Query: unknown quantities (fwd)

[Francois Patte]

Mary McGee wrote:

> Kim Plofker at Brown provided this response to the recent posting
> regarding mathematical texts.  I forward it as another piece of
> information on this matter.
>
> Mary McGee
>
> ---------- Forwarded message ----------
> Date: Tue, 22 Sep 1998 17:36:22 -0400 (EDT)
> From: Kim Plofker <Kim_Plofker at Brown.edu>
> To: Mary  McGee <mm383 at columbia.edu>
> Subject: Re: Query: unknown quantities (fwd)
>
> Mathematical texts generally use verbal abbreviations for unknown quantities
> (e.g., "ya" for the first syllable of "yavat").  I've read that different
> colors of ink were used for different variables (hence, I suppose, Bhaskara's
> terms "ekavarna" and "anekavarna" for equations in one or more unknowns,
> respectively), but I've never seen this used.  Look in Datta & Singh's
> _History of Hindu Mathematics_ or Hayashi's _The Bakhshali Manuscript_ for
> detailed discussions.
>
> Kim

Here is the stanza from Bhaskara's bijaganitam:

yaavattaavatkaalako niilako.anyo var.na.h piito
lohita"scaitadaadyaa.h|
avyaktaanaa.m kalpitaa maanasa.mj~naastatsa.mkhyaana.m
kartumaacaaryavaryai.h||

black, blue, yellow, red are the first names of unknown quantities that we use
to note: x, y, z, t ...

To calculate there is a formalism:

yaa 3 ruu 5 means: 3x + 5 (ruu stands for ruupa.m: "integer")

yaava 5 yaa 3 ruu 2 means: 5x^2 + 3x + 2 (va stands for varga.h: square)

This can be more sophisticated:

yaava 2 kaava 3 niiva 2 yaakaabhaa 23 yaaniibhaa 12 kaaniibhaa 6 yaa 2 kaa 9 nii
5 ruu 7

2x^2 + 3y^2 + 2z^2 + 23xy + 12 xz + 6 yz + 6x + 9y + 5z + 7

bhaa, in yaakaabhaa stands for bhaavita.m: "product"

There is also a minus sign: a dot over the number, but I don't know how to
produce it with my keyboard!

-- François Patte. UFR de mathématiques et informatique.
45 rue des St Pères. 75270 Paris Cedex 06
Tel: 01 44 55 35 59 -- Fax: 01 44 55 35 35
http://www.math-info.univ-paris5.fr/~patte