from Oxford English Dictionary
1. Gr. Antiq. The temple of Athene in ancient Athens, in which professors taught their students, and orators and poets rehearsed their compositions. (Similar institutions, with the same name, were afterwards established at Rome and Lyons.)
1727-51 CHAMBERS Cycl. s.v., The Athenæa were built in the form of amphitheatres.
2. In modern times often used as a title for: a. An association of persons interested in scientific and literary pursuits, meeting for the purpose of mutual improvement; a literary or scientific club.
1807 Monthly Anthol. May 226 The Trustees with their associates are made a body corporate by the title of the Proprietors of the Boston Athenæum. 1847 HOWE Ohio 390 The atheneum was commenced as a library company. 1864 in WEBSTER. 1882 E. K. GODFREY Nantucket 13 The Athenaeum and other literary societies.
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Moreb. A building or institution in which books, periodicals, and newspapers are provided for use; a literary club-room, reading-room, library. Esp. the Athenæum Club in London.
1799 (title) Laws and Regulations of the Athenæum in Liverpool. 1807 SOUTHEY Lett. from England II. xl. 224 The history of their [sc. Liverpool's] Athenæum is a striking instance of their spirit:by this name they call a public library, with a reading-room for the newspapers and other journals. 1822 J. FLINT Lett. Amer. 112 The Atheneum, or reading-room, is much frequented. Mod. The Manchester Athenæum. 1834 H. C. ROBINSON Diary 14 Mar. (1967) 132 When the alarm of the cholera took place two years ago he gravely proposed turning the Athenaeum into a cholera hospital. 1845 Ainsworth's Mag. VII. 424 It would almost seem that the Athenæum had a personal quarrel with Mr. Pettigrew. 1887 W. S. GILBERT Ruddigore (1899) III. p. 38 Who found Athenæums and local museums. 1936 N. & Q. CLXX. 386/1 Thackeray..was more of the Athenaeum type.
c. A periodical devoted to the interests of literature, science, and art, e.g. The Athenæum, published in London.
1835 DICKENS Let. 11 Jan. (1965) I. 54, I can't get an Athenæum, a Literary Gazetteno not even a penny Magazine. 1848 H. C. ROBINSON Diary 5 Aug. (1967) 248 There is in the Athenaeum a severe article as respects Talfourd's style.