Duncan Farquharson Gregory цитаты

Duncan Farquharson Gregory было британский математик.

✵ 13. Апрель 1813 – 23. Февраль 1844
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Duncan Farquharson Gregory: Цитаты на английском языке

“There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are
(1) ab(u) = ba (u),
(2) a(u + v) = a (u) + a (v),
(3) am. an. u = am + n. u.
The first of these laws is called the commutative law, and symbols which are subject to it are called commutative symbols. The second law is called distributive, and the symbols subject to it distributive symbols. The third law is not so much a law of combination of the operation denoted by a, but rather of the operation performed on a, which is indicated by the index affixed to a. It may be conveniently called the law of repetition, since the most obvious and important case of it is that in which m and n are integers, and am therefore indicates the repetition m times of the operation a.”

That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation.
p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Examples of the processes of the differential and integral calculus, (1841)

“It has always appeared to me that we sacrifice many of the advantages and more of the pleasures of studying any science by omitting all reference to the history of its progress: I have therefore occasionally introduced historical notices of those problems which are interesting either from the nature of the questions involved, or from their bearing on the history of the Calculus. …[T]hese digressions may serve to relieve the dryness of a mere collection of Examples.”

p. vi http://books.google.com/books?id=h7JT-QDuAHoC&pg=PR6, as cited in: Patricia R. Allaire and Robert E. Bradley. " Symbolical algebra as a foundation for calculus: DF Gregory's contribution http://poncelet.math.nthu.edu.tw/disk5/js/history/gregory.pdf." Historia Mathematica 29.4 (2002): p. 409.
Examples of the processes of the differential and integral calculus, (1841)

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