英语翻译4.5 Symbolical algebraIn the third and fourth decades of
英语翻译
4.5 Symbolical algebra
In the third and fourth decades of the nineteenth century British mathematicians,
notably Peacock,Gregory,and De Morgan,created what came to be known as
symbolical algebra.Their aim was to set algebra—to them this meant the laws of
operation with numbers,negative numbers especially—on an equal footing with
geometry by providing it with logical justification.They did this by distinguishing
between arithmetical algebra—laws of operation with positive numbers,and symbolical algebra—a subject newly created by Peacock which dealt with laws of operation with numbers in general.
Although the laws were carried over verbatim from those of arithmetical algebra,
in accordance with the so-called Principle of Permanence of Equivalent Forms,the
point of view was remarkably modern.Witness Peacock’s definition of symbolical
algebra,given in his Treatise of Algebra,as
The science which treats of the combinations of arbitrary signs and symbols
by means of defined though arbitrary laws.
Quite a statement for the early nineteenth century!Such sentiments were about a
century ahead of their time.And of course one did have to wait about a century to
have what Peacock had preached put fully into practice.Nevertheless,the creation
of symbolical algebra was a significant development,even if not directly related to
fields,signalling (according to some) the birth of abstract algebra.Moreover,although
Peacock did not specify the nature of the “arbitrary laws,” they turned later in the
century into axioms for rings and fields.See Chapter 1.8 for further details.
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