ABSTRACT
A vast amount of commentary has accumulated since ancient times around the Definitions, Postulates and Common Notions with which Euclid commences the Elements. In certain cases (one thinks immediately of the notorious fifth or ‘Parallel’ Postulate) much of the subsequent history of mathematics can be viewed as one extended commentary on this text! For the English reader, Heath's edition of the Elements surveys much of this commentary up to its publication date (2nd edn, 1925) and has the benefit of being easily available. 1 The analysis conducted below does not require an extensive familiarity with this material as it refers to the lines of commentary that have been generally pursued only to clarify the points at which it diverges from the various traditional approaches. At certain points, however, the analysis does turn on specific words or phrases in the Greek original. Where this is the case the appropriate philological or linguistic background is provided.
