Descartes actually published the law first. We do not know whether he
learned it from Snell, who published his version around 1620. Descartes
does not refer to Snell in his own writings. See Descartes' Optics,
"Discourse Two: Refraction" in The Philosophical Writings of Descartes,
Volume I, translated by John Cottingham, et. al. (Cambridge: Cambridge
University Press, 1985), page 163. In the Principia Newton inferred the
sine law for a "hypothetical" body moving under the influence of an
attractive force in Book I, Proposition XCV, Theorem XLIX and Proposition
XCVI, Theorem L. In the Scholium following these two Propositions, Newton
claims: "These attractions bear a great resemblance to the reflections and
refractions of light made in a given ratio of secants, as was discovered by
Snell; and consequently in a given ratio of sines, as was exhibited by
Descartes." Principia, page 229.
Pierre J. Boulos
Department of Philosophy Managing Editor
The University of Western Ontario Informal Logic
pboulos@julian.uwo.ca
infolog@uwindsor.ca
boulos@uwindsor.ca
-----Original Message-----
From: owner-historia-matematica@chasque.apc.org
[mailto:owner-historia-matematica@chasque.apc.org]On Behalf Of Roger Cooke
Sent: Sunday, October 18, 1998 11:08 PM
To: Rebecca Berg
Cc: historia-matematica@chasque.apc.org; ducel@vega.univ-fcomte.fr
Subject: Re: [HM] Snell, Fermat, light rays, and all that
At the time (17th century) I'm not sure, though I believe Descartes has
some claim to this law also. Refraction was studied by Ptolemy, who gave
a table of angles of refraction for a few media. However, the tables give
the angle of refraction as a strictly quadratic function of the angle of
incidence, which is very close to Snell's law, but not exact.
It would be interesting to know how Ptolemy decided to give these values,
since he didn't have the concept of a quadratic function, of course. I
suspect he DID have the concept of equal second differences, however, as
(I think) did the Chinese about the same time.
Roger Cooke