SOURCE: "Did Euclid's Elements, Book I, Develop Geometry Axiomatically?," in Archive for History of Exact Sciences, Vol. 14, 1974/1975, pp. 263-95.

In the following essay, Seidenberg challenges the assumption that Euclid, in Elements, developed geometry on an axiomatic basis. Seidenberg argues that, by insisting on this assumption, the work is viewed "from a false perspective" and its accomplishments are thus displayed "in a bad light."

Historians are fond of repeating that Euclid developed geometry on an axiomatic basis, but the wonder is that any mathematician who has looked at The Elements would agree with this. Anyone who looks at The Elements with modern hindsight sees that something is wrong; but we have all been told in our childhood that Euclid had the axiomatic method, so the usual reaction is to speak of "gaps". This word is hardly right, though, if there was nothing there in the first place.

Could it...