A WEEKLY ILLUSTRATED JOURNAL OF SCIENCE 
* To the solid ground 
Of Nature trusts the mind which builds for aye.” —WORDSWORTH 
THURSDAY, MAY 7, 1885 
GREEK MATHEMATICS 
A Short History of Greek Mathematics. 
M.A. 
or 
By James Gow, 
(Cambridge University Press, 1884.) 
HERE are three classes of persons who, being 
mathematical students, require to know some- 
thing of the history of their pursuit. The first want only 
a general view of leading points, such as can be furnished 
by one writer in a few volumes. The second wish to be 
able to compare the accounts given by different persons, 
and, up to a certain point, to examine the authorities 
used by those persons, or at least to keep watch upon 
their mode of using them. The third are desirous of 
being the critics of the historians, and of amending 
their works, if need be.” The catalogue, which the 
writer of this paragraph drew up, was intended for the 
second of the above classes. In some further remarks 
he arranges the histories under two heads—those which 
are written on the plan of Montucla, Bossut (we may now 
add M. Marie’s “ Histoire des Sciences mathématiques 
et physiques”), in which a general account is framed out 
of the writer’s notes or remembrances of miscellaneous 
reading; or in that of Delambre, Woodhouse (we may 
add here the name of Todhunter, whose great historical 
treatises the late Henry Smith pronounced to be “so 
suggestive of research, and so full of its spirit”), in which 
the successive writings of eminent men are examined 
and described one after the other, so that each chapter 
or section is a description of the progress of science in 
the hands of some one person, and is complete in itself. 
The latter, De Morgan goes on still further to say, is the 
plan which is most favourable to accuracy and most in- 
teresting to the inquirers of the third class; the former, 
while it better suits the first and second class, leaves the 
writer open to many sorts of error which the latter avoids.” 
1 De Morgan, ‘‘ References for the History of the Mathematical Sciences,” 
Companion to ‘* British Almanac” for 1843. 
2 Both M. Marie and Mr. Gow might profit by De Morgan’s remarks on 
Indices. ‘‘ No writer is so much read as the one who makes a good index, 
or so much cited.” The former author may intend to give a thoroughly 
full index at the end of his seven volumes ; the latter gives a fair index, but 
it is very far from being complete and satisfactory ; for instance, ‘‘e¢ passin” 
is not such a reference as one desires. 
VOL. XXX11.—NOo. 810 
Mr. Gow’s work being upon a special branch, viz. 
Greek mathematics—which he himself further limits to 
arithmetic, algebra, and geometry—comes under the 
second of the above two divisions, though for reasons. 
which are more than once put forward, it is not so 
thorough a treatise as we could have wished. When, 
however, we learn that the book “represents part of a 
collection of notes which I have for many years been 
making with a view to a general history of the great 
City of Alexandria,” and that “ the materials for an account 
of the Alexandrian Mathematical School grew to exceed 
the reasonable limits of a chapter,” we are glad that 
Mr. Gow determined to publish his results at an earlier 
date than he would otherwise have done. What of 
accuracy or perfection is sacrificed by a perhaps too 
early publication, he will have, we expect, an early 
opportunity of making good ina second edition, which we 
hope will be called for in the near future. Itis a great 
reproach to English mathematicians that such books as 
this and M. Marie’s have hitherto been conspicuous by 
their absence in this country. We can happily point to 
papers by De Morgan, to special treatises by Todhunter, 
to monographs by Allman, and to an interesting 7ésuié 
by Dr. C. Taylor, but we look in vain for anything of the 
nature of a history of mathematical or physical science in 
the English language. A tendency of late years to give 
small historical notices of mathematical discoveries in 
our school text-books has been displayed, and we trust 
the time is not far distant when we shall have, if not a 
great original work, for which we can hardly look, yet a 
primer or primers founded upon the works of Bret- 
schneider, Cantor, Hankel, Marie, and others. 
Almost every page puts in evidence how greatly Mr- 
Gow is indebted to German and French writers ; yet it is 
also evident, on a perusal of his work, that he is no blind 
follower of those predecessors in the field—he ‘calls no 
one of them master—but when occasion arises he boldly 
differs from them, and gives good reasons for so differing. 
We note here that he does not appear to be acquainted 
with M. Paul Tannery’s work in the same directions as 
his own. He refers to him but once (p. 101), and then he 
states he has not been able to find the article (quoted by 
Cantor). The journal in which the paper is published, 
B 
