I am reading from Heath's translation of Euclid's Elements. Most propositions either end with "QED" or with "QEF", when the first one is used for proving propositions that are not constructions and the second one is for constructions. However, in Heath's translation, the first three propositions (in book one) don't end with "QED" or "QEF", but with "Being what it was required to do". Why do the first three propositions end differently that all the others? Note that in other translations they don't have this issue.
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1Obviously, the abbreviations above are not in the original Greek text. – Mauro ALLEGRANZA Dec 12 '23 at 08:40
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Into Heath's edition of Elements, the first four Propositions of Bk.I end with "(Being) what it was required to do."
The original Greek formula is: ὅπερ ἔδει ποιῆσαι that reads more or less "what has to be done".
From Prop.5, see Heath's note to line 48 (page 252):
As "(Being) what it was required to prove" (or "do") is somewhat long, I shall henceforth write the time-honoured "Q. E. D." and "Q. E. F." for ὅπερ ἔδει δεῖξαι. and ὅπερ ἔδει ποιῆσαι.
Mauro ALLEGRANZA
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This is common knowlegde even if one has to use google translate, It does not at all explain the axiomatic approach of Euclid. So it's perhaps better to delete my explanation od our current knowledge of The Elements. For the much outdated account of the discussion of the propositions in the Elements see Heath, History of Geek Mathematic, Vol I p, 374. Γεια σου. – Roland F Dec 16 '23 at 19:46