> Philip G. Drazin, math and science contributor for the revision of
> the Oxford English Dictionary, asked whether readers of the math
> words web page I maintain could assist him in finding the earliest
> use in English of the term "continued fraction."
I'm afraid I can add only a little to what David Fowler already posted.
Julian Lowell Coolidge _The Mathematics of Great Amateurs_ (Oxford
University Press 1949, reprinted by Dover in 1963) has a chapter on
Brounker. Coolidge gives the following additional info:
- J. F. Scott _The Mathematical Work of John Wallis_ Oxford, 1936
discusses Wallis's and Brounker's work on continued fractions
- Coolidge references Wallis's _Arithmetica Infinitorum_, for which
the publication date given is 1665. Coolidge refers to "pp. 47-60";
it is not clear whether these are pages in Scott or in _Arithmetica
Infinitorum_
- Coolidge quotes Wallis (Opera volume i page 475) as saying "Esto
igitur fractio eiusmode continue fracta quaelibet sic deignata
a b c d e
------ ------ ------- ------- --------- etc
alpha beta gamma delta epsilon
(I have my computer set to Courier (a monospaced font) for typing the
above, so hopefully the spacing will be correct.)
- Coolidge's bibliographic reference to Schwenter is "Schwenter, Daniel,
1585-1636, Geometriae practicae novae et auctae Tractatus, Nuremberg,
1626, 138."
- Coolidge says that there were two Italian mathematicians, Raffaele
Bombelli and Peitro Cataldi, who worked with continued fractions, and
gives footnotes to Bortolotti, Ettore, 1866- , 'La scoperta della
frazioni continue', Bollettino della Methesis, Anno xi, 1919, 138.
and to Tropfke, Johannes, 1866-1939, Geschichte der Elementarmathematik,
2nd ed., Berlin, 1921, vol vi, pp. 75ff.
If the hypochondriac office photocopier hasn't thought of something
new, a copy of Coolidge will be in the mail to you shortly. I will also
check Struik pp. 244-251 (apparently David Fowler does not have access
to a copy) and see if it contains anything interesting.