From: Klaas Pieter Hart <hart@dutiaw4.twi.tudelft.nl>
Subject: Re: cauchy-bunyakovskii inequality
Date: Thu, 11 Feb 1999 09:15:59 +0100
Newsgroups: sci.math.research
Keywords: history of the "Cauchy-Schwarz inequality"

On Thu, 4 Feb 1999, G. A. Edgar wrote:

> My understanding is this:
> 
>   Cauchy was first, and stated it for sums.
>   Bunyakovskii was next, and stated it for integrals.
>   Schwarz was third, and stated it for arbitrary inner products.
> 

Actually, Schwarz stated it for integrals over surfaces; I traced it back
to this paper, which you can find in his own `Gesammelte Mathematische
Abhandlungen' of 1890.

@article{Schwarz1885,
author = "H. A. Schwarz",
title = "Ueber ein die {Fl\"achen} kleinsten {Fl\"acheninhalts}
         betreffendes Problem der {Variationsrechnung}",
journal = "Acta societatis scientiarum Fennicae",
volume = "XV",
year = 1885,
pages = "315--362"}

KP

E-MAIL: K.P.Hart@twi.tudelft.nl       PAPER: Department of Pure Mathematics
PHONE:  +31-15-2784572                       TU Delft
FAX:    +31-15-2787245                       Postbus 5031
URL:    http://aw.twi.tudelft.nl/~hart       2600 GA  Delft
                                             the Netherlands
==============================================================================

From: wcw@math.psu.edu (William C Waterhouse)
Subject: Re: cauchy-bunyakovskii inequality
Date: 11 Feb 1999 21:36:42 GMT
Newsgroups: sci.math.research

In article <110219991322315131%edgar@math.ohio-state.edu.nospam>, 
"G. A. Edgar" <edgar@math.ohio-state.edu.nospam> writes:
>...> 
> Does someone have a Buniakovsky date?  Is it earlier than 1885?

I haven't checked back to the source from which I drew (namely,
the Dictionary of Scientific Biography), but a paper I published about
fifteen years ago mentioned in passing that his version was published 
in 1859. The problem was that it appeared in a Russian-language pamphlet,
and so (unlike his French papers in journals) it did not attract 
attention elsewhere.

William C. Waterhouse
Penn State
==============================================================================

From: Klaas Pieter Hart <hart@dutiaw4.twi.tudelft.nl>
Subject: Re: cauchy-bunyakovskii inequality
Date: Mon, 15 Feb 1999 10:17:25 +0100
Newsgroups: sci.math.research

On Thu, 11 Feb 1999, G. A. Edgar wrote:

> 
> Does someone have a Buniakovsky date?  Is it earlier than 1885?
> 

I culled this from the Soviet Encyclopaedia of Mathematics
(available in translation from Kluwer).

@article{Bunyakovskii1859,
author = " V. Bunyakovski\u{\i}",
title = "Sur quelques in\'egalit\'es concernant les int\'egrales
         ordinaires et les int\'egrales aux diff\'erences finies",
journal = "M\'em. Acad. St. Petersbourg",
year = 1859,
volume = 1}

I never saw the paper though.

KP

E-MAIL: K.P.Hart@twi.tudelft.nl       PAPER: Department of Pure Mathematics
PHONE:  +31-15-2784572                       TU Delft
FAX:    +31-15-2787245                       Postbus 5031
URL:    http://aw.twi.tudelft.nl/~hart       2600 GA  Delft
                                             the Netherlands