Imaginary Quantities: Their Geometrical Interpretation

148 Pages·1881·4.418 MB·English

by  Jean Robert Argand

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lMjlGlî(AfiY Qu>î(TITIES:
THEIR GEOMETRICAL
INTERPRETATION,
.
Translated, fron-i the French of M. Argand
BY
HARDY.
Prof. A. S.
BEPBINTED FROM VAN NOSTRAND'S MAGAZINE.
NEW YORK:
D. VAN NOSTRAND, PUBLISHER,
23 MtiRRAT AND27 Warren Streets.
881.
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PRE
FACE.
The work now republished* is of that
small number which mark an epoch in
the history of science. In this short
treatise is found the germ of the true
theory of so-called hnaglnary quanti-
ties. Although generally attributed to
the genius of Gauss, this theory was not
pointed out by that great geometer until
twenty-five years after the publication of
Argand's work,t and it had been mean-
while re-discovered several times in both
France and England. On this point we
can cite no testimonv more convincing-
than that of a German geometer, whose
recent death is deplored by science.
Says Hankel,! -Hhe first to show how to
represent the imaginary forms A-i-B/ by
points in a plane, and to give rules for
*1stedition, Paris. Duminil-Lesueur, 1806.
tAnzeige zur '' Theotia residiiorion biquadroticuin
Vmnmeiitalto^e^'/nda,'^ 1831 (Gauss Werke, t. II, p. 174».
XVwiemiiigtii nberdieconipl^aen Zafden undihre/>io.<-
tioritm». (Leipzig. 18«T. p. 82>.
IV
their geometric addition and multiplica-
tion, was Argand, who established his
theory in a pamphlet printed in Paris, in
1806, under the title ^JEssai sur vne
manière de représenter les quantités im-
aginaires dans les constructions géomét-
onques.' Yet this paper did not meet
with public recognition until after the
insertion of a note by J. F. Français, in
the Annales de Gergonne, Vol. IV, 1813,
1814, p. 61, in which, at the same time,
Argand* also published two articles.
In these articles the subject was so
exhaustively treated that nothing new
has since been found to add to them,
and, unless some older work is dis-
covered, Argand must be regarded as
the true founder of the theory of com-
plex quantities in a plane.
....
" In 1831, Gausst devel-
oped the same idea, as is well known;
but, however great his merit, as bring-
ing this idea to the notice of science, it
is none the less impossible to claim for
him
i^riority."
*Vol. IV, p. 133. and \ul. V. p. V.\7.
! Works. Vol. II, J). 174.