164 A History ofMathematics
acknowledging the debt, its circulation was certainly more restricted. And yet the circle ofsavants
with whom the principals corresponded, and who were interested in the same questions was much
wider; such practical questions as, why did the planets move as they did? What was the reason for
the tides, and could they be predicted? What was the shape of a freely hanging chain, of a loaded
beam, or of a sail? It is rare to find this practical background included in modern discussions of a
body of work which, however clearly it constituted a ‘new mathematics’, was embedded in a whole
family of other practices which have now been forgotten.
Of these, more will follow later; but for the time being, we should refer to two key texts from
the 1930s. The first, the Soviet historian Boris Hessen’sThe Social Origins of Newton’s Principiain
Hessen (1971), is occasionally referred to as an example of the crude Marxist approach; however, it
has been recently reprinted, and is still worth reading. The second, the American sociologist Robert
Merton’s (1970), is a founding text for the sociology of science; but, as Merton acknowledges in his
introduction, subsequent readers have focused more on the early chapters which (following Weber
and Tawney) relate the pursuit of science to Puritanism and the ‘Protestant Ethic’ than on the later
ones which, qualifying and extending Hessen’s analysis, relate the problems studied by scientists
to the demands of expanding capitalism. Merton’s strength is his awareness of the wider (mainly
English) scientific community, so that figures like Halley and Wren who hold a minor place in the
mathematical history are seen as much more important in terms of ideology, patronage and influ-
ence. The specific nature of the calculus is not addressed by either writer; accordingly, as often in the
interface of mathematics and physics, the kinds of source material available for study are not easy
to harmonize. [And, it should be added, a problem for this chapter: how do we separate the history
of the calculus from Newton’sPrincipia? The latter is both broader (after all, Newton’s concern was
with physics, and the deduction of the system of the world from the basic laws of motion) and nar-
rower (because of the peculiar way in which the calculus was used, or not used in thePrincipia—see
later).]Note on the use of texts.Few periods in the history of mathematics have been as badly served in
translation as the prehistory and early history of the calculus. At a time when the exact notation
which was being used by the participants (some of whom used traditional geometrical language,
some cartesian equations, and many a confused mixture), many histories ‘translate’ the work of
Wallis, James Gregory, and the early Newton and Leibniz indiscriminately into language which the
modern reader can recognize—even when, like Gregory, they were hostile to Cartesian symbolism.
Both Hofmann’s (1974) and Westfall’s (1980) are given to a free use of translation—even if it is
usually acknowledged as such; so that for example, Collins is said in his 1675 report on English
work for Leibniz to have shown how the arc [of a circle]s=rtan−^1 (t/r)=∫t0r^2 ·dx/(r^2 +x^2 )may be found (Hofmann 1974, p. 135). The reader whose suspicions are aroused by the use of
the integral sign which Leibniz was to invent in October of that year (and not publish for another
ten years), will find on looking up the source that what Collins said was very different, but the fact
that most of the original sources are hard to come by and mainly in Latin makes the question of
accurate transcription the more important. Fortunately this situation is changing, and the more
recent works of Guicciardini and Bos are textually faithful.