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.
需要一个完整的翻译 太专业化了,有点小困难 我由衷的感谢,感激那些帮助我的人.公式 不翻译了就可以了.

在19世纪三十和四十年代,英国数学家们特别是Peacock, Gregory, and De Morgan创造了现在众所周知的符号代数.他们的目标是建立代数学——对于他们来说,这意味着使用数字尤其是负数的规则——通过给它符合逻辑的理由使它和几何学处于相同地位.他们通过与算数代数——使用正数的规则——相区别来达到目的.符号代数是由Peacock 新创建的笼统地处理数字操作的一门新学科.虽然规则的内容是根据算术代数推出的,和所谓的永久等效原则一致,这个观点还是很先进的.Peacock 在他的论文《代数学》中对于符号代数的定义,被认为是19世纪早期的的一个重要陈述.这种观点领先于他所生活的时代将近一个世纪!当然也要等一个世纪才能将Peacock 所陈述的付诸于实践.然而,创造符号代数是具有重大意义的发展,就算与抽象代数的诞生没有直接关系.此外,虽然Peacock 没有明确说明“任意规则”的含义,他们后来被发展为定理要知道更多的细节请看1.8节.
有些术语我也不是很清楚,希望可以帮到你.