id: 05853142
dt: j
an: 2011d.00067
au: Gandon, Sébastien
ti: The theory of relations in Augustus De Morgan. (La théorie des rapports
chez Augustus De Morgan.)
so: Rev. Hist. Sci. 62, No. 1, 285-311 (2009).
py: 2009
pu: Armand Colin, Paris
la: FR
cc: A30 E30 E40
ut: De Morgan; Euclid; ratios; syllogism; B. Russell
ci: JFM 41.0083.02; JFM 43.0093.03; JFM 44.0068.01
li: doi:10.3917/rhs.621.0285
ab: De Morgan presented his theory of ratios in a little-recognized work of
1836, {\it The connection of numbers and magnitude: An attempt to
explain the fifth book of Euclid}. De Morgan stated that it was a
treatise for the benefit of students. This paper aims to show that the
work was actually more than didactical when considered in the context
of De Morgan’s broader mathematical program. The topic of ratios of
ratios, for example, is shown to be related to the distinctively
British calculus of operators. Also, there is a link between De
Morgan’s composition of ratios and his relational theory of the
syllogism. The author suggests further that this demonstrates a direct
line of influence between the reading of the fifth book of Euclid and
the logical theory of relations developed in the second half of the
nineteenth century and elaborated on in {\it A. N. Whitehead} and {\it
B. Russell}’s Principia mathematica [Cambridge: University Press.
Vol. I (1910; JFM 41.0083.02), Vol. II (1912; JFM 43.0093.03), Vol. III
(1913; JFM 44.0068.01)].
rv: Albert C. Lewis (Austin)