Euclid's method of proof has often been described in textbooks as axiomatic, but was it really so? And if not, how else can Euclid's method be characterized?

  • 2
    @virmaior, I see your point. I mean - by philosophers in light of the history of philosophy. Am versed with Euclid's period but not with prior era and wondered of whether one could possibly provide me here with example of non-axiomatic proof prior to the systematization of geometry by Euclid. I am not familiar with history of the philosophy of proof but it is why I ask what I ask. – Penguin Jun 28 '18 at 0:06
  • 2
    I don't mean this is a "your question isn't on topic here" because I do think it's interesting and probably appropriate for this site, but I think it might be even more explicitly an appropriate question to have on the History of Science and Mathematics.SE instead. – Not_Here Jun 28 '18 at 1:08
  • 3
  • 2
    The "standard" of proof has evolved during time (and will change in the future) but the idea of demonstrative poof (an argument that "necessarily concludes" by way of necessity-preserving steps) as we can find into Euclid's Elements evolved in Ancient Greece from the inetrplay of philosophy (the Sophists, Socrates, Plato, Aristotle) and mathematics. Ancient "proofs" by way of pebbles and diagrams (see Netz) were transformed into full arguments. – Mauro ALLEGRANZA Jun 28 '18 at 8:34
  • 2
    That Euclid's method is axiomatic is a modern misconception. Recent in-depth research on his diagrammatic approach, which became the standard in antiquity, is referenced under What caused or contributed to Euclid's Elements and Synthetic Geometry falling into disfavor? on hsm SE. Euclid's contribution was to systematize and codify arguments that predated him, unfortunately we have almost no independent sources for them. – Conifold Jun 28 '18 at 18:45

Reading page 27 of Science Without Numbers by Hartry Field, it says Hilbert did an axiomatization of Euclidean geometry in 1905, leading one to believe Euclid's theories were not originally axiomatic. So no, they were not axiomatic.

  • 1
    Euclid made some theories from his perception of physical space(also on pg 27) – Math Bob Mar 6 at 21:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.