Modern axiomatically rigorous version of Euclid's Elements

Question

I have been wanting to read Euclid's Elements (Oliver Byrne's version) for a few months, but I have recently learned that a number of the proofs in Euclids Elements are not very rigorous, and that the axioms used by Euclid have been replaced by more rigorous ones. Can anyone suggest a comprehensive resource (ideally a textbook) that rederives Euclid's propositions with a more modern axiomatic approach?

Answer 1

Don't listen to the critics of Euclid. If you are a beginner, start with Euclid's Elements by Sir Thomas L. Heath (Dover, 3 Volumes paperback). You can also read, online the (1996?) posting by David E. Joyce. Once you are finished with Euclid, the you can read Hilbert's, "The Foundations of Geometry." For 2322 years Euclid was recognized as great, so you don't need to worry about his blemishes, until you know him very well.

PS: I have since re-read Robin Hartshorne on Euclid (cited above). Unfortunate this excellent mathematician launches quickly into Hilbert, and does not directly fill in the gaps in Euclid. So reading Hartshorne's Euclid is like reading a simplified version of Hilbert (1899) lectures. As far as I know, no one took Euclid's Elements and simply fill in the gaps, so to speak. However, there was a time in England, in the 19th century when Euclid was published along with Euclid's Data (another extant work of Euclid). I find this work very helpful in understanding or interpreting Euclid's Elements in modern terms. Here is one text online (at the Internet Archive) which includes both: https://ia800201.us.archive.org/17/items/elementseuclida00euclgoog/elementseuclida00euclgoog.pdf

Answer 2

In 1932 George D. Birkhoff published "Set of Postulates for Plane Geometry, Based on Scale and Protractor" which is available online here: http://ckraju.net/geometry/1932_Birkhoff.pdf