In the early modern period, a crucial transformation occurred in
the classical conception of number and magnitude. Traditionally,
numbers were merely collections of discrete units that measured
some multiple. Magnitude, on the other hand, was usually described
as being continuous, or being divisible into parts that are
infinitely divisible. This traditional idea of discrete number
versus continuous magnitude was challenged in the early modern
period in several ways.
This detailed study explores how the development of algebraic
symbolism, logarithms, and the growing practical demands for an
expanded number concept all contributed to a broadening of the
number concept in early modern England. An interest in solving
practical problems was not, in itself, enough to cause a
generalisation of the number concept. It was the combined impact of
novel practical applications together with the concomitant
development of such mathematical advances as algebraic notation and
logarithms that produced a broadened number concept.
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