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History of the Theory of Imaginary and Complex Quantities

Published online by Cambridge University Press:  03 November 2016

G. Windred
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Extract

It is worthy of note that the imaginary was introduced into mathematics in the course of strictly non-utilitarian researches on the theory of quadratic equations, being for a long time rejected by the mathematicians as an entirely useless conception. This formal condemnation of the imaginary seems less extraordinary when we recollect that at the time of its inception, and indeed for long afterwards, serious scruples were experienced by some mathematicians even regarding the admission of negative quantities in their results. The last writers who objected to the use of negative quantities were Baron Maseres, a Fellow of Clare College, Cambridge, and William Frend, a second wrangler. Both these men had written extensively in condemnation of the use of negative quantities; their attitude in this matter is clearly evinced by the following extract from the preface to Frend’s Principles of Algebra, published in 1796, at which period, strangely enough, the notion of the imaginary was firmly eatablished.

Type
Research Article
Information
The Mathematical Gazette , Volume 14 , Issue 203 , October 1929 , pp. 533 - 541
Copyright
Copyright © Mathematical Association 1929

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References

page 534 note * Also v. De Morgan’s review of his father-in-law’s book, Budget of Paradoxes, 1872, pp. 117-125.

page 535 note * The best account of Wallis’s graphical constructions is contained in the article “Die geometrische Darstellung imaginärer Grössen bei Wallis,” by G. Enestrom, Bibliotheca mathematica, series 3, vol. 7, 1906, pp. 263-269.

page 536 note * Vide G. H. Hardy, Some Famous Problems of the Theory of Numbers, Oxford, 1920, p. 14 et seqq.

page 538 note * For detailed references to these investigators, cf. J. L. Coolidge, Geometry of the Complex Domain, Oxford, 1924, p. 32 et seqq.

page 540 note * Hamilton derived this symbol from the initial letter of the Latin word Oppositio, distinguished by a bar across it from the same letter used for other purposes.

page 540 note † Op. cit. p. 417.

page 540 note ‡ Op. cit. p. 404.

page 541 note * Kant und die moderne Mathematik in Kant-Studien, xii. (1907), p. 34. Vide etiam, N. K. Smith, A Commentary to Kant’s “Critique of Pure Reason” (1918), p. 128 et seqq.

page 541 note ‡ Ibidem, p 135.