[FOM] origin of "real"

Irving Anellis irving.anellis at gmail.com
Tue Sep 20 14:29:00 EDT 2011

As Alasdair Urquhart wrote in reply to the question of Thomas Lord on
the origin of "real":

> The origin of the term lies in the 17th century,
> I think, in connection with the solution of
> algebraic equations.  For example, here is
> Descartes in "La Geometrie" (1637):
>  	Neither the true nor the false roots are
>  	always real, sometimes they are imaginary;
>  	that is, while we can always imagine as
>  	many roots for each equation as I have
>  	assigned, yet there is not always a definite
>  	quantity corresponding to each root we
>  	have imagined.
> Thus, the term "real" was introduced as a contrast
> to "imaginary."  This does have some connection
> with the explanation offered below, since
> Descartes no doubt thought of "real solutions"
> as being solutions in the "real world."

The term was introduced by Descartes in French in 1637 in order to
establish a contrast with "imaginary".

The term "real part" was used by Sir William Rowan Hamilton in an 1843
paper. He was referring to the vector and scalar portions of a
quaternion."Real part" also occurs in a paper by Hamilton in
Philosophical Magazine XXIX (1846), p. 26, where he wrote: "The
algebraically real part may receive, according to the question in
which it occurs, all values contained on the one scale of progression
of numbers from negative to positive infinity; we shall call it
therefore the scalar part, or simply the scalar of the quaternion, and
shall form its symbol by prefixing, to the symbol of the quaternion,
the characteristic Scal., or simply S"

Someone on a history of mathematics discussion group or history of
mathematics list should be able to provide a much more definitive and
detailed reply.

Irving H. Anellis

Visiting Research Associate
Peirce Edition Project
Indiana University-Purdue University at Indianapolis

More information about the FOM mailing list