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G35

syllogical substages of deduction, or definitory and ratiocinative
deduction. The former includes the analysis of concepts,
the acquisition of distinct ideas, and the transformation of
them into fruitful forms. A whole class of demonstrations that
have given mathematicians no little trouble, such for
example as that discovery of Euler's which forms the
25th proposition of the VIIth book of Legendre's Éléments
de géométrie, the sum of the number of faces and summits
of an ordinary polyhedron exceeds the number of edges by

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