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12 May 1815
Chrest. Tab. II Conclusion
Thus for the illustrious pair of Mathematicians. Now
those reasonings (raisonnement) so often mentioned, and
always as so many works or operations it perfectly distinct from those
which consist in the mere application of the Algebraic forms formulæ, what are they?
plainly the very things for the designation of which the word
contrivances for the coming at the solution of the problem
or some such words have all along been employed. This
much then is directly asserted: viz. that the operations, which
consist in the as it were mechanical application of them this set
of rules which for all cases is the same, on the one hand
and on the other hand those which cannot in the
other more particular contrivances for solving the particular
problem or part set of problems in question by
the application of those same general rules, are his
classes of operations perfectly distinct from each other.
But to moreover another thing which if though not directly
asserted seems all along to be implied, is that to
one or other of these two heads every thing that is or can
be done in the way of algebra is referable.
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