[Rarebooks] For Sale: A Unique and Important 19th Century Manuscript on the Geometry of Higher Dimensional Space

[Michael John Thompson]

GOSSET, Thorald. (1869–1962), English lawyer and an amateur mathematician.

ON THE REGULAR & SEMI-REGULAR FIGURES IN n 
DIMENSIONS. Original handwritten manuscript, 
circa 1899, 94 pp. on lined foolscap, 26 lines to 
a page, accompanied by 4 pages of diagrams. Also 
present are 2 Autograph Letters Signed, both 
dated 1899. The first letter is from the 
mathematician William Burnside (1852 - 1927) to 
James W. Glaisher, editor of the journal 
'Messenger of Mathematics', the second from 
Burnside to Gosset. In the first letter Burnside 
states that he has only read half the MS., and 
that he finds "the author's method, a sort of 
geometric intuition", unappealing. The second 
letter discusses Gosset's theories, refering to 
them as "geometrical intuition", but also stating 
that he should be sorry if Gosset was to discontinue his investigations.

According to H. S. M. Coxeter (Regular Polytopes, 
New York: Dover Publications, 3rd edition) 
Gosset, after attaining his law degree in 1895 
and having no clients, amused himself by 
attempting to classify the regular polytopes in 
higher dimensional (greater than three) Euclidean 
space. After rediscovering all of them, he 
attempted to classify the "semi-regular 
polytopes", which he defined as polytopes having 
regular cells and which are vertex-uniform, as 
well as the analogous honeycombs, which he 
regarded as degenerate polytopes. In 1897 he 
submitted his results to James W. Glaisher, then 
editor of the journal Messenger of Mathematics. 
Glaisher was favourably impressed and passed the 
results on to William Burnside and Alfred 
Whitehead. Burnside was not particularly 
impressed, and in the end Glashier published only 
a brief abstract of Gosset's results (in 
Messenger of Mathematics 29, 1900, pp 43-49), a 
photocopy of which is included here (heavily 
annotated with notes in pen by mathematician and 
mystical philosopher Charles Muses).

Gosset's results went largely unnoticed for many 
years. His semiregular polytopes were 
rediscovered by Elte in 1912 (The Semiregular 
Polytopes of the Hyperspaces, University of 
Groningen, 1912) and later by Coxeter who gave both Gosset and Elte due credit.

While a brief abstract of this MS was published 
in 1900, the MS has never been published in its entirety.

 From the library of Charles Muses.

With thanks to Wikipedia for information on Gosset.


$500.00 Cdn, postpaid

Pictures and description:

http://www.mjtbooks.com/gosset/



---
Michael John Thompson
ABAC / ILAB
5275 Jerow Road
Hornby Island, BC
Canada V0R 1Z0
250-335-1182

http://www.ThompsonRareBooks.com
http://www.BeltaneBooks.com
http://www.Mjtbooks.com