Euclid21: Euclid's Elements for the 21st Century - Future Work

We have learned from Colin McKinney [5] that in fact Euclid never gave explicit references in his proofs, although he did sometimes allude to previous propositions. Apparently, he assumed the reader would master everything that came before each proposition.

Making explicit reference to prior propositions appears to be an innovation of Euclid's modern editors, but they do not agree. More precisely, different editors chose different dependencies to make explicit. Since our book uses Fitzpatrick's [2] translation, which is based on Heiberg's edition of the Greek text, the dependency structure we display is necessarily incomplete. For example, in Heiberg's translation Axiom 4 is never explicitly referenced, whereas in Heath's translation [3] it is.

It would be interesting to gather the dependency data from another authoritative translation, Heath's for example, for comparison. If they are combined with the data we already have, an even more complete dependency graph would be possible. That project is ongoing.

There are other documents and books, especially in mathematics, which are organized in a similar fashion. Our code could be modified to handle any such document, however we are not currently investigating this. Instead our code is freely available, licensed under the Gnu Open Software License so that others can make any such changes should they choose to. That is, anyone is free to use and/or modify the code for any non-commercial purpose.

Finally, while The Elements may or may not be, as Dodgson believed, the perfect text for teaching plane geometry, it is unique in the history of our species. It may well be the most read, most published book in history, outstripping even the various religious documents ([7], p. 55). For that reason alone, quite apart from its intrinsic value to mathematics, we should continue to find ways to pass it on to each successive generation. This is our contribution to that cause.