Hamilton, W. R. (1837): Theory of Conjugate Functions, or Algebraic Couples

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Hamilton (1837): William Rowan Hamilton; Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time; The Transactions of the Royal Irish Academy; Band: 17; Seite(n): 293 – 422; Verlag: Dublin; Web-Link; 1837; Quellengüte: 5

1 Attribute

KürzelHamilton (1837)
QuellenartKonferenzartikel
Autor(en)William Rowan Hamilton
TitelTheory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time
BuchtitelThe Transactions of the Royal Irish Academy
Band17
Seite(n)293 – 422
VerlagDublin
URLhttps://archive.org/details/transactionsofro17iris
SpracheEnglisch
Jahr1837
Datum1837
Quellengüte5

2 BibTeX

 @inproceedings{GlossarWiki:Hamilton:1837, 
   author = {Rowan Hamilton, William}, 
   title = {Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time}, 
   booktitle = {The Transactions of the Royal Irish Academy}, 
   publisher = {Dublin}, 
   volume = {17}, 
   pages = {293--422}, 
   year = {1837}, 
   url = {https://archive.org/details/transactionsofro17iris}, 
   quality = {5}, 
   note = {}
 }

3 Zitiert durch

4 Ausschnitt

Von diesem Papier, das 1937 publiziert wurde, reichte Hamilton 1933 eine erste Version ein.
Seite 293, Letzter Abschnitt des Titelbereichs:

Read November 4th, 1833, and June 1st, 1835.

Hamilton fordert, dass die komplexen Zahlen als reelwertige Paare aufgefasst werden sollten.
Seite 297, Fußnote ‡:

The author acknowledges with pleasure that he agrees with M. Cauchy, in considering every (so-called) Imaginary Equation as a symbolic representation of two separate Real Equations; but he differs from that excellent mathematician in his method generally, and especially in not introducing the sign $\sqrt{-1}$ until he has provided for it, by his Theory of Couples, a possible and real meaning, as a symbol of the couple $(0,1)$.

Die Idee, dass komplexe Zahlen als Paare reeler Zahlen aufgefasst werden sollten, hat Hamilton schon 1834 in Edinburgh vorgetragen; der Vortrag wurde 1835 publiziert: „On Conjugate Functions, or Algebraic Couples“.

Hamilton formuliert in diesem Papier für den von ihm geprägten Paarbegriff erstmals das Paaraxiom.

Considering now any two other dates $C$ and $D$, we perceive that they may and must represent either the same pair of moments as that denoted by the former pair of dates $A$ and $B$, or else a different pair, according as the two conditions,

[math]C = A[/math], and [math]D = B[/math],

are, or are not, both satisfied.

Hamilton betont, dass die Idee der Konjugierten Funktionen auf seinen Freund und Kollegen John T. Graves zurückgeht.
S 392:

... suggested by those researches of Mr. Graves respecting the general expression of powers and logarithms, which were the first occasion of the conception of that Theory of Conjugate Functions to which we now proceed.

Die von John Graves im Jahr 1829 publizierten Resultate[1] wurden teilweise von anderen Mathematikern angezweifelt. Hamilton bewies dieselben Resultate mit Hilfe seine Algrabraischen Paare nochmals.

5 Quellen

  1. John Graves, An Attempt to Rectify the Inaccuracy of Some Logarithmic Formulae, in: Philosophical Transactions of the Royal Society of London, Vol. 119 (1829), pp. 171-186