(Yes, this is part II. I got interested in the topic.)

I empathize with the difficulty of defining 'educated person.' As you rightly point out, there are different threads in what an "education" means. http://www.educationengland.org.uk/history/chapter03.html goes into the three main groups - 'public educators', 'industrial trainers', and 'old humanists' - which participated in that debate, ending "The curriculum which evolved during the 19th century was 'a compromise between all three groups, but with the industrial trainers predominant' (Williams 1961:142). This was 'damaging both to general education and to the new kinds of vocational training' (Williams 1961:143).

For purposes of this discussion, I think it's reasonable to refine the meaning of "educated person" specifically to "expected from someone who has graduated from a liberal arts college." I think this definition works for most of the last 500 years of having liberal arts colleges, up until the mid-1900s.

My definition specifically excludes religious and industrial education, which I think is appropriate for the intent.

Now, I noted that the Elements book I pointed to was meant for "elementary" students. I think that means up to age 12 or so. It's definitely no later than what the 1868 Taunton Report proposed:

> first-grade schools with a leaving age of 18 or 19 would provide a 'liberal education' - including Latin and Greek - to prepare upper and upper-middle class boys for the universities and the older professions;

(vs. second- and third-grade educations meant for the middle classes and lower.)

So the two pieces of evidence I have, for why someone in 1913 with a liberal arts education (an 'educated person') would have likely studied the Elements is first, the two forewords for a text book meant for 'elementary' students, and second, the number of reprintings of the text book, which implies that many were published.

I can now add more data points. In "THE RIVER WAR: An Account of the Reconquest of the Sudan" by Winston S. Churchill, 1902 edition, from http://www.gutenberg.org/files/4943/4943-h/4943-h.htm :

> The whole journey by rail from Merawi to Dakhesh occupied four days, whereas General Hunter with his flying column had taken eight—a fact which proves that, in certain circumstances which Euclid could not have foreseen, two sides of a triangle are together shorter than the third side.

Why would Churchill use this reference if the readers, educated in the mid- to late-1800s, are not expected to understand it?

There was a big debate in the UK in and around 1902 about the teaching of Euclid.

In Google Scholar's preview for "SOME RECENT DISCUSSION ON THE TEACHING OF MATHEMATICS", WW Beman - School Science and Mathematics, 1903 - Wiley Online Library "I may add that the address was given in full in the Educational Review for February, 1902. This discussion of the teaching of mathematics in England particularly with regard to the retention of Euclid as a test-book of geometry is by no means a new one." See also a letter in Nature http://adsabs.harvard.edu/abs/1902Natur..66..103S pointing out that Schopenhauer was also critical. And a 1903 Nature followup at http://adsabs.harvard.edu/abs/1903Natur..68R...7P saying "I WILL not deny that some reformers desire to abolish Euclid and establish another sequence of propositions in abstract geometry for schoolboys .. Two per cent. of schoolboys take to abstract reasoning as ducks take to water, and they ought not to be discouraged from the study of Euclid, but they and all the other boys ought to study geometry experimentally, logic entering into the study just as it enters into other parts of experimental physics. If the best modern books have a fault, it lies in the absurd assumption that an experimental sequence ought to have some connection with the Euclidean sequence."

In http://www.jstor.org/discover/10.2307/3603959?uid=3738984&ui... I read a page from a 1901 paper for the Mathematical Gazette (London) saying "(ii) The question of the retention of Euclid as a text-book was again raised. It was urged with considerable force that our retention of a book discarded by other nations had at any rate a presumption against it, and that it was wrong to sacrifice the interests of education to the east of the examiner. (iii) More than one speaker pointed out that if the experimental or intuitional method of introducing the truths of Mathematics, and especially of Geometry, were used from the lowest classes of our schools upwards, the strictly deductive course would not lose but gain in effectiveness."

So, it looks like the end of the 1800s was the death-knell for Euclid's Elements, but it was in the UK where it hung around the longest, perhaps for another 20 years.