In answer to Julio's question, Ball is one of the people I quote
as having misunderstood the nature of Maclaurin's influence.
Instead, please see my paper, "Was Newton's Calculus a
Dead End? The Continental Influence of Maclaurin's Treatise of
Fluxions," Am. Math. Monthly May 1997, 393-410.
Briefly summarizing:
Maclaurin taught Newtonian science to all of Britain, and his
work on the shape of the earth, elliptic integrals, the Euler-
Maclaurin series and its applications, maxima and minima and
orders of contact, and even the foundations of the calculus,
influenced Continental mathematicians in significant ways.
The idea that British mathematics in general, and Maclaurin's
work in particular, were nonexistent in the eighteenth century
is considerably exaggerated at best and false at worst.
It arises in part from the early-19th-century English
mathematicians, especially the Cambridge Analytical Society
(Babbage's Decline of Science in England being one expression
of their views), who wanted Britain to support science and
who furthered this aim by downgrading their past. There are
other historiographical causes as well, from Scottish
historians who promoted the antispecialist tradition in
Scotland to the mathematicians who looked only for
named results in modern notation.
For a great more detail, I recommend the fine book of
Niccolo Guicciardini, The Development of Newtonian Calculus
in Britain.
Best wishes,
Judith Grabiner