Re: [HM] James Gregory and Brook Taylor

James A Landau (JJJRLandau@aol.com)
Wed, 13 Jan 1999 22:14:41 EST

In a message dated 99-01-13 12:38:12 EST, David Fowler quoted Dennis Almeida:
<<
> From: Dennis Francis Almeida <D.F.Almeida@exeter.ac.uk>
> To: dfh@maths.warwick.ac.uk
> Subject: James Gregory and Brook Taylor
>
> I write to you in regard to a research enquiry. This
> relates to the epistemological similarities between medieval
> Indian mathematics and the precalculus works in Europe. I
> would be grateful for advice on reliable papers in English
> which analyse Gregory's 'Geometriae pars Universalis' and
> Taylor's 'Methodus incrementorum directa et inversa'.
>
> Many thanks,
>
> Dennis Almeida, Lecturer in Mathematics Education,
> University of Exeter
>>

Our correspondents in India are working on a similar topic. Consult the HM
archive at
http://forum.swarthmore.edu/epigone/historia_matematica/

and look for a thread from 16 Jul 1998 about "RA in History of the Calculus"

I don't know if it will be useful, but you might try to find H.W. Turnbull,
ed _James Gregory Tercentenary Memorial Volume_ London: 1939.

Turnbull and J.F. Scott edited the 4-volume _The Correspondence of Isaac
Newton_ (Cambridge England: The University Press, 1959), which contains
considerable interesting material about Newton and his contemporaries but
does not offer much in the way of epistemology.

And now for something that is probably useless. The only way that I can
think of for transmission of mathematical ideas between India and Europe
in the era 1500-1700 is via Catholic missionaries who went to India after
Vasco da Gama opened a sea route from Europe to India. It is plausible
that among these missionaries were some who were well trained in math and
who took the trouble to read, and translate into Latin, the works of Indian
mathematicians such as Madhava.

I have no idea of where to look for books in Portugal but I have a little
familiarity with www.bne.es, which is the on-line catalog of the Biblioteca
Nacional de Espan~a.
A quick search showed 15 titles in math dating from before 1700, of which
the following two might just have some material on Indian mathematics and
epistemology:

Hugonis Sempilii ... Societate Iesu De Mathematieis disciplinis libri duode
Seplinius, Hugo (S.J.), 1635

Methodus admirandorum mathematicorum : novem libris exhibens universam math
Alsted, Johann Heinrich, 1641