Searching for the historical development of the quadratic formula

[BURT]

Who was the first mathematician to developed the quadratic equation?

[Dave L. Renfro]

BURT wrote:

> Who was the first mathematician to developed the
> quadratic equation?

This is quite a bit more complicated than you might
have thought. (I assume you meant "developed a method
for solving quadratic equations" instead of "developed
the quadratic equation".) For example, does a geometric
method that makes little reference to numerical magnitudes
qualify? What about solutions that avoid negative numbers?
What about solutions to specific equations that implicitly
give a method for solving a general class of equations,
but the generalization is never explicitly mentioned?

Also, several methods date back to the Greeks (Euclid's
era) and even earlier, but in most (all?) these cases, no
specific person can be identified with the methods. Instead,
the identification is to a certain culture of people and to
a period of time that might only be known to within several
hundred years.

http://www.google.com/search?q=Babylonians+quadratic+equations

The best historical reference I know of is:

Solomon Gandz, "The origin and development of the quadratic
equations in Babylonian, Greek, and early Arabic Algebra",
Osiris 3 (1937), 405-557. [yes, this paper is 154 pages]

Also useful are:

Sister M. Thomas A. Kempis Kloyda, "Linear and quadratic
equations 1550-1660", Osiris 3 (1937), 165-192.

Caroline Eucebia Schuler [Shuler], "Application of
professional treatment to the quadratic function",
School Science and Mathematics 37 #5 (May 1937), 536-548.

For some methods for solving quadratic equations, see:

http://groups.google.com/group/sci.math/msg/e68fe847c3cbea56

http://www.pballew.net/quadsol.doc

I happen to have .pdf files of the Gandz and Kloyda papers.
Assuming the e-mail associated with your post (as viewed
at google-groups) is valid, they should be in your mailbox
now. I also have a high quality 130% magnification photocopy
of the Schuler paper, but right now it's in a second floor
hallway (along with several thousand books and over 100,000
pages of manuscripts, preprints, photocopies of papers and
rare and/or out-of-print math books, etc.) of my apartment
building that is presently surrounded by, and whose first
floor level (where my apartment is/was) is filled with,
about 4 feet of flood water.

Dave L. Renfro

[mahfoud belhadj]

it's the same question as " who invented the wheel " and probably the same
answer. No one in particular, many were involved.