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What's wrong with Euclid Book V
Author(s) -
Zeeman E. C.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm104
Subject(s) - mathematics , axiom , subtraction , calculus (dental) , mathematical economics , discrete mathematics , arithmetic , geometry , medicine , dentistry
Not having the real numbers, Euclid defined ratios abstractly in Book V for use in geometric theorems, but failed to define ratios of ratios, in effect blocking certain further developments of Greek mathematics. We introduce a new axiom that can be used instead of subtraction, not only to prove the propositions of Book V but also to define ratios of ratios.