2 
Journal of the Mitchell Society. 
[May 
dations of geometry. For precise reasons, the names of 
Euclid and Newton stand above all other names in the fasti 
of mathematics; and the reasons are strikingly similar in the 
two cases. In writing of The Wonderful Century , the nine- 
teenth, Alfred Russel Wallace says of all time before the 
seventeenth century: “Then, going backward, we can find 
nothing of the first rank except Euclid’s wonderful system of 
geometry, perhaps the most remarkable mental product of 
the earliest civilizations.” In modern times, Newton’s colos- 
sal figure occupies the centre of the stage, looming large, as 
he himself explained, because he stood upon the shoulders of 
giants. Like Euclid, his claim to pre-eminence rests less 
upon the discovery of new principles than upon the immeas- 
urably greater service of the universal formulation and 
grounding of mathematics. Newton brought all natural phe- 
nomena under the reign of universal law, Euclid reduced 
all geometrical knowledge to system. 
“It is certain,” says Philip Kelland, “that from its com- 
pleteness, uniformity and faultlessness, from its arrangement 
and progressive character, and from the universal adoption of 
the completest and best line of argument, Euclid’s Elements 
stand pre-eminently at the head of all human productions. In 
no science, in no department of knowledge, has anything ap- 
peared like this work: for upwards of 2,000 years it has com- 
manded the admiration of mankind, and that period has sug- 
gested little toward its improvement.” Indeed it is no cranky 
enthusiasm, but absolute conviction that prompts the mathe- 
matician to say that geometry is ultimately fundamental for 
the progress of science and thea dvancement of humanity. It 
is continually bringing to pass those epoch-making events in 
the history of science whereby what one day seems to be the 
purest science becomes the next a vitally important piece of 
applied science. Such events enable us to realize that pure 
science and utilitarian science are not differentiable, butat 
bottom and in essence one and the same thing. “I often find 
the conviction forced upon me,” said the brilliant English 
