I can't find the exact date when the Archean began to mean "the middle of the Precambrian", as opposed to the beginning or the whole thing. It is some time after 1925 and before 1972.
Before the Hadean Eon was recognized, the Archean spanned Earth's early history from its formation about 4,540 million years ago until 2,500 million years ago.
The Hadean was identified in 1972.
So I see a contradiction, because a 1969 World Book Encyclopedia article divided the Precambrian into the Azoic, Archaeozoic, and Proterozoic.
All three of these terms were once synonymous, different geologists' ways of referring to the entire Precambrian. But some time in the intervening years, they came to mean different time periods. (As it stands now, "Azoic" is considered an obsolete synonym for Hadean; likewise "Archaeozoic" for "Archean").
My reference for the state of affairs in 1925 is the USGS publication at https://pubs.usgs.gov/bul/0769/report.pdf but I will only include paraphrases.
Dana (1872) originally coined "Archean" to refer to the entire Precambrian, replacing the older "Azoic".
Proterozoic is less problematic, because Emmons(1888), and Chamberlain and Salisbury (1906) proposed a definition of Proterozoic that roughly corresponded to its modern meaning, the time between the Archaen and the Paleozoic.
However, it seems that for a time, the USGS went along with a 1908 proposal by Van Hise that "Proterozoic" refer to the entire Precambrian. This seems to be a debate the older definition won.
Note: As I am challenging an assertion made in Wikipedia, sources other than Wikipedia are preferred for answers.