collection of properties which are common to all of them. 2nd. Their general solution, which consists in finding an expression composed of the coefficients of the given equation, and which, replacing the unknown, satisfies this equation identically, so that everything vanishes simply through cancellation.
Some of these may be not so much mis-spellings as dated usage, such as ‘tems’ for ‘temps’. Others may be not so much mis-spellings as haste—a circumflex accent might easily emerge like a grave accent late on a pre-duel evening. The lists below are unlikely to be complete—I did not start compiling them until well into the work. I hope, however, that they may give the reader some idea of the problem. Now that images of the manuscripts have (from June 2011) become available through web-publication in digitised form (see [Galois (2011)], p.
Abelian Harmonic Analysis Theta Functions and Function Algebras on a Nilmanifold by L. Auslander, R. Tolimieri